How do we know how hot the big bang was from the CMB?

[wolram]

How do we know how hot the big bang was, is there some way to extrapolate back from the
CMB, if there is i would like to know how such accuracy was achieved.

Thanks.

 

[bcrowell]

In classical models based on GR, the temperature approaches infinity as as you approach the singularity.

At temperatures comparable to the Planck temperature, we don't expect GR to work well. We need a theory of quantum gravity instead. Since we don't have a working theory of quantum gravity, we can't say much about the temperature at times earlier than the time at which the temperature was the Planck temperature.

 

[Chalnoth]

In classical models based on GR, the temperature approaches infinity as as you approach the singularity.

At temperatures comparable to the Planck temperature, we don't expect GR to work well. We need a theory of quantum gravity instead. Since we don't have a working theory of quantum gravity, we can't say much about the temperature at times earlier than the time at which the temperature was the Planck temperature.

I think most expect that the big bang theory no longer describes our universe at rather lower temperatures than the Planck temperature, however. The Planck temperature is just where we are sure the big bang theory is no longer valid.

The hottest temperature our universe achieved was most likely the temperature at the end of reheating after inflation ended. That temperature, then, would be due to the energy density of the field which drive inflation being converted into thermal energy. This initial thermal energy might be thought of as the temperature of the big bang.

Unfortunately, we don't yet know the details of the field which drove inflation, so we can't be quite sure what that temperature was. I believe it had to be below the GUT temperature, however, or else our universe would be nearly all magnetic monopoles.

 

[wolram]

Thanks bcrowell, Chalnoth, that's given me something to think about.

 

[clamtrox]

The temperature after inflation ended had to be below the GUT scale, which is something of the order of 10²⁹ Kelvin.

 

[jimgraber]

The temperature after inflation ended had to be below the GUT scale, which is something of the order of 10²⁹ Kelvin.

The real hard question is "What was the temperature at the start of inflation?".

I vaguely remember reading that the temperature was higher by about e^65 times.*
Obviously, this is ridiculously hot, but not infinitely hot.

*At least the expansion is sometimes quoted as approximately 65 e-folds.

Jim Graber

 

[Chalnoth]

The real hard question is "What was the temperature at the start of inflation?".

I vaguely remember reading that the temperature was higher by about e^65 times.*
Obviously, this is ridiculously hot, but not infinitely hot.

*At least the expansion is sometimes quoted as approximately 65 e-folds.

Jim Graber

Well, it's not really possible for the temperature at the start of inflation to be all that high, as you still need the inflaton to dominate the energy density to have inflation at all. Before reheating, the temperature was zero for all intents and purposes.

 

[clamtrox]

The real hard question is "What was the temperature at the start of inflation?".

I vaguely remember reading that the temperature was higher by about e^65 times.*
Obviously, this is ridiculously hot, but not infinitely hot.

*At least the expansion is sometimes quoted as approximately 65 e-folds.

Jim Graber

Inflation indeed cools the universe by a factor of e^60 or so... That's OK though. What happens when inflation ends is that the field responsible for inflation decays into hot radiation and reheats the universe.

As for before inflation, well, that doesn't really matter at all. There doesn't even need to be any particles (and thus no temperature).

 

[bcrowell]

Unfortunately, we don't yet know the details of the field which drove inflation, so we can't be quite sure what that temperature was. I believe it had to be below the GUT temperature, however, or else our universe would be nearly all magnetic monopoles.

You seem to be assuming that inflation occurred (for which there is some evidence, but nothing definitive) and that GUTs are valid (for which there is no empirical evidence). There's a nice quote by Martin Rees about this issue: "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!"

If you're trying to claim that inflation removes the big bang singularity in temperature, then you're incorrect. Here is a paper on that topic: Arvind Borde, Alan H. Guth, and Alexander Vilenkin, Inflationary spacetimes are not past-complete, http://arxiv.org/abs/gr-qc/0110012

 

[Chalnoth]

If you're trying to claim that inflation removes the big bang singularity in temperature, then you're incorrect.

Right. Minimal inflation (General Relativity + effective field theory) still has a singularity in the math. But I don't think anybody believes there actually was such a singularity. I wasn't claiming that the model of inflation avoids the singularity, but rather that the singularity unlikely to have actually occurred.