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Understanding Commercial Contracts in the United Kingdom
Posted by Mark Cowling on Sep 22nd, 2020
Understanding Commercial Contracts from formation to execution
A contract comprises a "legally enforceable agreement containing terms and conditions, defining the rights, duties and obligations of the parties".
HOW IS A CONTRACT CREATED?
For a contract to exist the following four basic elements must be satisfied:
1. An offer.
An offer is defined as a promise by one party to enter into a contract with another party on certain terms. The offer must be complete, specific, capable of being accepted and made with the intention of being bound by acceptance.
2. There must be an acceptance.
An acceptance is a final and unqualified assent to an offer.
The acceptance must be made in response to the offer, must correspond with the terms of the offer and must be communicated to the person making the offer.
3. There must be consideration.
Consideration means some right, interest, profit or benefit accruing to the one party or some forbearance, detriment, loss or responsibility given, suffered or undertaken by the other at his request.
In simple terms it means the price that one party is paying the other.
As a general rule a court will not concern itself with the adequacy of the consideration. That is, a court will make no attempt to audit the bargain made by the parties to see if it is a fair one.
4. Intention to create legal relations.
An "agreement" will not be enforceable unless there is an intention to create legal relations.
In most cases involving commercial parties it will be clear that there is an intention to create legal relations.
Notwithstanding these apparent complicated rules, it is very easy to satisfy the requirements of offer, acceptance, consideration and intention to create legal relations. Note therefore that:
contracts do not have to be in writing;
contracts can be created by email;
contracts can be created by correspondence;
contracts can be created by issue of an purchase order which a supplier accepts in writing or by conduct, ie performance of order.
contracts can be created over the telephone; and
contracts can be created by face-to-face meetings.
There are some exceptions to this. For example, the following have to be in writing:
contracts for the sale of real property/land.
A transfer of copyright.
guarantees, that is a promise by a third party who is not a party to a particular contract, guaranteeing the liability of a party to that contract.
IMPLIED TERMS
Sale of Goods Act 1979
In contracts for the sale of goods, where the seller sells the goods in the course of business, the Sale of Goods Act 1979 implies a number of terms relating to the goods:
Section 8- where price is not agreed, a buyer of goods must pay a reasonable price for them.
Section 12 – A condition that the seller has the right to sell the goods and warranties that:
no third party has any rights over the goods which the seller has not disclosed to the buyer; and
the buyer will have quiet possession of the goods.
Section 13 – A condition that the goods conform to their description.
Section 14(2)(A) – A condition that the goods are of satisfactory quality. This means that the goods must meet the standard that a reasonable person would regard as satisfactory taking into account description, price, appearance, finish, freedom from minor defects, safety, durability and fitness for all normal purposes.
Section 14(3) – A condition that the goods will be reasonably fit for any purpose expressly or impliedly made known to the seller.
Section 28 – If no time for payment is stated, it is implied that the buyer must pay cash on delivery.
Section 29 – If no place for delivery is agreed, it takes place at the seller's place of business.
NB – Sale of Goods Act is favourable to Buyers/Customers.
Supply of Goods and Services Act 1983
The Supply of Goods and Services Act 1983 applies to contracts for works and materials. With regard to the work element, section 13 provides that the services will be carried out with reasonable care and skill.
OTHER USUAL TERMS
The terms implied by sections 13 and 14 of the Sale of Goods Act 1979 and by section 13 of the Supply of Goods and Services Act 1983 can be a little imprecise and uncertain. It is therefore common to include a more precise definition of the quality of goods that the buyer can expect from a seller. For example a seller may warrant that the goods will be without defect for a period of sale 12 months from the date of delivery.
Unless there is agreement to the contrary, it will be implied that goods will be paid for on delivery.
Consideration should be given in the case of a seller to payment in advance or a deposit or for interest in the event of late payment. Under the Late Payment of Commercial Debts (Interest) Act 1998 unpaid creditors are entitled to claim interest at 8% above the Bank of England base rate. This rate applies if the contract does not specify a rate which parties agree should apply instead.
Consideration should be given to as to which party is responsible for delivery and what happens if goods are damaged in transit.
It is usual for a seller to seek to exclude or limit its liability for breach of contract. For example, in the case of a sale of goods, typically a seller will normally seek to limit its liability to an obligation to replace defective goods. Provided that it replaces those defective goods it would wish to ensure it had no further liability. If the contract is silent the seller will have unlimited liability.
Retention of Title
Typically a seller will seek to retain ownership of goods until it has been paid. A customer will want ownership to transfer as early as possible so it can resell the goods it has purchased in the ordinary course of business.
USUAL TERMS IN A LONG-TERM GOODS OR SERVICES SUPPLY AGREEMENT
Length of contract
The main distinction between a one-off supply or order by order basis from a long-term supply agreement is the duration and therefore this should be clearly stated. Typically, a customer will want the duration to be subject to a three or six month without cause right of exit so any contract be ended easily and supply sourced elsewhere if need be.
Minimum purchase requirements
A seller will normally push for some additional commitment from the buyer to make the long-term contract worthwhile.
This long-term commitment can either be achieved by way of minimum purchase requirements or exclusivity (see below).
A customer will seek to resist such commitments.
Alongside the minimum purchase requirement a seller may push to require a buyer under a long-term purchase agreement to purchase exclusively from the seller. A customer will usually require all contracts to be non-exclusive. If there is a better opportunity or a better price elsewhere, or the customer is not satisfied with supply, it will want to go elsewhere, which the customer cannot do if it has agreed to an exclusive purchase obligation.
Under a long-term supply agreement a seller may want the right to vary the prices during the term of the agreement but a customer will want pricing fixed for as long as possible. Price rise mechanisms should be agreed with caution and ideally be non-binding. These could be inflationary rises although careful consideration should be given to which index to use, eg. RPI/RPIX. Alternatively, a more complicated price review could be based upon changes in the cost to the seller, eg open book.
Termination and its consequences
Consideration should be given to what events should trigger termination and which party buyer/seller both has termination rights. Typical events of termination will include a serious breach of contract, and insolvency.
TUPE
The Transfer of Undertakings (Protection of Employment) Regulations 2006 ("TUPE").
This is a very complicated topic. Alarm bells should be ringing where services are outsourced or there is a long-term supply of services agreement.
Essentially under TUPE where the services of a company are outsourced, those employees of the outsourcing company who are dedicated to the function being outsourced will transfer to the new service provider under their existing terms and conditions of employment.
Where a supplier of services has a dedicated workforce (which may be one employee) who provides services wholly or mainly for a particular customer, on termination of that contract, that employee will transfer either to that customer (if that customer brings those services in-house) or to a new service provider.
BATTLE OF THE FORMS
Where both the seller and the buyer purport to impose their own standard terms into a contract, difficulties can arise in determining which terms prevail. This is known as the 'battle of the forms'.
Where the seller offers to contract on its own terms and the buyer purports to accept these but at the same time seeks to impose the buyer's own terms, there is no acceptance at all. Instead this is a counter offer which is open to acceptance by the seller either expressly or by performance.
In practical terms, this means that the last set of terms despatched prior to acceptance or performance (ie the last shot fired in the battle of the forms) will prevail.
In the face of a battle of the forms, the other party can decide to deal with the conflict of terms directly by discussing and agreeing terms with the other side. This of course involves negotiation and consequently incurs time and expense which the use of standard terms is designed to avoid.
However, in high value or risk contracts or where there is the possibility of significant repeat business, the time and effort involved may be justified.
The alternative solution is to try to include your own standard terms in as many pre-contractual documents as possible in the hope that you will fire the last shot. This is always a risky strategy in that the other party may succeed in firing the last shot.
1. Incorporation of terms and conditions
Standard terms and conditions will only take effect if they have been incorporated into the agreement between the buyer and the seller. Standard terms and conditions must therefore form part of the offer. Sellers must ensure that their terms and conditions of sale are brought to the attention of the customers at the earliest possible opportunity and certainly before the contract is made.
This means that terms should be set out:
on websites;
in brochures;
on quotation forms;
on acknowledgement of confirmation of order of seller;
on invoices.
Invoices are post contractual documents so that it would not normally be brought to the attention of a buyer before the contract is made. However, if the terms and conditions regularly appear on the back of invoices, it is possible to imply prior knowledge by way of a course of dealings.
Care should be taken that where terms appear on the reverse of a document, that reverse is drawn to the buyer's attention.
2. Misrepresentation
Misrepresentation is an untrue statement of fact or law made by Party A (or his agent for the purposes of passing on the representation acting within the scope of his authority) to Party B which induces Party B to enter the contract thereby causing Party B loss.
It is usual to try to exclude liability for misrepresentation under an exclusion or limitation clause.
There are three types of misrepresentation:
fraudulent misrepresentation;
negligent misrepresentation; and
innocent misrepresentation.
The remedies for each are different.
Whether misrepresentation is fraudulent or negligent, the claimant can rescind the agreement and claim damages. However where the misrepresentation is innocent the court can order damages in lieu of rescission or just rescind the contract. The court cannot award both damages and rescission in the case of innocent misrepresentation.
Rescission means that the contract is set aside and the parties are put back in the position they would have been in before the contract was made.
Therefore if a buyer is buying goods, the seller will get the goods back and the buyer will get the buyer's money back. Rescission is not available where it is no longer possible for the parties to be restored to their original position.
Also the right to rescind is lost if the contract is affirmed. This means that once a buyer becomes aware of the misrepresentation but does an act implying that he continues to be bound by the contract, the right to rescind is lost. An act of affirmation will include payment of any monies after becoming aware of the misrepresentation.
3. Limitation and exclusion clauses.
Most sellers or providers of services will wish to exclude or limit.
Under the Unfair Contract Terms Act 1977 ("UCTA") a business cannot exclude or restrict liability for death or personal injury caused by its negligence. Also it cannot exclude liability for breach of the condition in section 12 of the Sale of Goods Act 1979 that a seller has good title to the goods.
Other exclusions of liability are possible. However, where parties are dealing on standard written terms, exclusion of liability for negligence (other than the way death or personal injury is caused), breach of any of the statutory implied terms such as satisfactory quality or fit for purpose, breach of contract or misrepresentation is subject to a reasonableness test under UCTA.
Where dealing with consumers, it is very difficult to exclude any liability.
When considering the reasonableness test, a court will pay attention to the resources available to the supplier and in particular the insurance cover that is available.
Trading on the internet can bring about its own special problems, for example pricing errors for goods sold online.
The problem can be overcome by having appropriately worded terms and conditions of sale which means that the acknowledgement is not actually an acceptance of the customer's offer to buy and a contract is only formed after payment for and dispatch of goods.
There are special rules applicable to online selling to consumers which online traders have to comply with and are enforced by trading standards.
5. Overseas contracts
When contracting overseas a number of additional considerations need to be considered. For example:
which law applies to the contract? Do not leave it to chance but agree the governing law;
agree which courts have a jurisdiction to hear any disputes;
seek local law advice where possible. For example, will a retention of title clause be enforceable in the jurisdiction?
are there any special rules applicable in that jurisdiction? For example, in certain European jurisdictions on termination of distribution agreements, the distributor is entitled to compensation;
do not assume that English law principles will apply. For example, many European jurisdictions have a civil code which will overwrite anything agreed under the contract.
Execution – under English law contracts have to be executed by overseas companies in accordance with the laws in which they are incorporated/their constitutions
6. Competition law issues
As a starting point, businesses should be wary of any agreement between undertakings that may affect trade in the UK or between member states of the European Union and which have the object or effect of restricting competition within the UK, part of the UK or the European Union.
Breach of these provisions means that an agreement is void and the parties may be liable to substantial fines. In addition, third parties harmed by such agreements have a claim to damages.
Common restrictions which are anti-competitive and therefore unenforceable include:
any restriction on the buyer's ability to determine its sale price. It is possible to impose a maximum re-sale price (over which the buyer cannot sell the goods) or set recommended resale price but a seller cannot impose a minimum resale price;
a seller cannot restrict the territories into which or customers to whom its buyer may sell goods. However, a seller can restrict active sales into the exclusive territory or to an exclusive customer group reserved to the supplier or allocated by the supplier to another buyer. It is not permitted to restrict passive sales. An active sale means actually approaching individual customers inside another distributor's exclusive territory or exclusive customer group. Passive sales are sales made to unsolicited requests from customers.
7. Tenders
If you submit a tender then that tender is likely to be an offer which the customer can accept thereby creating binding contract without the need for any further documentation to be signed. The difficulty for bidders/tenderers is that the rules of the tender normally prevent the giving of conditional tenders. By including any provisions to the effect that the tender is not an unconditional offer, the tenderer may be excluded from the tender process.
8. The small print
Whilst there are numerous items of small print that parties should be aware of, here are two common issues:
8.1 A contract may be expressed to be, say, a three or five year term. The seller believes that the buyer is entering into a long term commitment with the seller because the buyer has agreed to such a three or five year contract. However in the "small print" it is often the case that the buyer has the right to terminate on, say, three months' notice. Therefore the agreement is really no more than a three month agreement except that the seller is committed to supply for the full term of the agreement, ie three or five years. The buyer however has a get-out by giving three months' notice.
8.2 Reasonable endeavours. Sometimes obligations are not obligations at all. For example, in many maintenance contracts the maintainer does not guarantee to fix a problem but merely agrees to use reasonable endeavours to fix that problem. Accordingly the maintainer's obligation is to try to fix the problem. Accordingly if the problem is not resolved, the customer has no comeback against the maintainer if the maintainer has used reasonable endeavours to try to fix that problem.
9. Other statutory rules
The basic position under English law is that parties are free to agree whatever terms they like and that a court will not normally interfere with that bargain. However, there are exceptions. See Unfair Contract Terms Act 1977 above. Other common exceptions include:
9.1 Consumer protection rules for contract terms used to trade with consumers- for example the Consumer Rights Act 2015.
9.2 Consumer credit and consumer hire agreements. There are strict formalities for entering into consumer credit and consumer hire agreements which, if they are not followed, can result in the whole agreement being unenforceable.
9.3 Intellectual Property agreements. There are some special rules that apply to transfers or licensing of intellectual property.
9.4 GDPR clauses – GDPR may require certain clauses to be included such as data processing clauses or model data transfer clauses.
9.5 The Commercial Agents (Council Directive) Regulations 1993. These apply where a principal appoints a self-employed intermediary who has continuing authority to negotiate the sale or purchase of goods on behalf of that principal or can negotiate including the sale or purchase of goods on behalf of or in the name of that principal. There are various provisions of the Commercial Agents Regulations which cannot be contracted out of. By way of example, the Regulations:
set out minimum notice periods in respect of termination of the agency agreement; and
provide for the payment of a lump sum on termination of the agency agreement.
The only circumstances in which a lump sum is not payable is where the principal terminates because of a breach by the agent which would justify summary termination.
Disclaimer: This article is for general information only and is not intended to be a substitute for specific legal advice. You should obtain specific legal advice before taking or refraining from any action. Nothing in this article constitutes legal advice
©Mark Cowling 200920 All rights reserved.
About Mark Cowling
Mark is a Commercial & Intellectual Property Solicitor who trained and worked for several years at leading New Zealand law firm Minter Ellison and is qualified as a non-practising solicitor and barrister in New Zealand. He relocated to the United Kingdom and has worked for the past 11 years as an inhouse solicitor at Next Retail Limited and as lead counsel for two of it's subsidiaries, Lipsy Limited and Marie Claire Beauty Limited.
The Jonathan Lea Network is an SRA regulated firm that employs solicitors, trainees and paralegals who work from a modern office in Haywards Heath. This close-knit retain team is enhanced by a trusted network of specialist self-employed solicitors who, where relevant, combine seamlessly with the central team.
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Lena Nyman-priset är ett pris som Lena Nyman-sällskapet delar ut årligen den 23 maj till Lena Nymans minne. Det ska gå till en skådespelare, artist eller konstnär, som verkar i Lena Nymans anda. Priset delades ut första gången samtidigt med sällskapets bildande den 23 maj 2014, vilket skulle ha varit Lena Nymans 70-årsdag. Det består av en flaska Dom Perignon som var hennes favoritchampagne och delas ut vid hennes grav på Norra begravningsplatsen i maj.

