<p>No - the decreasing energy in the CMB is already well modeled in the <A HREF="https://en.wikipedia.org/wiki/Friedmann_equations">Friedmann equations</A>. The term in the density parameter that is proportional to $a^{-4}$ is the contribution of radiation energy density to the evolution of the universe, the term proportional to $a^{-3}$ is matter density (mostly dark, but includes ordinary matter), $a^{-2}$ is the contribution of the curvature of space-time itself, and the term without any factors of $a$ is the contribution of dark energy. The size of the radiation density, today, is already a small fraction of the matter density (about 0.03% of the matter density, 0.01% of the density of the universe overall - ordinary matter is about 5% overall). </p>

<p>The last time the energy density in the radiation fields was the same size as what's in the matter fields was <A HREF="https://lambda.gsfc.nasa.gov/product/map/current/params/lcdm_wmap9.cfm">around $z=3,300$</A>.</p>

<p>I also disagree with @J.Chomel's answer - the energy stored in the radiation field is decreasing. Then energy density in the radiation field scales like $a^{-4}$, and the volume scales like $a^3$. Since the total energy is the energy density times the volume, the total energy scales like $a^{-1}$, just as you would expect with the number of photons being fixed, but the energy in each photon scaling as $a^{-1}$ as the wavelength increases. </p>

CC BY-SA 3.0
2017-01-19T10:03:32.430Z
Then where does the diminished energy go?
Deschele Schilder
CC BY-SA 3.0
2017-01-19T10:19:37.950Z
The question of ["energy" in general relativity](http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html) is more subtle than I can fully address in a comment, and care to address in an answer. Follow the link for a good analysis.
Sean Lake
CC BY-SA 3.0
2017-01-19T10:21:22.763Z
The energy diminishes *relatively*. This is what I was trying to say; it diminishes because CMBR photons EM waves stretch.
J. Chomel
CC BY-SA 3.0
2017-01-19T12:18:42.380Z
Okay, but if the total number of photons stays the same, the total CMBR-energy lowers. The cause of this lowering (the stretching of the photon wavelengths is due to the stretching of space) is not relevant. The energy diminishes absolutely. What do you mean if you say the energy diminishes relatively? Relative to the stretching space? Why doen't that diminish the energy absolutely?
Deschele Schilder
CC BY-SA 3.0
2017-01-20T08:09:20.320Z
@descheleschilder It doesn't diminish it if you look at the universe from outside the universe :)
J. Chomel
CC BY-SA 3.0
2017-01-20T12:33:13.180Z
@J.Chomel: The energy _does_ diminish. You cannot "look at the Universe from outside the Universe", not even theoretically.
pela
CC BY-SA 3.0
2017-01-20T12:45:58.680Z
@pela, maybe *you look* is too vague; let's say you don't look at it, but someone else *think* about it from another one? Don't we have theories about other universe?
J. Chomel
CC BY-SA 3.0
2017-01-20T12:57:07.810Z
@J.Chomel: I'm not really opposing to the idea of "looking" (even as a thought experiment). The Universe is everything, it is not expanding into a higher dimension (but yes, there _are_ theories of multiverses, but I don't think they include the possibility of observing one universe from another). Anyway, this doens't really have anything to do with the energy of its constituents. The energy simply does decrease, but this doesn't contradict our theories. Have a look at [Is the Universe Leaking Energy?](https://people.smp.uq.edu.au/TamaraDavis/papers/SciAm_Energy.pdf), it's a great article. :)
pela
CC BY-SA 3.0
2017-01-20T13:03:23.070Z
yes thanks! It says "*On the scale of individual photons, 
energy is always conserved, even as light gets red-shifted.*" ... still confusing to me, if number of CMBR photons stay the same.
J. Chomel
CC BY-SA 3.0
2017-01-20T13:28:07.027Z
It says it also at the end! "*the drop in energy is just a matter of **perspective and relative motion**.*"
J. Chomel
CC BY-SA 3.0
2017-01-19T09:42:31.977Z
2017-01-19T09:42:31.977Z
Sean Lake
<p>I was just told the CMBR energy diminishes with time. Can it be that the lost energy is somehow transferred to spacetime, causing the expansion to accelerate?</p>

<expansion><dark-energy><cosmic-microwave-background>
Can the diminishing energy of the CMBR be the source of dark energy?
Deschele Schilder
# Can the diminishing energy of the CMBR be the source of dark energy?

