Chapter 13
Cosmological Preliminaries
Abstract Observations of the universe on the largest scale of billions of light years
indicate that it is expanding, is filled with cosmic microwave background (CMB)
radiation, and is approximately homogeneous. These facts motivate the choice
of an appropriate form of metric called the FLRW metric (Friedmann, Lemaitre,
Robertson, and Walker), which we will derive in this chapter. The FLRW metric
contains a fundamental function describing the expansion of the universe, called the
scale factor. The FLRW metric leads to an elegant description of some physical properties of the expanding universe, such as cosmic horizons. One particular example of
an FLRW metric is that of de Sitter, which is mainly of theoretical and mathematical
interest.
13.1 Basic Observations and Assumptions
We begin our study of cosmology with three basic observational facts related to the
observed universe on a very large scale. By that we mean a scale of billions of light
years, whereas the distance between galaxies is only some millions or tens of millions
of light years.
A. The Universe is expanding. Distant galaxies are observed to have spectra which
are Doppler shifted to the red, indicating that they are receding from us. This
was first discovered by Hubble in 1929, and has been quite well confirmed since
then (Hubble 1929). The velocity of recession v of relatively nearby galaxies is
observed to be approximately proportional to their distance L from us, which is
known as Hubble’s law.
v = H 0 L , Hubble’s law,
H 0 = 70 ± 5(km/s)/Mpc Hubble’s constant−our error estimate. (13.1)
The original rough data on which this relation is based is shown in Fig. 13.1; it
has been superseded by much more accurate data, so Fig. 13.1 is only of historical
© 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_13
203
Cosmological Preliminaries
Abstract Observations of the universe on the largest scale of billions of light years
indicate that it is expanding, is filled with cosmic microwave background (CMB)
radiation, and is approximately homogeneous. These facts motivate the choice
of an appropriate form of metric called the FLRW metric (Friedmann, Lemaitre,
Robertson, and Walker), which we will derive in this chapter. The FLRW metric
contains a fundamental function describing the expansion of the universe, called the
scale factor. The FLRW metric leads to an elegant description of some physical properties of the expanding universe, such as cosmic horizons. One particular example of
an FLRW metric is that of de Sitter, which is mainly of theoretical and mathematical
interest.
13.1 Basic Observations and Assumptions
We begin our study of cosmology with three basic observational facts related to the
observed universe on a very large scale. By that we mean a scale of billions of light
years, whereas the distance between galaxies is only some millions or tens of millions
of light years.
A. The Universe is expanding. Distant galaxies are observed to have spectra which
are Doppler shifted to the red, indicating that they are receding from us. This
was first discovered by Hubble in 1929, and has been quite well confirmed since
then (Hubble 1929). The velocity of recession v of relatively nearby galaxies is
observed to be approximately proportional to their distance L from us, which is
known as Hubble’s law.
v = H 0 L , Hubble’s law,
H 0 = 70 ± 5(km/s)/Mpc Hubble’s constant−our error estimate. (13.1)
The original rough data on which this relation is based is shown in Fig. 13.1; it
has been superseded by much more accurate data, so Fig. 13.1 is only of historical
© 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_13
203