Pristagare
 2014 – Edda Magnason, sångerska, musiker, skådespelare
 2015 – Alexander Mørk-Eidem, regissör
 2016 – Malin Levanon, skådespelare
 2017 – Liv Strömquist och Ada Berger, serietecknare respektive regissör
 2018 – Sara Danius,  litteraturvetare, författare
 2019 – Andreas T. Olsson, skådespelare och manusförfattare
 2020 – Gina Dirawi, författare och programledare
 2021 – Lisa Nilsson, sångerska
 2022 - Kayo, sångerska & skådespelare

Källor

Kulturpriser i Sverige
Priser och utmärkelser instiftade 2014

redpajama_set_name: RedPajamaWikipedia


Tyson Foods Earns Top Marks for LGBTQ Equality | Tyson Foods, Inc.
Springdale, Ark. – Nov. 9, 2017 – Tyson Foods, Inc. (NYSE: TSN) proudly announced that it received a perfect score of 100 percent on the 2018 Corporate Equality Index (CEI), a national benchmarking survey and report on corporate policies and practices related to lesbian, gay, bisexual, transgender and queer (LGBTQ) workplace equality, administered by the Human Rights Campaign Foundation. Tyson Foods is one of 609 major U.S. businesses which also earned top marks this year.
The 2018 CEI rated 947 businesses in the report, which evaluates LGBTQ-related policies and practices including non-discrimination workplace protections, domestic partner benefits, transgender-inclusive health care benefits, competency programs and public engagement with the LGBTQ community. Tyson Foods satisfied all of the CEI's criteria and earned the designation as a Best Place to Work for LGBTQ Equality.
This is the second year Tyson Foods achieved a perfect score on the Corporate Equality Index, demonstrating the company's commitment to building an inclusive culture. For more information on the 2018 Corporate Equality Index, or to download a free copy of the report, visit www.hrc.org/cei.