(Asked by: username_0 on 2017-01-19)

I was just told the CMBR energy diminishes with time. Can it be that the lost energy is somehow transferred to spacetime, causing the expansion to accelerate?

**Tags:** expansion, dark-energy, cosmic-microwave-background

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## 1 answers

### Answer by username_1 on 2017-01-19. Score: 8

No - the decreasing energy in the CMB is already well modeled in the [Friedmann equations](https://en.wikipedia.org/wiki/Friedmann_equations). The term in the density parameter that is proportional to $a^{-4}$ is the contribution of radiation energy density to the evolution of the universe, the term proportional to $a^{-3}$ is matter density (mostly dark, but includes ordinary matter), $a^{-2}$ is the contribution of the curvature of space-time itself, and the term without any factors of $a$ is the contribution of dark energy. The size of the radiation density, today, is already a small fraction of the matter density (about 0.03% of the matter density, 0.01% of the density of the universe overall - ordinary matter is about 5% overall).

The last time the energy density in the radiation fields was the same size as what's in the matter fields was [around $z=3,300$](https://lambda.gsfc.nasa.gov/product/map/current/params/lcdm_wmap9.cfm).

I also disagree with @J.Chomel's answer - the energy stored in the radiation field is decreasing. Then energy density in the radiation field scales like $a^{-4}$, and the volume scales like $a^3$. Since the total energy is the energy density times the volume, the total energy scales like $a^{-1}$, just as you would expect with the number of photons being fixed, but the energy in each photon scaling as $a^{-1}$ as the wavelength increases.

> **Comments:**
> **username_0**: Then where does the diminished energy go?  
> **username_1**: The question of ["energy" in general relativity](http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html) is more subtle than I can fully address in a comment, and care to address in an answer. Follow the link for a good analysis.  
> **username_2**: The energy diminishes *relatively*. This is what I was trying to say; it diminishes because CMBR photons EM waves stretch.  
> **username_0**: Okay, but if the total number of photons stays the same, the total CMBR-energy lowers. The cause of this lowering (the stretching of the photon wavelengths is due to the stretching of space) is not relevant. The energy diminishes absolutely. What do you mean if you say the energy diminishes relatively? Relative to the stretching space? Why doen't that diminish the energy absolutely?  
> **username_2**: @descheleschilder It doesn't diminish it if you look at the universe from outside the universe :)  
> **username_3**: @J.Chomel: The energy _does_ diminish. You cannot "look at the Universe from outside the Universe", not even theoretically.  
> **username_2**: @pela, maybe *you look* is too vague; let's say you don't look at it, but someone else *think* about it from another one? Don't we have theories about other universe?  
> **username_3**: @J.Chomel: I'm not really opposing to the idea of "looking" (even as a thought experiment). The Universe is everything, it is not expanding into a higher dimension (but yes, there _are_ theories of multiverses, but I don't think they include the possibility of observing one universe from another). Anyway, this doens't really have anything to do with the energy of its constituents. The energy simply does decrease, but this doesn't contradict our theories. Have a look at [Is the Universe Leaking Energy?](https://people.smp.uq.edu.au/TamaraDavis/papers/SciAm_Energy.pdf), it's a great article. :)  
> **username_2**: yes thanks! It says "*On the scale of individual photons,  energy is always conserved, even as light gets red-shifted.*" ... still confusing to me, if number of CMBR photons stay the same.  
> **username_2**: It says it also at the end! "*the drop in energy is just a matter of **perspective and relative motion**.*"  

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