17.1 Radiation and Temperature in Earlier Times
265
It is important to trace the evolution of the CMB spectrum during the expansion
of the universe and verify that it does not change, that is (17.3) remains correct. To
do this we consider the scaling of the various quantities in the Planck distribution
as the scale factor expands to its present value of a 0 . The behavior of the physical
volume is simple, as we have already mentioned in Chap. 16; as we look back in
time the volume changes according to
V → V 0 =
a 0
a
3
V.
(17.4)
We also already know from Chap. 13 that the wavelength of a photon changes in
proportional to the scale factor, and the frequency thus scales inversely proportional
to the scale factor, so
λ → λ 0 =
a 0
a
λ, and ν → ν 0 =
a
a 0
ν.
(17.5)
From (17.2) the temperature scales as
T → T 0 =
a
a 0
T.
(17.6)
From the scaling relations (17.4)–(17.6) it is thus clear the Planck distribution does
not change during expansion; that is
dN → dN 0 =
8πν
2
0 dν 0
c 3 (e hν 0 /kT 0 − 1)
V 0 =
8πν
2 dν
c 3 (e hν/kT − 1)
V = dN .
(17.7)
Equivalently, we can say the scaling relations (17.4)–(17.7) are consistent.
There is now little doubt that the general picture of the CMB radiation being the
remnants of the primordial big bang fireball is correct, due to its consistency and
the excellent agreement with the black body spectrum. The general standard model
scenario of the evolution of the universe during the LCDM era is also very likely
to be correct; but we can also go much further back in time, into the radiation era,
when the universe was filled with and dominated by radiation and hot plasma, quite
near to time zero. Indeed our standard model of high energy particle physics allows
us to understand with excellent confidence what happened as early at a second or so,
and beyond that to about a microsecond with rather good confidence. These were
the times when all the ordinary material of the present universe came into being,
so this is an impressive claim. One of the reasons for such confidence is that some
properties of the particles in the universe become simpler early in the radiation era
due to the high temperature. For example, the hot quark gluon plasma prevalent at
about a microsecond is probably well described as an ideal gas, since quarks and
265
It is important to trace the evolution of the CMB spectrum during the expansion
of the universe and verify that it does not change, that is (17.3) remains correct. To
do this we consider the scaling of the various quantities in the Planck distribution
as the scale factor expands to its present value of a 0 . The behavior of the physical
volume is simple, as we have already mentioned in Chap. 16; as we look back in
time the volume changes according to
V → V 0 =
a 0
a
3
V.
(17.4)
We also already know from Chap. 13 that the wavelength of a photon changes in
proportional to the scale factor, and the frequency thus scales inversely proportional
to the scale factor, so
λ → λ 0 =
a 0
a
λ, and ν → ν 0 =
a
a 0
ν.
(17.5)
From (17.2) the temperature scales as
T → T 0 =
a
a 0
T.
(17.6)
From the scaling relations (17.4)–(17.6) it is thus clear the Planck distribution does
not change during expansion; that is
dN → dN 0 =
8πν
2
0 dν 0
c 3 (e hν 0 /kT 0 − 1)
V 0 =
8πν
2 dν
c 3 (e hν/kT − 1)
V = dN .
(17.7)
Equivalently, we can say the scaling relations (17.4)–(17.7) are consistent.
There is now little doubt that the general picture of the CMB radiation being the
remnants of the primordial big bang fireball is correct, due to its consistency and
the excellent agreement with the black body spectrum. The general standard model
scenario of the evolution of the universe during the LCDM era is also very likely
to be correct; but we can also go much further back in time, into the radiation era,
when the universe was filled with and dominated by radiation and hot plasma, quite
near to time zero. Indeed our standard model of high energy particle physics allows
us to understand with excellent confidence what happened as early at a second or so,
and beyond that to about a microsecond with rather good confidence. These were
the times when all the ordinary material of the present universe came into being,
so this is an impressive claim. One of the reasons for such confidence is that some
properties of the particles in the universe become simpler early in the radiation era
due to the high temperature. For example, the hot quark gluon plasma prevalent at
about a microsecond is probably well described as an ideal gas, since quarks and