# Is the microwave background radiation still decreasing?

goldust
And if so, at a rate faster or slower or the same compared to at earlier times of the universe?

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Staff Emeritus
As the universe continues to expand the energy of the CMB will continue to decrease. I can't say by how much, though.

goldust
From what I understand so far, the expansion of the universe is accelerating and faster than ever. However, given how big the universe already is, it is possible that the decreasing marginal return of the universe's expansion on the reduction of the CMBR increasingly outweighs the effect of the accelerating expansion in the size of the universe on the reduction of the CMBR, which results in the reduction of the CMBR exponentially decreasing over time. I wonder if there's been any recent study on the topic of whether the CMBR is decreasing to a particular asymptotic value?

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Staff Emeritus
Every time the universe doubles in size the energy of the CMB is reduced to 1/4 of its previous amount, I think. So earlier in time the CMB was more energetic and earlier doublings reduced the CMB energy by a greater flat amount. Even if the rate of expansion increases, it will never reach this same amount of reduction because there isn't enough energy left now.

Staff Emeritus
Gold Member
Keep in mind that your question is somewhat vague. Is what about the CMB still decreasing? In any case, it is true that CMB photons will continue to become more and more redshifted as time goes on, thus losing energy. We can be a little quantitative about this.

First of all, I'll introduce the concept the scale factor, a. The scale factor is just the factor by which distances are stretched by the expansion of the universe (so it increases with time). For instance, we can take a = 1 today, and at some time t in the past, when a = 1/2, ANY distance you consider (between any two objects at large distances from each other, like galaxies) was half as much back then as it is today. So, if two galaxies are separated by 100 Mpc today, at the time in the past when a was 1/2, they would have only been separated by 50 Mpc. There is also the redshift z = (observed wavelength - emitted wavelength)/(emitted wavelength). There is a relationship between a and z, namely a = 1/(1+z). I won't prove this here, but it is relatively straightforward.

Second, we can consider how the energy density (energy per unit volume) of photons decreases with time due to the expansion of the universe. Heuristic argument: consider a box of photons. As the box's volume increases, there are two effects: 1. the total number of photons remains fixed, but they are spread over a larger volume, so the photon density goes down inversely with the volume (V-1). Since volume is proportional to a3, this introduces an a-3 factor. 2. The wavelength of a photon is stretched out as the box expands, therefore it is proportional to a. As a result, the energy PER photon decreases as a-1, since quantum mechanics says a photon's energy is inversely proportional to its wavelength. So if the photon number density decreases as a-3 and the energy PER photon decreases as a-1, the end result is the energy density of the CMB radiation field decreases as a-4, which is (1+z)4. Another way to look at this: as you go into the past and z increases, the energy density of the CMB radiation increases roughly as the fourth power of z (or actually 1+z).

Third: another way to think about this is in terms of the CMB temperature. Right now the CMB corresponds to an almost perfect blackbody with a radiation temperature of T = 2.723 K. The relationship between the radiation temperature and the spectrum of a blackbody emitter is given by the Planck function: http://en.wikipedia.org/wiki/Planck's_law. If we could figure out how the CMB temperature will decline with time, that would tell us exactly how the CMB spectrum (intensity vs. wavelength) would vary (diminish) with time. It's fairly easy to do this given the information in my second point above, and one other factoid: for an isotropic radiation field (like the CMB) the energy density is proportional to the fourth power of the temperature. See here for details: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/raddens.html. What this means is that if the density varies as a-4, then the temperature (which is density to the 1/4 power) varies as a-1. In other words, the CMB radiation temperature varies inversely with scale factor, or linearly with redshift. At the time the CMB photons were first emitted, at a redshift of just over 1000, the CMB temperature would have been more than 1000 times what it is now (so around 3000 K). The CMB temperature will just continue to decline in this way as time goes on.

EDIT: Drakkith: no, not quite. A doubling of the scale factor would decrease the energy density of the radiation field by a factor of 16. See above.

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Staff Emeritus
EDIT: Drakkith: no, not quite. A doubling of the scale factor would decrease the energy density of the radiation field by a factor of 16. See above.

Ah, okay. Thanks.

Staff Emeritus
Homework Helper
And if so, at a rate faster or slower or the same compared to at earlier times of the universe?

Who can say? After all, measurements have only been made over the last 50 years or so. That's a less than microscopically small fraction of the age of the universe.

Hornbein
And if so, at a rate faster or slower or the same compared to at earlier times of the universe?

I would say that the total energy in the CMB is a constant. Its density is decreasing.

On a linear scale the density is decreasing more slowly now. On a logarithmic scale, I'm not sure, but would guess it is decreasing more rapidly due to the celebrated dark energy.