Things to do in Denver this weekend, Feb. 16-18 - Denverite, the Denver site!
Feb. 16, 2018, 6:45 a.m.
There are so many things to do and if you try really hard you could probably do, like, five of them.
Best bet: Declaration Brewing's Third Anniversary Olympiad. Today: WiiNTER Games. King/Queen of the Console Competition, Drinko Plinko for discounts and prizes. Declaration Brewing, 2030 S. Cherokee St. 11 a.m.-10 p.m.
Cheer to Three Years. Beer releases: Kumquat Clementine Sour, Glorieta Colorado IPA. Live music from Bellhoss and Alec Ryan. Food from Goldie's food truck. Factotum Brewhouse, 845 Lipan St. Noon-10 p.m.
"Detroit '67." Chelle and Lank run an unlicensed bar in their Detroit basement as police crack down on after-hours joints in black neighborhoods. When Lank offers shelter to an injured white woman, tensions escalate both in their home and in their community. Curious Theatre Co., 1080 Acoma St. 8 p.m. $42-48.
"STOMP." Buell Theatre, 1350 Curtis St. 7:30 p.m. $25-95.
"American Mariachi." Lucha and Boli are ready to start their own all-female mariachi band, but they'll have to fight a male-dominated music genre and pressure from their families to get it done. Stage Theatre, 1101 13th St. 7:30 p.m. $20-65.
"Zoey's Perfect Wedding." Disaster after disaster follow one unfortunate bride down the aisle in this comedy. Stage Theatre, 1101 Speer Blvd. 7:30 p.m. $20-65.
Stravinsky's "Rite of Spring" performed by the Colorado Symphony. Boettcher Concert Hall, 1000 14th St. 7:30 p.m. $20-94.
Neck Deep. Ogden Theatre, 935 E. Colfax Ave. 7 p.m. $23-25.
Radio Moscow. Larimer Lounge, 2721 Larimer St. 9:30 p.m. $17-20.
Waker. Lost Lake, 3602 E. Colfax Ave. 9 p.m. $13-17.
Tim Barry. Hi-Dive, 7 S. Broadway. 8:30 p.m. $13-15.
MURS. Cervantes Other Side, 2637 Welton St. 9 p.m. $18-20.
Pimps of Joytime. Cervantes Masterpiece Ballroom, 2637 Welton St. 9 p.m. $22-25.
Judge. Marquis Theater, 2009 Larimer St. 7 p.m. $20-22.
René Marie & Experiment in Truth. Dazzle Jazz, 1512 Curtis St. 6 p.m. and 8:30 p.m. $10-40.
Sophie W. Lion's Lair, 2022 E. Colfax Ave. 9 p.m. $8.
Bonnie and The Clydes. The Black Buzzard at Oskar Blues, 1624 Market St. 9 p.m. $5.
Wendy Clark Band. Walnut Room, 3131 Walnut St. 8 p.m. $10-15.
Annie Booth Trio: Beatles Uncovered. Nocturne, 1330 27th St. 7 p.m. $15.
Todd Glass. Comedy Works, 1226 15th St. 7:30 p.m. and 9:45 p.m. $24.
Midnight Madness: "Mind Games." Esquire Theatre, 590 Downing St. Midnight. $9.50.
Scream Screen presents "AS SEEN on TV!" Tonight, this series celebrating the best horror films from the golden age of made-for-TV movies features "Don't Be Afraid of the Dark." Sie Film Center, 2510 E. Colfax Ave. 9:30 p.m. $7-11.50.
Sarah Bowling and Mario Zoots: "Point of Friction" reception. DATELINE, 3004 Larimer St. 6-11 p.m.
"Things That Go" storytime. Second Star to the Right, 4353 Tennyson St. 10:30-11:30 a.m.
Real Baby storytime. Stories and coupons for the neighborhood baby boutique. BookBar, 4280 Tennyson St. 10:30-11:30 a.m.
That's My Jam! "The Office" vs. "Parks & Rec" trivia. Stoney's Bar and Grill, 1111 Lincoln St. 6:30-11 p.m.
The Unicorn Love Party – Illuminaughti. DJs and circus performances by Fractal Tribe and Rainbow Militia to benefit the Gathering Place and billboard space in key swing states prior to the 2018 midterm election. Oriental Theater, 4335 W. 44th Ave. 8 p.m. $15-25.
Colorado Avalanche at Winnipeg Jets, 6 p.m.
Best bet: Declaration Brewing's Third Anniversary Olympiad. Today: singles events and PawsCo adoption event. Beer Can "Nordic Combined," Beer "Stein-Mina" Competition, The Triassic Chug Off. $1 per featured pint sold goes to PawsCo. Meet adoptable dogs. Live music from Bottle Rocket Hurricane from 3-5 p.m. Declaration Brewing, 2030 S. Cherokee St. 11 a.m.-10 p.m.
Cheer to Three Years. Beer releases: Glorieta Colorado IPA, Napoleon's Best Friend Russian Imperial Stout, My Winter Cardigan Stout by Lady Justice Brewing. Live music from Bark Wilson from 2-5 p.m. Food from Mile High Cajun Food Truck. Factotum Brewhouse, 845 Lipan St. Noon-10 p.m.
Beer, Bacon, Coffee Fest. Denver Beer Co., 1695 Platte St. 8 a.m. $40.
Valentine's Cookie + Beer Pairing with Good Sugar Baking. Mockery Brewing, 3501 Delgany St. 3-5 p.m. $12.
Chinese New Year Pop-up with WongWay Dim Sum. Art Gym Denver, 1460 Leyden St. 6 p.m. and 8 p.m. $35.
Chocolate Milkshake IPA crowler release. 1-6 p.m. Station 26 Brewing Co., 7045 E. 38th Ave.
Brunch with Wes Watkins. Ophelia's Electric Soapbox, 1215 20th St. 10:30 a.m.-2 p.m.
Best bet: Colorado New Play Summit. Reading: "Christa McAuliffe's Eyes Were Blue" by Kemp Powers. Jones Theatre, Speer Blvd. & Arapahoe Ave. 10:30 a.m. "Mama Metallica" by Sigrid Gilmer. Ricketson Theatre, 1400 Curtis St. 2 p.m. $23-36.80.
Best bet: Doug Loves Movies. Comedy Works, 1226 15th St. 4:20 p.m. $22.
"Detroit '67." Featuring post-show guest Andre Carbonell, poet. Chelle and Lank run an unlicensed bar in their Detroit basement as police crack down on after-hours joints in black neighborhoods. When Lank offers shelter to an injured white woman, tensions escalate both in their home and in their community. Curious Theatre Co., 1080 Acoma St. 8 p.m. $42-48.
"STOMP." Buell Theatre, 1350 Curtis St. 2 p.m. and 7:30 p.m. $25-95.
Hippie Sabotage. Ogden Theatre, 935 E. Colfax Ave. 9 p.m. $30-35.
Viceroy (live set). Bluebird Theater, 3317 E. Colfax Ave. 9 p.m. $18-22.
PnB Rock. Gothic Theatre, 3263 S. Broadway. 8 p.m. $30.
Van William. Larimer Lounge, 2721 Larimer St. 9:30 p.m. $10.
The Hacks. Lost Lake, 3602 E. Colfax Ave. 9 p.m. $5-10.
Hackensaw Boys. Globe Hall, 4483 Logan St. 9:30 p.m. $12.75-15.
Allout Helter. Hi-Dive, 7 S. Broadway. 9 p.m. $10.
Duey N' Decibels do Guns N' Roses. Cervantes Other Side, 2637 Welton St. 9 p.m. $10-15.
Praang. Cervantes Masterpiece Ballroom, 2637 Welton St. 9 p.m. $25-30.
The Long Run (Eagle's tribute) and My Blue Sky (Allman Bros. tribute). Oriental Theater, 4335 W. 44th Ave. 7:30 p.m. $18.
The Hits album release. Marquis Theater, 2009 Larimer St. 7 p.m. $10-12.
Lee Clark Allen. Syntax Physic Opera, 554 S. Broadway. 8 p.m. $7.
Jyemo Club. Dazzle Jazz, 1512 Curtis St. 9 p.m. $10.
When Darkness Falls. Lion's Lair, 2022 E. Colfax Ave. 9 p.m. $8.
Best bet: CultureHaus: Art of the Figure. An early look at "Degas: A Passion for Perfection," Colorado Ballet dancers, live figure drawing, an art grab, a DJ and drinks. Denver Art Museum, 100 W. 14th Ave. Parkway. 7-11 p.m. $80-95.
"Wrong Women: Myths from Sky" by Eriko Tsogo opening reception. Leon, 1112 E. 17th Ave. 7-11 p.m.
Artist talk with Kevin Sloan. K Contemporary, 1412 Wazee St. 3-4 p.m.
Painting With Words: Teen Writing Workshop. Ekphrastic creative writing session in partnership with Lighthouse Writers Workshop. Clyfford Still Museum, 1250 Bannock St. 1-4 p.m. Free, limited space.
Drink with owls. Fundraisers for Nature's Educators. Brewability Lab, 12445 E. 39th Ave. 4-9 p.m.
Best bet: Declaration Brewing's Third Anniversary Olympiad. Today: team events. Relay Beerathlon, Beer Can Curling, Beer Pong – American Revolution-style. Declaration Brewing, 2030 S. Cherokee St. 11 a.m.-10 p.m.
Beer, Bacon, Coffee Fest. Denver Beer Co., 1695 Platte St. 11 a.m. $40.
Best bet: Colorado New Play Summit. Reading: "Celia, A Slave" by Barbara Seyda. Ricketson Theatre, 1400 Curtis St."The Couches" by David Jacobi. 10:30 a.m. Jones Theatre, Speer Blvd. & Arapahoe Ave. 2 p.m. Local Playwrights' Slam hosted by Lighthouse Writers Workshop. Jones Theatre, Speer Blvd. & Arapahoe Ave. 6:30 p.m. $23-36.80.
Best bet: Stravinsky's "Rite of Spring" performed by the Colorado Symphony. Boettcher Concert Hall, 1000 14th St. 1p.m. $20-94.
"Detroit '67." Featuring post-show guestNorma Johnson, Ppoet, activist and racial justice consultant. Chelle and Lank run an unlicensed bar in their Detroit basement as police crack down on after-hours joints in black neighborhoods. When Lank offers shelter to an injured white woman, tensions escalate both in their home and in their community. Curious Theatre Co., 1080 Acoma St. 2 p.m. $42-48.
The Wind and The Wave. Bluebird Theater, 3317 E. Colfax Ave. 8 p.m. $18-20.
Majid Jordan. Gothic Theatre, 3263 S. Broadway. 9 p.m. $29.50-34.50.
Rocky Diamonds. Larimer Lounge, 2721 Larimer St. 9:30 p.m. $10-12.
Shaky Hand String Band. Lost Lake, 3602 E. Colfax Ave. 8 p.m. $8-12.
John Gorka. Swallow Hill Music, 71 E. Yale Ave. 7 p.m. $26.
New Mexican. Lion's Lair, 2022 E. Colfax Ave. 7 p.m.
Todd Glass. Comedy Works, 1226 15th St. 7 p.m. $16.
Hair of the Dog Comedy Showcase. The Lobby, 2191 Arapahoe St. 2-3 p.m.
The My Bloody Violent-Tine Film Festival. Bug Theatre, 3654 Navajo St. 6 p.m. $10-30.
Best bet: Colorado Convention Center Public Art Tour. Led by Denver Arts & Venues Public Art Program. Colorado Convention Center, 700 14th St. 2-3:30 p.m. Free.
Lecture: Jose Francisco Xavier de Salazar y Mendoza with Juddith Bonner. Denver Art Museum, 100 W. 14th Ave. Parkway. 1:30-2:30 p.m. Free for Alianza members and students with ID, $5 for DAM members, $10 for others.
Day of Remembrance marking FDR's signing of Executive Order 9066, authorizing the internment of of American citizens of Japanese ancestry and immigrants from Japan. Hosted by the MIle High JAC. History Colorado Center, 1200 Broadway. 1-3 p.m. Free.
Colorado Avalanche vs. Edmonton Oilers, 7 p.m.


