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If the universe was at so much heat at the singularity point at big bang , Then the light of CMB must be gamma rays (high energy photons) but how did they transfer into microwaves?

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The very early universe was unimaginably hot. But we don't get any signal from this period of time because it was also opaque.

The early universe was full of plasma - the form of matter which is so hot that electrons are free from their nuclei. Plasma is normally opaque. When the universe cooled to a temperature about 3000 Kelvin, it was cool enough for electrically neutral atoms to form, and this gas is transparent. That was 300000-400000 years after the big bang. So the background light was emitted as blackbody radiation of about 3000K - which would appear "orange" (but actually contains a mixture of yellow, red and infrared wavelengths).

We don't see the background radiation as orange, because redshift has stretched the wavelength of the light by a factor of over 1000, shifting it from visible to microwave radiation and giving an apparent temperature of 2.7K

So two factors. One it was never gamma rays from a point in time soon after the big bang, but orange light from the time when atoms first formed. Secondly redshift makes distant things appear cooler.

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    $\begingroup$ Thank you for the answer ! $\endgroup$
    – Naveen V
    Feb 13, 2023 at 9:23
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    $\begingroup$ I don't think the opaqueness of the Universe is really the issue, only the expansion/cooling, for the following reason: Even if hydrogen had never recombined, radiation would keep redshifting, both in the early and the late Universe. At $t\sim1$ s, photons were in the gamma-ray regime, later they were X-ray, UV, and so on. Today, they would be microwaves whether or not they were "primordial", or emitted by recombining hydrogen later on. Today the Universe is indeed reionized, but has expanded so much that the mean free path of photons is larger than the size of the observable Universe. $\endgroup$
    – pela
    Feb 13, 2023 at 12:25
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    $\begingroup$ @pela Not sure (exactly) about that. You need $T \propto a^{-1}$ but that isn't the case for a matter-dominated universe. That means between the epoch of matter-domination and the epoch of recombination, the universe doesn't have a temperature that falls as $a^{-1}$. I think this means that the exact temperature of the CMB does depend on when the radiation decoupled (if it decouples after matter density dominates). Perhaps the epochs are close enough together that it doesn't change a broad "the CMB would be microwaves" statement though. $\endgroup$
    – ProfRob
    Feb 13, 2023 at 20:15
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    $\begingroup$ @ProfRob I don't quite understand: $T$ should always follow $a^{-1}$, no matter how $a$ evolves, no? Although $a$ itself evolves with time $t$ on different ways, depending on which ingredient dominates the density, so $T$ also evolves similarly differently with time. $\endgroup$
    – pela
    Feb 14, 2023 at 11:42
  • $\begingroup$ @pela How did you derive $T \propto a^{-1}$ in a matter-dominated universe? The usual derivation would assume that the energy density scales as $T^4$, which wouldn't be true. Pretty sure that non-relativistic particles cool as $T \propto a^{-2}$. arxiv.org/pdf/physics/0603087.pdf $\endgroup$
    – ProfRob
    Feb 14, 2023 at 12:59
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You forget that the universe cools as it expands - as do all gases if there is no further heat input.

At first, the cooling gas and the radiation it emits are in equilibrium with each other, at the same temperature. Gamma ray photons are both emitted and absorbed in equal numbers.

Gradually, as temperatures lower, the wavelengths of the emitted radiation gets bigger; X-rays, then UV, then visible light predominate. But there comes a point at which the universe is much less dense, hydrogen atoms have formed and the universe becomes transparent to its own radiation. Emitted light is then no longer absorbed and this light forms the cosmic background radiation.

This transparency happens about 400,000 years after the Big Bang, when the universe has cooled to 3000 K (or about 2700 $^{\circ}$C). The cosmic background is then in the form of red and infrared photons.

The "stretching" to microwave wavelengths occurs after that and is the same redshifting effect we see from distant objects in the universe. In this case, the cosmic background photons we observe on Earth have travelled for 13.7 billion years at the speed of light and in the meantime their wavelengths have been redshifted or stretched by a factor of 1100.

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    $\begingroup$ Thank you very much for this explaination ! $\endgroup$
    – Naveen V
    Feb 13, 2023 at 9:22
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The cosmic microwave background radiation was emitted 300 to 400 thousand years after the big bang. At the time, the radiation was primarily in the near infrared range, what a blackbody at about 3000 kelvins would radiate. (That's about where a red giant or red dwarf radiates.) The expansion of space has made the frequency shift from the near infrared to microwave frequencies.

The universe was opaque before that time. Any thermally induced electromagnetic radiation that was omitted by something would very quickly have been absorbed by something else. The cosmic microwave background radiation resulted when the universe cooled to the point where it became clear to thermal radiation. Scientists have to infer what happened prior to that based on theory and observations of the cosmic microwave background radiation.

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    $\begingroup$ thank you so much ! $\endgroup$
    – Naveen V
    Feb 13, 2023 at 9:22

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