<p>Yes. The energy density in the radiation field scales like $a^{-4}$, and the volume scales like $a^{3}$. Since the total energy is the density times the volume, the total energy scales like $a^{-1}$. Note that $a$ is called the "scale factor" and $a = \frac{1}{1+z}$, where $z$ is the redshift, assuming $z=0$ now.</p>

CC BY-SA 3.0
2017-01-19T07:29:52.187Z
@SeanLake-Why is z=0 nowadays? And if so, then nowadays the energy isn't diminishing, because the inverse of a is 1. I thought that nowadays there is still redshift.
Deschele Schilder
CC BY-SA 3.0
2017-01-19T07:48:31.383Z
Time and redshift are related. $z=0$ now purely by convention/definition. In the future redshift will be negative, and if the universe doesn't recollapse, will go to $-1$ in the infinitely distant future.
Sean Lake
CC BY-SA 3.0
2017-01-19T20:43:31.327Z
You need to make it clear that you are talking about a co-moving volume and correct the OP's misconception/confusion about the "size" of the universe.
ProfRob
CC BY-SA 3.0
2017-01-19T07:17:03.433Z
2017-01-19T07:17:03.433Z
Sean Lake
<p>Is the total energy of the CMBR diminishing with time? Since it's existence the volume of the Universe (at least the visible part) has grown by a factor three, which is to say, the number of photons per unit volume is diminished by a factor 27. But the wavelength of these photons has grown by a much bigger factor. So you should think the total energy of all the CMBR photons has become less over time. </p>

CC BY-SA 3.0
2017-01-19T10:09:03.813Z
The CMB was emitted at $z\simeq1100$, so the volume of the Universe has increased by a factor $1100^3\sim10^9$ since the CMB was emitted, i.e. much, much more that 27.
pela
CC BY-SA 3.0
2017-01-19T14:36:09.470Z
This question is ambiguous. Are you talking about total energy or energy density? They're not the same. You specifically say "total energy", but then mention photons per volume, indicating you're talking about energy density.
zephyr
CC BY-SA 3.0
2017-01-19T16:37:41.703Z
@pela-Since the emergence of the CMBR, about 300 000 years after the big bang, space has stretched with a factor 3 (that's why the radius of the visible Universe is now about 40 000 000 000 lightyears). So per unit volume the number of photons has decreased by a factor 27. I think you mean the radius of the visible Universe has increased by a factor $\  10^9$ since 300 000 years after the big bang.This doesn't change the fact that every unit of volume has increased by a factor 27, and the number of photons décreased by the same factor.
Deschele Schilder
CC BY-SA 3.0
2017-01-19T16:49:36.197Z
@zephir-II mean the total energy of the CMBR, and mentioned that the number of photons per unit volume has decreased by a factor 27 because if the number of photons in one unit of volume has decreased, the number of photons for the whole volume of the Universe has decreased by the same factor. It's like the number of atoms in a gas with volume V. If you increaese each unit volume by a factor 3, then the whole volume is also increased by a factor three, and the number of atoms per unit volume dercreases by a factor 27, like is the case for the whole volume V.
Deschele Schilder
<cosmic-microwave-background>
Is the total energy of the CMBR diminishing with time?
Deschele Schilder
# Is the total energy of the CMBR diminishing with time?

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

Is the total energy of the CMBR diminishing with time? Since it's existence the volume of the Universe (at least the visible part) has grown by a factor three, which is to say, the number of photons per unit volume is diminished by a factor 27. But the wavelength of these photons has grown by a much bigger factor. So you should think the total energy of all the CMBR photons has become less over time.

**Tags:** cosmic-microwave-background
> **Comments:**
> **username_1**: The CMB was emitted at $z\simeq1100$, so the volume of the Universe has increased by a factor $1100^3\sim10^9$ since the CMB was emitted, i.e. much, much more that 27.  
> **username_2**: This question is ambiguous. Are you talking about total energy or energy density? They're not the same. You specifically say "total energy", but then mention photons per volume, indicating you're talking about energy density.  
> **username_0**: @pela-Since the emergence of the CMBR, about 300 000 years after the big bang, space has stretched with a factor 3 (that's why the radius of the visible Universe is now about 40 000 000 000 lightyears). So per unit volume the number of photons has decreased by a factor 27. I think you mean the radius of the visible Universe has increased by a factor $\  10^9$ since 300 000 years after the big bang.This doesn't change the fact that every unit of volume has increased by a factor 27, and the number of photons décreased by the same factor.  
> **username_0**: @zephir-II mean the total energy of the CMBR, and mentioned that the number of photons per unit volume has decreased by a factor 27 because if the number of photons in one unit of volume has decreased, the number of photons for the whole volume of the Universe has decreased by the same factor. It's like the number of atoms in a gas with volume V. If you increaese each unit volume by a factor 3, then the whole volume is also increased by a factor three, and the number of atoms per unit volume dercreases by a factor 27, like is the case for the whole volume V.  

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## 1 answers

### Answer by username_3 on 2017-01-19. Score: 1

Yes. The energy density in the radiation field scales like $a^{-4}$, and the volume scales like $a^{3}$. Since the total energy is the density times the volume, the total energy scales like $a^{-1}$. Note that $a$ is called the "scale factor" and $a = \frac{1}{1+z}$, where $z$ is the redshift, assuming $z=0$ now.

> **Comments:**
> **username_0**: @SeanLake-Why is z=0 nowadays? And if so, then nowadays the energy isn't diminishing, because the inverse of a is 1. I thought that nowadays there is still redshift.  
> **username_3**: Time and redshift are related. $z=0$ now purely by convention/definition. In the future redshift will be negative, and if the universe doesn't recollapse, will go to $-1$ in the infinitely distant future.  
> **username_4**: You need to make it clear that you are talking about a co-moving volume and correct the OP's misconception/confusion about the "size" of the universe.  

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