text:
\section{Introduction}

As is well known, the Standard Model of particles predicts the existence of a zero point energy density $\rho_{vacuum} \rightarrow \infty$.
In an effective field theory approach, this is
interpreted as
$$\rho_{vacuum}\sim -(n_{B}-\zeta(E)n_{F})M_{UV}^{4}$$
where $n_{B}$ and $n_{F}$ are the numbers of bosons and fermions,
$\zeta(E)$ is a coupling ratio running with energy, $M_{UV}$ is the UV Pauli-Villars cutoff scale.
In fact, bubble diagrams of matter, gauge sector and Higgs sector will badly generate quartic divergences
at the leading order plus subdominant divergences.
 Such a vacuum energy would lead to a sudden super-inflation of space-time
 in a Planckian (cosmological frame) time.
 On the other hand, a very tiny dark energy density is observed, i.e. around $10^{-122}\, \rm M_{Pl}^{4}$.
 This is the well known cosmological problem: even starting with a zero or very small Einstein's cosmological constant,
 this will be destabilized by quantum corrections, up to $\Lambda \rightarrow M_{UV}^{2}$.
In (SM) $+$ (quantum gravity), the UV cutoff is the Planck scale $M_{UV}=M_{Pl}\simeq 10^{19}\, {\rm GeV}$
leading to a vacuum energy density $10^{122}\rho^{exp}_{\Lambda}$, where $\rho_{\Lambda}^{exp}$ is the energy density associated
to the experimental cosmological constant.

In this paper, we
will discuss another aspect of the cosmological problem
related to a second paradox of quantum field theories and quantum gravity.
We argue that quantum field theories inevitably lead to the presence of virtual particles
in a volume cell of space-time.
This implies  that, in every volume cell, virtual particles contribute to the energy density
with their own masses. In other words, the expectation value of the energy-momentum tensor
gets a contribution from virtual masses floating in vacuum.
This effect is analogous to virtual electric charges in electrodynamics,
screening bare electric charges.
However, the difference is that negative and positive electric charges contribute as
$\langle 0|Q|0 \rangle=0$ while negative masses cannot exist in general relativity.
Even if this effect is an obvious consequence of quantum field theory coupled to gravity,
it was never discussed  as
a relevant contribution to the vacuum energy density in any papers or reviews in literature
(See for example some reviews on these subjects
\cite{Weinberg:1988cp,Dolgov:1997za,Straumann:1999ia,Sahni:1999gb,Weinberg:2000yb,Carroll:2000fy,Rugh:2000ji,Padmanabhan:2002ji,Yokoyama:2003ii,Polchinski:2006gy,Martin:2012bt}).

The most important contribution comes from
{\it Virtual Black Holes} (VBHs).
Heisenberg's indetermination principle will inevitably lead to the conclusion that,
localizing the position $\Delta x \rightarrow 0$,  the curvature fluctuations will diverge
$\Delta R \rightarrow \infty$. This leads to the pair creation of virtual black holes in vacuum.
The quantum gravity scale imposes a bound on the Schwarzschild micro-black hole
mass of $M_{BH}\geq \sqrt{\pi} M_{Pl}$.
Such a bound can be obtained as a solution of
$\lambda_{c}=r_{S}$, where $\lambda_{c}$ is the universal definition of Compton wave-lenght
$\lambda_{c}=2\pi/M$ while $r_{S}=2G_{N}M$ is the Schwarzschild radius.
As pointed out by S. Hawking, a virtual black hole bubble is topologically equivalent to
$S^{2}\times S^{2}$, obtained by gluing two Eguchi-Hanson metric with opposite directions \cite{Hawking:1995ag}.
The Heisenberg's principle inevitably suggests the average presence of virtual micro black holes
with a minimal mass $\sqrt{\pi}M_{Pl}$ in a Planck volume $l_{Pl}^{3}$.
Other larger mass virtual black holes clearly are possible, but the saturation density limit must be $\sqrt{\pi}M_{Pl}/l_{Pl}^{3}$,
i.e. the black hole density is cut-off by the Planck density scale.
For instance a micro-black hole with $2\sqrt{\pi}M_{Pl}$ will occupy $2l_{Pl}^{3}$,
one with $3\sqrt{\pi}M_{Pl}$ will occupy $3l_{Pl}^{3}$ and so on.
As shown by S. Hawking, the quantum gravity ground state
minimizing the semiclassical action corresponds
to approximately one Planck mass micro-black hole
for Planck volume \cite{Hawking2}.
So that, a {\it space-time foam} with a leading topology $(S^{2})^{2N}$ with $N>>1$ was suggested
\footnote{But the same S. Hawking has not pointed out the possible relevance of the contribution of virtual BH masses to the renormalization of the vacuum energy. }
\footnote{More precisely, also the presence of $K_{3},\bar{K}_{3}$ are possible, while $CP_{2},\bar{CP}_{2}$
are not possible for a spin-structured metric gravity. }.
This leads to the catastrophic conclusion that space-time has an enormous intrinsic energy density of $\rho_{vacuum}\sim M_{Pl}^{4}$
even without on-shell matter sources. In fact if a space-time has an intrinsic energy density, this will source its
curvature to $\langle R \rangle \rightarrow l_{Pl}^{-2}$.