Staff Emeritus
I would say that the total energy in the CMB is a constant. Its density is decreasing.

I don't think that's correct. See post 5.

goldust
This thread really should be in the cosmology section. Would appreciate it if it gets moved there. Back to the topic. Methinks, assuming the universe does get bigger and bigger, the density of the universe and therefore the intensity of the cosmic microwave background radiation would decrease, sort of like the golden ratio spiral. In other words, in the first tiny fraction of a second, the intensity of CMBR dropped to 50% of its value at Big Bang, then after a second or so, it dropped to 25% of its value at Big Bang, and now is like 0.00000001% and dropping but it would it take another billion years for it to drop to 0.000000001% and then it would take a trillion years for it to drop to 0.0000000001% and then it would take a quadrillion years for it to drop to 0.00000000001% and so on and so forth. Might be an exaggeration, but methinks it goes something along those lines. That's why we won't be able to detect any drop in the intensity of the CMBR in our lifetimes. It is likely, over the next thousands of years, no matter how sensitive instruments can get, no decrease in the CMBR's intensity could ever be detected because it's decreasing so slowly now.

There's another thing I don't understand now. If the Big Bang occurred in one location, then why is there CMBR all around us? All the light from the Big Bang's location would have been be traveling away from that location in every direction, so why is every location in the universe getting hit by CMBR from every direction? Logic would state that any location in the universe can only be hit by CMBR from only 1 side, which must be the side aligned with the location of the Big Bang, because that is the only side from which radiation from the Big Bang can come from. Would appreciate it if someone can shed some light on this. Last edited:
There's another thing I don't understand now. If the Big Bang occurred in one location, then why is there CMBR all around us? All the light from the Big Bang's location would have been traveling away from that location, so why is every location in the universe getting hit by CMBR from every direction? Logic would state any location in the universe can only be hit by CMBR from only 1 side, which must be the side aligned with the location of the Big Bang. Would appreciate it if someone can shed some light on this. If you'll stick around the forums you'll see that it's a very common misconception.
To wit: the BB did not occur at some singular point. It "occured" everywhere at once, so there's always some CMBR passing us by from every direction.

goldust
If you'll stick around the forums you'll see that it's a very common misconception.
To wit: the BB did not occur at some singular point. It "occured" everywhere at once, so there's always some CMBR passing us by from every direction.

I think I get it now. It's because there was no space before the Big Bang, which means as space expanded, the CMBR is trapped in the expanding space and is therefore everywhere and hitting every location, sort of like water in a fish tank. Is this correct?

goldust
Would this analogy be correct? A very tall and very slender cup filled with water is like the universe before the Big Bang filled with CMBR. The Big Bang is like pouring all the water out of the cup and onto the floor. The water spreads out on the floor, just like the universe spreads out after the Big Bang. The height of the water from the cup decreases as the water spreads out on the floor, just like the CMBR's intensity decreases as the universe spreads out after the Big Bang.

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Staff Emeritus
I think I get it now. It's because there was no space before the Big Bang, which means as space expanded, the CMBR is trapped in the expanding space and is therefore everywhere and hitting every location, sort of like water in a fish tank. Is this correct?

Kind of, but imagine a fish tank of infinite size, or one that geometry allows to wrap around on itself.

Would this analogy be correct? A very tall and very slender cup filled with water is like the universe before the Big Bang filled with CMBR. The Big Bang is like pouring all the water out of the cup and onto the floor. The water spreads out on the floor, just like the universe spreads out after the Big Bang. The CMBR's intensity is like the how tall the water is. The intensity of the CMBR decreases as the universe spreads, just as the height of the water from the cup decreases as the water spreads out on the floor.

I don't really think this analogy works at all. The expansion of the universe is nothing like this.

Imagine the early universe about 300,000 years after the big bang. The density and temperature of the universe is still too high to allow charged particles to combine, and light cannot travel. The universe is "opaque", like very very thick mist. As the universe expands, this mist becomes thinner and thinner until suddenly about 380,000 years after the big bang it cools off enough for protons and electrons to combine. In a very short amount of time nearly all of the protons and electrons combine to form hydrogen, helium, and lithium, and the universe is now transparent. The mist is gone.

BUT, remember that we just had a hot gas everywhere. This hot gas was emitting radiation from every point in space. This radiation didn't just disappear. As soon as the universe became transparent it was able to travel from every point in space out towards every other point in space instead of being absorbed. So now you have light from every direction coming at you. The longer the universe goes on, the further this light has had to travel, and thanks to the continuing expansion it is redshifted more and more in addition to being spread out. So not only do you have less photons per volume of space, these photons also have less energy thanks to redshift. So it's like a double whammy to the energy density.