Chapter 17
Earlier Times and Radiation
Abstract The CMB at present is very cold and has a very low energy density;
however if we extrapolate back to earlier times, to a redshift of more than about
1000, we find that the temperature and energy density of the radiation was high
enough that it was critically important in the evolution and behavior of the universe
and its constituents. Indeed the atoms we observe today did not exist and a hot plasma
dominated the universe until a few hundred thousand years. In this chapter we will
study the scale factor and properties in the radiation era. The nearly perfect current
isotropy of the CMB presents a theoretical problem and has led to the idea of inflation,
wherein the universe underwent an extraordinary expansion in the very beginning.
Moreover the very small anisotropies of the current CMB constitute essentially a
photograph of the big bang which can give us a great deal of information about the
earliest times.
17.1 Radiation and Temperature in Earlier Times
In the preceding chapters we considered a universe containing vacuum energy and
matter at negligible pressure, as is well-justified for the present era. We only briefly
mentioned earlier times, before galaxies were formed, and when the universe was
hotter and radiation was important. Now we explicitly focus on such times with
emphasis on the relative importance of matter and radiation to see explicitly how
radiation becomes dominant.
Let us begin by considering the temperature and energy density of the cosmic
microwave background (CMB) that fills today’s universe, which we have already
discussed in Chap. 13. The present CMB temperature is about 2.725 K. We can easily
show that the temperature is inversely proportional to the scale factor. A well-known
result from statistical mechanics and thermodynamics is that the energy density of
black body radiation is proportional to the fourth power of its temperature, given by
the Stefan-Boltzmann relation as
ρ r = a rad T
4
, a rad = 5.6 × 10
−16 J/K
4 m
3
.
(17.1)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. J. Adler, General Relativity and Cosmology, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-61574-1_17
263
Earlier Times and Radiation
Abstract The CMB at present is very cold and has a very low energy density;
however if we extrapolate back to earlier times, to a redshift of more than about
1000, we find that the temperature and energy density of the radiation was high
enough that it was critically important in the evolution and behavior of the universe
and its constituents. Indeed the atoms we observe today did not exist and a hot plasma
dominated the universe until a few hundred thousand years. In this chapter we will
study the scale factor and properties in the radiation era. The nearly perfect current
isotropy of the CMB presents a theoretical problem and has led to the idea of inflation,
wherein the universe underwent an extraordinary expansion in the very beginning.
Moreover the very small anisotropies of the current CMB constitute essentially a
photograph of the big bang which can give us a great deal of information about the
earliest times.
17.1 Radiation and Temperature in Earlier Times
In the preceding chapters we considered a universe containing vacuum energy and
matter at negligible pressure, as is well-justified for the present era. We only briefly
mentioned earlier times, before galaxies were formed, and when the universe was
hotter and radiation was important. Now we explicitly focus on such times with
emphasis on the relative importance of matter and radiation to see explicitly how
radiation becomes dominant.
Let us begin by considering the temperature and energy density of the cosmic
microwave background (CMB) that fills today’s universe, which we have already
discussed in Chap. 13. The present CMB temperature is about 2.725 K. We can easily
show that the temperature is inversely proportional to the scale factor. A well-known
result from statistical mechanics and thermodynamics is that the energy density of
black body radiation is proportional to the fourth power of its temperature, given by
the Stefan-Boltzmann relation as
ρ r = a rad T
4
, a rad = 5.6 × 10
−16 J/K
4 m
3
.
(17.1)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. J. Adler, General Relativity and Cosmology, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-61574-1_17
263