Of course, the BH mass bound can be deformed for electrically charged and/or rotating virtual black holes.
More precisely, for non-extremal Kerr black holes with $M>J$,
the mass bound is obtained solving the equation $\lambda_{c}=r_{outer} $, where
$r_{outer}=\frac{1}{2}\left(r_{S}+\sqrt{r_{s}^{2}-4\alpha^{2}\cos^{2}\theta}\right)$,
where $\alpha=J/M$ and $J$ the Spin parameter,
where $\theta$ parametrizes the angular variation of the radius in the oblate spheroidal horizon.

In the next subsection, we will provide a complete introduction to
the classical cosmological problem
and its completion with the second cosmological problem
introduced in this paper.

\subsection{Cosmological problems}

Let us consider the
Einstein-Hilbert lagrangian with a bare cosmological constant
and coupled with matter:
\be{SS}
S=\frac{1}{2\kappa}\int d^{4}x \sqrt{-g}(R-2\Lambda_{B})+S_{matter}[g_{\mu\nu},\Phi]
\end{equation}
where $\kappa=8\pi G_{N}=1/M_{Pl}^{2}$
where $M_{Pl}$ is the reduced Planck mass.
In quantum field theory,
the vacuum expectation value of the
energy momentum tensor
is not zero even without any matter sources:
\be{Tmunu}
\langle 0|T_{\mu\nu}|0 \rangle=-\langle 0| \frac{2}{\sqrt{-g}}\frac{\delta W}{\delta g^{\mu\nu}} |0\rangle =-\rho_{vac}g_{\mu\nu}
\end{equation}
where
\be{W}
W=-i \log Z[0],\,\,\,Z[0]=\int \mathcal{D}{\Phi}e^{i S_{matter}[\Phi]}
\end{equation}
and $\Phi$ are all SM particles and $Z$ is the full SM partition function,
supposing to start the field quantizations from an almost flat background.

Eq.(\ref{Tmunu}) contributes to the Einstein's field equation
as
\be{con}
R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}+\Lambda_{B}g_{\mu\nu}=\kappa T_{\mu\nu}^{matter}+\kappa \langle T_{\mu\nu} \rangle
\end{equation}
In other words, the effective cosmological constant
is
\be{eff}
\Lambda_{eff}=\Lambda_{B}+\kappa \rho_{vac}
\end{equation}
The SM complete vacuum energy is
\be{rho}
\rho_{vac}=\rho_{B}+\sum_{i}c_{i}\frac{m_{i}^{4}}{64\pi^{2}}\ln\left(\frac{m_{i}^{2}}{\mu^{2}} \right)+\rho_{vac}^{UV}+\rho_{vac}^{EW}+\rho_{vac}^{QCD}+...
\end{equation}
$$\simeq \rho_{B}-2 \times 10^{8}\, {\rm GeV}^{4}++\rho_{vac}^{UV}+\rho_{vac}^{EW}+\rho_{vac}^{QCD}+...$$
where $\sum_{i}$ is done all over Standard Model particles
and in particular we use current data
$m_{H}\simeq 125\, {\rm GeV}$;
$c_{quarks}\simeq -4$, $m_{u}\simeq 2.3\, {\rm MeV}$,
$m_{d}\simeq 4.6\, {\rm MeV}$, $m_{s}\simeq 0.104\, {\rm GeV}$
$m_{c}\simeq 1.27\, {\rm GeV}$,
$m_{b}\simeq 4.2\, {\rm GeV}$, $m_{t}\simeq 171.2\, {\rm GeV}$;
 $m_{e}\simeq 0.511\, {\rm MeV}$,
 $m_{\mu}\simeq 105\, {\rm MeV}$,
 $m_{\tau}\simeq 1.77\, {\rm MeV}$,
 (we ignore neutrinos),
 $M_{Z}\simeq 91\, {\rm GeV}$,
 $m_{W_{\pm}} \simeq 80\, {\rm GeV}$,
 $c_{H}=1,c_{q}=-4,c_{l}=4,c_{Z}=c_{W}=3$;
 \be{UV}
 \rho_{vac}^{UV}=-\kappa \frac{1}{4}\sum_{F,B}\left[c^{B}(E)m_{B}^{4}(E)D^{B}(0)-c^{F}(E)m_{F}^{4}(E)D^{F}(0)\right]
 \end{equation}
 where $D^{F,B}(0)$ are bubble diagrams $=\langle \Phi(0) \Phi(0) \rangle$
of all SM particles (F=fermions, B=bosons)  and we assume $M_{UV}=M_{Pl}$;
 \be{EW}
 \rho_{vac}^{EW}=-\frac{\sqrt{2}}{16}\frac{m_{H}^{2}}{G_{F}^{2}}\simeq -1.2\times 10^{8}\,{\rm GeV}^{4};
 \end{equation}
 \be{QCD}
 \rho_{vac}^{QCD}\simeq (\langle \bar{q}q\rangle)^{4/3} \simeq 10^{-2}\, \rm GeV^{4};
 \end{equation}
 Let us note that in Eq.\ref{UV}, $m_{B,F}^{4}D_{B,F}(0)\sim M_{UV}^{4}$ for $m_{B,F}\rightarrow 0$.

 Now, let us include the contributions of virtual masses into Eqs.(\ref{UV},\ref{EW},\ref{QCD})
 \be{vmc1}
 \rho_{vac,TOT}^{VBH}= \rho_{vac}^{UV}+\sum_{VBH} c_{VBH}(E)  M_{Pl}^{4}
 \end{equation}
 \be{vmc2}
 \rho_{vac,TOT}^{EW}= \rho_{vac}^{EW}+\sum_{SM}\frac{1}{8\pi^{3}} m_{SM}^{4}(E)
 \end{equation}
 \be{vmc3}
\rho_{vac,TOT}^{QCD}= \rho_{vac}^{QCD}+\sum_{WL,G} \frac{1}{8\pi^{3}} m_{WL,G}^{4}(E)
 \end{equation}
 where $\sum_{VBH}$ is on all virtual Black Hole species,
$\sum_{SM}$ is performed on all SM particle masses,
$\sum_{WL}$ is performed all over the
quark-antiquark Wilson lines (WL) and glueballs (G).
For instance the mass of SM particle is averagely distributed
in every associated Compton volume  $\lambda_{c}^{3}\sim m_{SM}^{-3}$
and so on.
One can note that there is a coincidence in order of magnitude
among various counter-terms.
For example, the sum on all SM particles masses have approximately the same
order of the vacuum expectation value but with an inverted sign.
As well, QCD Wilson lines and Glueballs have a mass scale density of the same order $(1\div 10)$ of
the QCD confinement energy density, but with again an inverted sign.
Finally, the most important contributions coming from the Planck scale cutoff
are from UV divergent loops and virtual black holes mass density, again expected
with the same order of magnitude but inverted signs if $M_{UV}=M_{Pl}$.
This alleviates the fine-tuning of the cosmological constant invoked in literature.
However, at this level of analysis is not possible to predict how much it can be alleviated,
i.e. if the cancellation is down to namely $1/2$ or  $...$  or $10^{-50}$ or $...$ or $10^{-122}$ or $...$ or $<<10^{-122}$ of $O(1)M_{Pl}^{4}$.
To demonstrate the exact cancellation among all these contributions
seems impossible in framework of an effective quantum gravity theory.
For instance, calculations of precise coefficients in Eq.(\ref{vmc1})
request an UV completed theory of quantum gravity
because at $E\simeq M_{Pl}$ various radiative correction loops must contribute order $O(1)$
and they cannot be controlled in the effective quantum gravity framework.
Another source of uncertainty comes from a possible unknown embedding of
the SM in a larger group: clearly in this case the number of new particles
as well as new introduced VEVs would contribute to the vacuum energy density.

