206
13 Cosmological Preliminaries
above, but the error bars of the separate techniques do not overlap, so the agreement
is not good enough to satisfy many cosmologists (Reiss 2019; Planck 2018). Some
cosmologists refer to the situation as a “tension” rather than an outright disagreement
(Crane 2019; Freedman 2019). Appendix 1 has more information on estimates for
the Hubble constant and its uncertainty. Because of the tension we will here use
only the rough conservative estimate H 0 = 70 ± 5 (km/s)/Mpc for our pedagogical
purposes.
Finally we note that the Hubble constant can also be determined a number of other
ways. One example is to use gravitational lensing to determine distances (Schutz
2009; Chen 2019); another is to use gravitational wave data to determine both distance
and velocity of black hole and neutron star sources, which we alluded to in Chap. 11
(Holz 2018). See Appendix 1 for more information on such measurements (Schutz
1986; Holz 2005).
C. The distribution of visible matter on the largest scale is approximately homogeneous and isotropic. On a cosmological scale the distribution of clusters of
galaxies, the most visible matter of the universe, appears to be homogeneous and
isotropic—that is approximately the same in all directions and uniform in space.
On a smaller scale there is of course an obvious hierarchy of clustering—stars
cluster into galaxies, galaxies form clusters, and so forth. On an intermediate
scale, that is large compared to galaxies and small compared to the cosmological scale, the universe has sheets and filaments of galaxies with large voids
between them. It has been compared to a foam of liquid, for example the head
of foam on a glass of beer.
For our theoretical study we use three fundamental assumptions, which are largely
based on the above observations. Like all theoretical assumptions they should not be
treated as absolute, but subject to further experiments and observations.
1. Gravity, as described by general relativity, dominates the universe. No other
forces appear to be relevant on a cosmological scale. For example electric and
magnetic fields are important on a stellar scale and for clusters of stars, but become
less important on a galactic and cosmological scale. Thus the gravitational field
equations of general relativity are assumed to describe the universe.
2. The cosmological material can be treated as a perfect cosmic fluid. The many
billions of galaxies that now make up the visible universe behave as a lowpressure perfect fluid. For earlier times the universe was undoubtedly dominated
by radiation and hot gases, which also behaved as a perfect fluid with high
pressure. The invisible dark matter that appears to be a fundamental component
of the present universe apparently also behaves like a low-pressure perfect fluid.
Finally the dark energy behaves like a perfect fluid with pressure equal to the
negative of the constant energy density. For the very earliest times assumptions
about the nature of the cosmic fluid vary widely, as we will later discuss.
3. On the cosmological scale the geometry of the universe is approximately homogeneous and isotropic. Because of the isotropy and homogeneity of the visible
galaxies and the observed isotropy of the black body radiation we assume that the
13 Cosmological Preliminaries
above, but the error bars of the separate techniques do not overlap, so the agreement
is not good enough to satisfy many cosmologists (Reiss 2019; Planck 2018). Some
cosmologists refer to the situation as a “tension” rather than an outright disagreement
(Crane 2019; Freedman 2019). Appendix 1 has more information on estimates for
the Hubble constant and its uncertainty. Because of the tension we will here use
only the rough conservative estimate H 0 = 70 ± 5 (km/s)/Mpc for our pedagogical
purposes.
Finally we note that the Hubble constant can also be determined a number of other
ways. One example is to use gravitational lensing to determine distances (Schutz
2009; Chen 2019); another is to use gravitational wave data to determine both distance
and velocity of black hole and neutron star sources, which we alluded to in Chap. 11
(Holz 2018). See Appendix 1 for more information on such measurements (Schutz
1986; Holz 2005).
C. The distribution of visible matter on the largest scale is approximately homogeneous and isotropic. On a cosmological scale the distribution of clusters of
galaxies, the most visible matter of the universe, appears to be homogeneous and
isotropic—that is approximately the same in all directions and uniform in space.
On a smaller scale there is of course an obvious hierarchy of clustering—stars
cluster into galaxies, galaxies form clusters, and so forth. On an intermediate
scale, that is large compared to galaxies and small compared to the cosmological scale, the universe has sheets and filaments of galaxies with large voids
between them. It has been compared to a foam of liquid, for example the head
of foam on a glass of beer.
For our theoretical study we use three fundamental assumptions, which are largely
based on the above observations. Like all theoretical assumptions they should not be
treated as absolute, but subject to further experiments and observations.
1. Gravity, as described by general relativity, dominates the universe. No other
forces appear to be relevant on a cosmological scale. For example electric and
magnetic fields are important on a stellar scale and for clusters of stars, but become
less important on a galactic and cosmological scale. Thus the gravitational field
equations of general relativity are assumed to describe the universe.
2. The cosmological material can be treated as a perfect cosmic fluid. The many
billions of galaxies that now make up the visible universe behave as a lowpressure perfect fluid. For earlier times the universe was undoubtedly dominated
by radiation and hot gases, which also behaved as a perfect fluid with high
pressure. The invisible dark matter that appears to be a fundamental component
of the present universe apparently also behaves like a low-pressure perfect fluid.
Finally the dark energy behaves like a perfect fluid with pressure equal to the
negative of the constant energy density. For the very earliest times assumptions
about the nature of the cosmic fluid vary widely, as we will later discuss.
3. On the cosmological scale the geometry of the universe is approximately homogeneous and isotropic. Because of the isotropy and homogeneity of the visible
galaxies and the observed isotropy of the black body radiation we assume that the