<p><a href="https://astronomy.stackexchange.com/questions/25982/is-hubble-constant-dependent-on-redshift">This answer</a> to the question “Is the Hubble constant dependent on redshift?” gives the formula (a form of the Friedmann equation) for the Hubble parameter <span class="math-container">$H(z)$</span> as a function of redshift <span class="math-container">$z$</span>:</p>
<p><span class="math-container">$$ H(z)^2 = H_0^2 \left[ (1+z)^4 \Omega_r + (1+z)^3 \Omega_M + (1+z)^2 \Omega_k +  \Omega_\Lambda \right] $$</span></p>
<p>where the <span class="math-container">$\Omega$</span> terms are the fractional densities in radiation, matter, curvature, and dark energy, respectively.</p>
<p>Using that, plus the knowledge that the redshift of the CMB is <span class="math-container">$z \simeq 1100$</span>, you can plug in values for the densities (I used WMAP values quoted <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/denpar.html" rel="nofollow noreferrer">here</a>) and get that <span class="math-container">$H$</span> at the time of the CMB was about 22,000 times larger than the current value.</p>
<p>That answer also gives a graph of the value of the Hubble parameter as a function of time.</p>

CC BY-SA 4.0
2024-09-21T23:28:35.827Z
Hi, in the above equation, and pretending you don't know how to derive the Hubble constant from the local universe, how do you derive the value of $H_0^2$ to determine the value of $H(z)^2$ at any redshift?
Tivity
CC BY-SA 4.0
2020-08-01T13:41:06.027Z
2020-08-01T13:41:06.027Z
Eric Jensen
<p>What about its value roughly 9 billion years after the Big Bang, when dark energy started to 'take over' and accelerate the expansion of the universe?</p>
<p>Is there a timeline or chart somewhere that shows approximate, theoretical values of Hubble's not-so-constant constant throughout the lifetime of the Universe?</p>

<universe><expansion><hubble-constant>
What was the the value of the Hubble constant at the time of the CMB's 'release' (i.e., 379,000 years after Big Bang)?
Kurt Hikes
# What was the the value of the Hubble constant at the time of the CMB's 'release' (i.e., 379,000 years after Big Bang)?

(Asked by: username_0 on 2020-07-31)

What about its value roughly 9 billion years after the Big Bang, when dark energy started to 'take over' and accelerate the expansion of the universe?

Is there a timeline or chart somewhere that shows approximate, theoretical values of Hubble's not-so-constant constant throughout the lifetime of the Universe?

**Tags:** universe, expansion, hubble-constant

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## 1 answers

### Answer by username_1 on 2020-08-01. Score: 3

[This answer](https://astronomy.stackexchange.com/questions/25982/is-hubble-constant-dependent-on-redshift) to the question “Is the Hubble constant dependent on redshift?” gives the formula (a form of the Friedmann equation) for the Hubble parameter $H(z)$ as a function of redshift $z$:

$$ H(z)^2 = H\_0^2 \left[ (1+z)^4 \Omega\_r + (1+z)^3 \Omega\_M + (1+z)^2 \Omega\_k + \Omega\_\Lambda \right] $$

where the $\Omega$ terms are the fractional densities in radiation, matter, curvature, and dark energy, respectively.

Using that, plus the knowledge that the redshift of the CMB is $z \simeq 1100$, you can plug in values for the densities (I used WMAP values quoted [here](http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/denpar.html)) and get that $H$ at the time of the CMB was about 22,000 times larger than the current value.

That answer also gives a graph of the value of the Hubble parameter as a function of time.

> **Comments:**
> **username_2**: Hi, in the above equation, and pretending you don't know how to derive the Hubble constant from the local universe, how do you derive the value of $H_0^2$ to determine the value of $H(z)^2$ at any redshift?  

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