\section{Path integral reformulation}

In this section, we will reformulate the cosmological problem in full SM $+$ quantum gravity path integral.
All bubble diagrams contribute to the full partition function
of Standard Model sector (or probably extensions)
and quantum gravity: the partition function is nothing but
an amplitude
$Z=\langle vacuum| vacuum \rangle$.

The partition function of the Euclidean effective quantum gravity theory is the following path integral:
\be{chi}
Z=\int \mathcal{D} g \mathcal{D}\psi \mathcal{D} \phi \mathcal{D} A_{\mu} e^{-I[g,\psi,\phi,A]}
\end{equation}
where $g$ is the Euclidean metric tensor and $\phi,A_{\mu},\psi$ are all SM scalars, bosons and fermions.
The following argument can be generalized for a SM extension.

In general the problem of quantum gravity is that this path integral has an UV divergence at 1-loop.

In semiclassical limit
\be{I}
I_{E}=-\int_{\Sigma}\sqrt{g}d^{4}x\left(\mathcal{L}_{m}+\frac{1}{16\pi}(R-2\Lambda)\right)
\end{equation}
$$+\frac{1}{8\pi}\int_{\partial \Sigma}\sqrt{h}d^{3}x(K-K^{0})$$
where $\mathcal{L}_{m}$ is the matter Lagrangian and $G=c=1$. We will consider the case of $\Lambda=0$, i.e. the initial cosmological term is zero
$K$ is the trace of the curvature induced on the boundary $\partial \Sigma$
of the region $\Sigma$ considered, $h$ is the metric induced on the boundary $\partial \Sigma$, and
$K^{0}$ is the trace of the induced curvature embedded in flat space.
The last term is a contribution from the boundary.
We consider infinitesimal perturbations of matter and metric
as $\phi=\phi_{0}+\delta \phi$,
$A=A^{0}+ \delta A$, (...)
and $g=g_{0}+\delta g$,
so that
\be{Is} I[\phi,A,...,g]=I[\phi_{0},A_{0},..g_{0}]+I_{2}[\delta \phi,\delta A,...\delta g]+\mbox{higher orders}\,,\end{equation}
\be{Is1} I_{2}[\delta \phi,\delta A,..,\delta g]=I_{2}[\delta \phi,\delta A,...]+I_{2}[\delta g]\,.\end{equation}
\be{logZ}
{\rm log} Z=- {\rm log} Z[\phi_{0},A_{0},...,g_{0}]
\end{equation}
$$+{\rm log} \int \mathcal{D}\delta \phi \mathcal{D}\delta A(...) e^{-I_{2}[\delta \phi,\delta A,...]}+{\rm log}\int \mathcal{D}g e^{-I_{2}[\delta g]}$$

So that, according to Gibbons and Hawking, the Standard Model can be decoupled by gravitational fluctuations up to higher order corrections \cite{Euclidean1, Euclidean2}
in semiclassical limit.
A conceptual problem of the decoupling limit comes from the fact the
SM partition function is UV divergent and it is highly backreacting on the gravitational metric.
At this point, the semiclassical limit seems not allowed.
In other words, the full theory is not converging to a SM in a flat background in the limit of $E<<M_{Pl}$.
The expectation value of the energy-tensor in vacuum has a non-zero component
$$\langle vacuum| \tilde{T}_{00}| vacuum \rangle_{SM{-}integrals+EW+QCD}$$
But we have also to consider
$$\langle vacuum| \tilde{T}_{00}| vacuum \rangle_{Virtual-Masses}$$
where
$$\tilde{T}_{00}=T_{00}-\frac{1}{2}g_{00}T$$
where the main contribution of $\langle vacuum| \tilde{T}_{00}| vacuum \rangle_{Virtual-Masses}$ comes from
$$\langle vacuum| \tilde{T}_{00}| vacuum \rangle_{S_{2}\times S_{2}}=c^{VBH}(E)M_{Pl}^{4}$$
corresponding to $\langle vacuum| I_{m}| vacuum \rangle \neq 0$.
A classification of possible quantum gravity bubbles can be done
on the basis of rigorous topological arguments \cite{Hawking:1995ag} .
Quantum bubbles are classified by their topological invariants
and in particular by their Eulero number and signature
\be{chi}
\chi=\nu+B_{2}^{+}+B_{2}^{-}=\frac{1}{128\pi^{2}}\int d^{4}x \sqrt{g} R_{abcd} R_{a'b'c'd'}\epsilon^{aba'b'} \epsilon^{cdc'd'}
\end{equation}
\be{chi}
\tau=B_{2}^{+}-B_{2}^{-}=\frac{1}{96\pi^{2}}\int d^{4}x \sqrt{g} R_{abcd} R_{a'b'}^{cd}\epsilon^{aba'b'}
\end{equation}
where $\nu=+2$ for compact manifolds and $\nu=+1$ for non-compact manifolds,
and $B_{2}^{\pm}$ are the second Betti numbers of harmonic and anharmonic two
forms respectively.
In the case of non-compact manifold boundary terms will contribute to the integral.

All bubbles are topologically equivalent to only three possible classes:
$S^{2}\times S^{2}, CP^{2}$ and $K^{3}$.
Of course $CP^{2},K^{3}$ can be inversely oriented,
 two possible anti-bubbles $\bar{CP}^{2},\bar{K3}$.
 $S^{2}\times S^{2}$ has $(\chi,\tau)=(4,0)$,
$CP^{2}$ has $(3,1)$, $\bar{CP}^{2}$ has $(3,-1)$
$K3$ has $(24,16)$ and $\bar{K3}$ has $(24,-16)$.
 In space-time with a spin structure, $CP^{2},\bar{CP}^{2}$ are not possible.
 On the other hand $K3,\bar{K3}$ bubbles contribute to gravitational anomalies
 and they can change helicity and chirality of particles.
 But, their contribution in the path integral is expected to be subdominant:
Atiyah-Singer index theorem guarantees that they will have fermionic zero modes.
This implies that the only relevant diagrams are associated to $S^{2}\times S^{2}$,
corresponding to virtual black holes pairs.

So that, the partition function can be fractioned in two parts as
\be{separation}
{\rm log} Z_{0}+{\rm log}Z_{\delta (SM), \delta g}
\end{equation}
where $Z_{0}$ is referred to the partition function of SM in Euclidean flat background
and
\be{deltaSM}
Z_{\delta (SM), \delta g}=\int \mathcal{D}g \mathcal{D}\phi \mathcal{D}A_{\mu}\mathcal{D}\psi e^{-\langle\delta I_{m}\rangle+...}
\end{equation}
where
\be{coincidence}\langle \delta I_{m}\rangle=-\langle \delta I_{m} \rangle_{SM{-}integrals}+\langle \delta I_{m} \rangle_{Virtual{-}masses}+...
\end{equation}
The vacuum energy will  decouple by gravitational $\sqrt{-g}$ inside the matter action $I_{m}$ if
\be{deltaLm}
\langle \delta \mathcal{L}_{m} \rangle_{SM-Integral}=-\langle \delta \mathcal{L}_{m} \rangle_{Virtual-masses}
\end{equation}
so that they decouple by gravitational factor $\sqrt{-g}$ inside the matter action $I_{m}$.
Then a separation of (\ref{deltaSM}) is possible by virtue of the miraculous coincidence (\ref{coincidence}):
  the partition function can be expressed as a product of separate Feynman's path integrals

  $$\left(\int \mathcal{D}\delta g \,e^{-I_{2}[\delta g]}\right)\left(\int \mathcal{D}\delta \phi ... \, e^{-I_{2}[\delta \phi,...]}\right)$$

More precisely, the virtual black hole action is
\be{stf}
I_{1}\sim\frac{m_{BH}^{2}}{M_{Pl}^{2}}
\end{equation}
and ignoring the interactions among $N$ black holes with the same mass (dilute gas approximation)
\be{stfn}
I_{N}\sim N\frac{m_{BH}^{2}}{M_{Pl}^{2}}
\end{equation}
 we can evaluate the partition function of $N$ identical BH in a box of volume $V$
as
\be{Z}
Z_{0,BH}\sim \int_{0}^{\infty}dm_{BH} \sum_{N}\frac{1}{N!}\left(\frac{V}{l_{Pl}^{3}} \right)^{N}e^{-4\pi N\frac{m_{BH}^{2}}{M_{Pl}^{2}}}
\end{equation}
This partition function is minimized by \cite{Hawking2}
\be{nBH}
\langle n_{BH} \rangle \sim 1,\,\,\,\langle m_{BH}^{2} \rangle \sim M_{Pl}^{2}
\end{equation}
coinciding with its saddle point \footnote{
The integral on all BH masses is expected to be an approximation of a discrete
sum, i.e. BH masses are expected to be disposed in a discrete spectrum
from arguments on the BH entropy \cite{Dvali:2011nh}. }.
This implies that the spacetime must be repleted with Planck mass black holes, with a density of order one for Planckian volume.
This contributes to the complete partition function of SM and quantum gravity, as mentioned above.
The problem is that virtual black holes are also gravitationally coupled with space-time
and so that each others, i.e. the diluite gas approximation can be used only as a valid estimator
of virtual black hole package.
The curvature of space-time
is maximized in modulus by (\ref{nBH}) if $M_{UV}\sim M_{Pl}$
and the main contribution is coming by virtual black holes gravitational attraction
$\langle V \rangle \sim G_{N} M_{Pl}^{2}/l_{Pl}\sim M_{Pl}$.

At this point we could be concern about possible non-perturbative quantum gravity corrections.
For example, a black hole bubble can be corrected by infinite loops by gravitons, gauge bosons and so on.
We can expect that  any possible loop corrections to black-hole bubble
also correct SM bubbles, and the leading divergence is the same.
Then, the limit of the space-time package of virtual Black holes cannot exceed
$l_{Pl}^{4}$. But as stressed above, we have not the control of the running of couplings as mention above
and we can consider the problem only at the level of effective field theory.
This is the no-go edge for our approach based on effective quantum gravity.

\subsection{$\Lambda\neq 0$ and real black hole pairs in de Sitter }

Now let us discuss the case of an initial cosmological constant $\Lambda \neq 0$.
The presence of a bare cosmological constant can source the creation of a black hole pair in a de Sitter space.
This process is mediated by a $S_{2}\times S_{2}$ gravitational instanton, generating an imaginary rate in the euclidean partition functional \cite{GP}.
The topology of the gravitational instanton is exactly the same of virtual black hole bubbles,
and
the expansion energy can promote virtual black holes to a real pair.
The nucleation rate is
\be{nucleation}
\Gamma=Ae^{-(I_{S_{2}\times S_{2}}-I_{b.g.})}
\end{equation}
where $A$ includes quantum corrections, $I_{S_{2}\times S_{2}}$ is the action associated to the gravitational instanton,
$I_{b.g.}$ is the gravitational action of the background metric.
As shown in \cite{GP}, the associated solution contains a negative mode. So that, the partition function becomes complex.
This is the signal of an instability, leading to a spontaneous nucleation.
The black holes are degenerate Schwarzschild-de Sitter black holes, or Nariai black holes, with Schwarzschild radius of $r_{H}=1/\sqrt{\Lambda}$
and tunneling rate $\Gamma\sim e^{-\pi G_{N}^{-1}\Lambda^{-1}}$.
For $\Lambda<<G_{N}^{-1}\sim M_{Pl}^{2}$, the tunneling rate is exponentially suppressed.
However, if $\Lambda=M_{Pl}^{2}$ the process cannot be calculated in semiclassical approximation
and the system will disastrously nucleate into real black hole pairs with $100\%$ of probability.
But if SM bubbles are cancelled by virtual black hole bubbles, they cannot source any instabilities.

 Eq.(\ref{nucleation}) is related to partition functions of $S_{4}$ and $S_{2}\times S_{2}$ as
\be{rate}
\Gamma=-\frac{1}{\pi}\sqrt{\frac{\Lambda}{3}}\frac{{\rm Im}Z[S_{2}\times S_{2}]}{Z[S_{4}]}
\end{equation}
As shown in \cite{GP,Volkov:2000ih,Elizalde:1999dw,Nojiri:1998ph}, this path integral can be computed by integrating over
the Fourier expansion coefficients of metric scalar, vector and tensor perturbations,
obtaining an infinite product all over the eigenvalues.
However, the conformal negative modes contributing to the integration are a finite set
associated to the conformal operator
 $\Delta_{0}=-3\nabla_{\mu}\nabla^{\mu}-4\Lambda$.
The final result is independent by the gauge-fixing choice
and the
Fadeev-Popov operator contains the zero-modes
of the background isometries.

 $\delta g_{\mu\nu}$ can be decomposed in scalar, vector and tensor modes:
\be{decomposition}
\delta g_{\mu\nu}= \varphi_{\mu\nu}+\frac{1}{4}\delta g g_{\mu\nu}+\nabla_{\mu} \zeta_{\nu}+\nabla_{\nu} \zeta_{\mu}-\frac{1}{2}g_{\mu\nu}\nabla_{\sigma}\zeta^{\sigma}
\end{equation}
under metric perturbations $g_{\mu\nu}+\delta g_{\mu\nu}$, the Einstein-Hilbert part of the action is perturbed as
\be{delta2}
\delta^{(2)} I_{\delta g}=\frac{1}{2}\langle \varphi^{\mu\nu},\Delta_{2}\varphi_{\mu\nu}\rangle-\frac{1}{16}\langle \tilde{h}, \Delta_{0}, \tilde{h}\rangle
\end{equation}
where $\delta^{(2)}$ is the 2th order perturbation,
$\tilde{h}=h-2\nabla_{\sigma}\zeta^{\sigma}$,
\be{deltanabla2}
\Delta_{2}\varphi_{\mu\nu}=-\nabla_{\sigma}\nabla^{\sigma}\varphi_{\mu\nu}-2R_{\mu\nu\rho\sigma}\varphi^{\rho\sigma}
\end{equation}
and the scalar product in a compact $\Lambda>0$ manifold is
\begin{equation} \label{deltaa}
\langle \varphi_{\mu\nu}, \varphi^{\mu\nu}\rangle =\frac{1}{32\pi G_{N}}\int_{\Sigma}d^{4}x\sqrt{g}\varphi^{\mu\nu}\varphi_{\mu\nu}
\end{equation}
\be{deltab}
\langle \zeta_{\mu},\zeta^{\mu}\rangle =\frac{1}{32\pi G_{N}}\int_{\Sigma}d^{4}x\sqrt{g}\zeta_{\mu}\zeta^{\mu}
\end{equation}
Let us consider the partition function perturbed at the 2th order:
\be{contributionVari}
Z^{(2)}=\int \mathcal{D} g \mathcal{D} \phi \mathcal{D} A\mathcal{D}\psi e^{
I_{0}+
\frac{1}{2}\langle \varphi^{\mu\nu},\Delta_{2}\varphi_{\mu\nu}\rangle-\frac{1}{16}\langle \tilde{h}, \Delta_{0} \tilde{h}\rangle + \delta I_{m}+\delta I_{g.f.}}
\end{equation}
where $\delta I_{m}$ contains SM and virtual black hole bubbles,
$\delta_{g.f}$ the a gauge fixing term
\be{gaugefixing}
\delta I_{g.f}=\gamma \langle \nabla_{\sigma} h^{\sigma}_{\rho}-\frac{1}{\alpha}\nabla_{\rho} h , \nabla^{\alpha} h_{\alpha}^{\rho}-\frac{1}{\alpha}\nabla^{\rho} h  \rangle
\end{equation}
where $\gamma, \alpha$ are real constants. The gauge fixing term can be choose so that it not contains zero modes: $\gamma=1$, $\alpha=2$ \cite{Volkov:2000ih}.
Again, assuming $\langle \delta I_{m} \rangle=0$, the decoupling is safe.

The bubble nucleation process is sourced by the classical action $I_{0}$ with $\Lambda>0$
causing negative modes the gravitational term (\ref{delta2}).
On the other hand, we have shown that SM vacuum energy cannot source $O(1)$ nucleation instabilities
if completely screened by Virtual masses.
At this point, the effective 2th order action is exactly the same solved in literature \cite{GP,Volkov:2000ih,Elizalde:1999dw,Nojiri:1998ph},
with exactly the same calculation procedure.

\section{Conclusions}
In this paper, we have shown how the cosmological constant is
corrected by other counter-terms
coming from the masses of virtual particles - still  not
considered in the literature.
The most important contribution comes from
virtual black hole bubble diagrams.
In order to distinguish this problem from the original stated cosmological problem,
we define it {\it cosmological problem of the second type}.
The initial Einstein's cosmological constant is corrected combining integrated UV divergent SM bubble diagrams
plus virtual masses.
We have also discussed this problem in the path integral framework.
In particular, we have discussed the cancellation mechanism with a null bare cosmological constant $\Lambda=0$
and with an initial small bare cosmological constant $\Lambda>0$.
In doing this, we have tacitly assumed that CPT and unitarity are not violated by virtual black holes.
In other words, we have assumed that the information paradox would be not seriously interpreted
as a violation of quantum mechanics principles. A possible decoherence effect by quantum gravity is assumed to be null.
Of course, the information paradox is another different problem for an unknown microscopic theory of black holes
\footnote{We have suggested that semiclassical black holes could be reinterpreted as an effective geometry, composed of a large ensamble of horizonless naked singularities
(imagined smoothed at the planck lenght)
  \cite{Addazi:2015gna,Addazi:2015hpa,Addazi:2015bee}: the information paradox would be understood as a chaotization of the infalling information.
  In this approach, a BH horizon does not exist and it is only an approximated geometry.
  Paradoxical BHs are substituted by new geometric solutions dubbed {\it frizzyballs}, which recover all
observable proprieties of astrophysical BH.
In frizzyballs, the no hair theorem is avoided and they carry informations in gravitational geometric hairs. }.

To conclude,
the presence of UV divergent counter-terms to the usual cosmological vacuum energy
implies a strong reduction of the cosmological fine-tuning suggested in literature.
This also seems a relevant counter-argument against the usual disentanglement limit
of particle physics and quantum gravity, always applied in all quantum field theory calculations.
 Such a procedure seems
justified in most of the scattering processes tested in laboratory.
But as shown above, such a procedure is not fully correct
in the estimation of the vacuum energy density.
For instance, the contribution of virtual black holes to the vacuum energy is
not negligible as thought by most of theoretical physicists,
but it is order $M_{Pl}^{4}$.
Because of that, we hope that our arguments would be useful for a future clarification of the most serious unsolved problem of theoretical physics.
The final dream is to demonstrate an exact cancellation among all terms in the framework of a UV completed theory of quantum gravity or a theory of everything.
We think that this problem could be analogous to the old dream to calculate the electron mass from first principles
\footnote{ The cosmological problem has also a crucial importance in phenomenology:
if the SM vacuum energy density was zero despite of $10^{-122}M_{Pl}^{4}$,
the cosmological term would be generated by an unknown mechanism
with possible predictions in phenomenology.
For instance, we have suggested that the cosmological constant
could be generated by a dark strong condensate,
also providing a natural candidate for dark matter
\cite{Addazi:2016sot,Addazi:2016nok}.
Another interesting alternative is the reinterpretation of the vacuum energy density as
generated by a Born-Infeld (BI) electrodynamic condensate.
In this framework, we have shown how neutrino masses would be dynamically generated
if neutrinos were coupled with the new BI vector boson \cite{Addazi:2016oob}. Finally,
contributions of chiral symmetry violating bubbles as $K_{3},\bar{K}_{3}$ or more complicated
space-time composed topologies can source a gravitational topological vacuum susceptibility
 term $\langle \tilde{R}R\rangle \neq 0$ contributing to the vacuum energy and possibly generating a neutrino mass term.
 This last possibility is connected to the recent suggestion of Ref.\cite{Dvali:2016uhn}. }.

\vspace{3cm}

{\large \bf Acknowledgments}
\vspace{3mm}

I would like to thank Massimo Bianchi, Salvatore Capozziello, Gia Dvali, Lena Funcke, Antonino Marciano and Sergei Odintsov
for valuable discussions and remarks on these subjects.
I also would like to thank
 Fudan University (Shanghai)
for the hospitality during the preparation of this paper.
My work was supported in part by the MIUR research grant Theoretical Astroparticle Physics PRIN 2012CP-PYP7 and by SdC Progetto speciale Multiasse La Societ\'a della Conoscenza in Abruzzo PO FSE Abruzzo 2007-2013.

redpajama_set_name: RedPajamaArXiv


In the first round of last season's Western Conference playoffs, the 51-31 Portland Trail Blazers were the 4th seed, while the the 55-27 Memphis Grizzlies were the 5th seed. Yet, despite being the higher seed, Portland started the playoffs on the road. It was the result of the NBA's awkward playoff seeding rules, which placed each of the three division winners as one of the top four seeds in the conference, but settled home court advantage by record, not seed.
The NBA announced Tuesday that, going forward, the top eight teams in each conference will be seeded for the playoffs based solely upon record, eliminating any advantage for winning a division. This was a logical change for the NBA to make, especially considering some divisions (like the Southwest one, with the Spurs, Rockets, Mavericks, Pelicans, and Grizzlies) are so ludicrously overpowered that they regularly have multiple teams finish with better records than one of the other division winners.
While the NBA didn't mention anything of the sort, it's a good bet that this change is a step towards eliminating divisions altogether. Without any playoff seeding advantage, the only difference between divisions now is the schedule they play, and only slightly. Each team shares at least 74 of 82 games with the teams in its conference. Division are arcane, leftover from when teams flew coach and regional rivalries really mattered.
The fun question is whether or not the NBA should eliminate conferences. I say yes! Teams are already flying all across the country, and the NBA has repeatedly said that it would like an entire division based in Europe one day; clearly they think the players can deal with additional travel. During the "Western" Conference playoffs this year, the NBA champion Golden State Warriors beat teams in New Orleans, Memphis, and Houston. If you check out a map, you'll see that those teams are all much closer to the East Coast than West. Eliminating conferences also eliminates travesties like having to watch the 38-44 Nets in the playoffs instead of the Russ Westbrook-led Thunder.


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Lesley M.M. Blume gathers a panoply of eccentric biographical data ahead of the star's return to the Netflix rom-com.
GIRLS' GIRL Jacobs, photographed in Los Angeles.
Some women appear to have it all: brains, looks, talent, and wit. Actress Gillian Jacobs, 34, is among these rarefied creatures, but she is not above envy. She watched the launch of the HBO series Girls with mixed feelings: "At the time, I was on Community, and we were always fighting to stay on the air," she recalls. "I was excited for Lena, but there's also a natural jealousy." Well, if you can't beat 'em, join 'em, which is just what Jacobs did: in Season Four, she joined the cast of Girls as the cult-favorite character Mimi-Rose Howard, arguably the most defiant and least needy female on the show. She now stars in her own Judd Apatow-created Netflix rom-com series, Love (which returns for a second season on March 10), as well as a slate of upcoming films (Dean and Magic Camp). Jacobs is quickly emerging as a patron saint of smart alecks and independent souls—even if her knees still sometimes knock and her teeth chatter during auditions. Below, she talks about the advantages of having been an oddball child, her unlikely penchant for Hannibal Lecter, and marriage in the realm of millennials.
HER MOTHER also called her "Bubby," after former Steelers quarterback Bubby Brister.
TO THIS day, she has no idea why her mother nicknamed her after a football player.
SHE LOVES fellow theater nerds ("You can spot one a mile away") but has never dated another actor. She says her current paramour is "creative," but not stage- or camera-inclined.
THE HISTORICAL role she would most like to reprise: tough-talking female reporter Hildy Johnson in His Girl Friday, originally played by Rosalind Russell in 1940.
HANGING NEXT to the Dries in her closet: childhood Halloween costumes made by her seamstress grandmother, including a green velvet T. rex affair, a vampire-bat ensemble, and matching bathrobes created for her and her childhood Barbie.
HER ONLY vices: black coffee and binge-watching Vanderpump Rules.


BEIJING (Reuters) - U.S. short-term rental service Airbnb Inc has hit a wall with its newest marketing scheme in China, after regulators objected to a promotion offering sleepovers on the Great Wall of China.
The San Francisco-based company last week asked users in China to compete for four slots to stay at a "Great Wall Wonder house", sleeping overnight in one of the wall's guard towers.
However, a district cultural commission said on Monday that it did not support the promotion as it was not in line with conservation plans for the wall, a UNESCO world heritage site.
The Yanqing District cultural commission, however, said on its verified Weibo account on Monday that it had not received or approved any application from Airbnb. Local media reported the exchange on Thursday.
The Great Wall is among 28 sites in the company's latest round of contests, which also offer opportunities to sleep out at Australia's Great Barrier Reef, Boston's Fenway Park baseball ground and the Paris Catacombs.
It is not the first time Airbnb has had a run-in with authorities in China. It has previously had to shutter services during politically sensitive events, and comply with strict regulations as the homestay accommodation industry remains a gray area in China.
Last year, the company said it would start disclosing host information to government agencies in line with rules requiring citizens and tourists to register their addresses with police within 24 hours when they arrive in China or stay at a hotel.
Airbnb is expanding its business in China and hoping to spur growth in the world's most populous country. Last year it said it would more than triple its local workforce and double its investment in the region.