248
16 Some Properties of the LCDM Universe
We have already discussed the measured values of the Hubble constant in
Appendix 1 in Chap. 13. In short summary the primary measurements involve a
“distance ladder," in which the distance to relatively nearby objects, in particular
Cepheid variable stars, is measured using parallax; the Cepheids then provide a
standard candle for larger distances since their periodicity is related to their
brightness in a known way; finally the Cepheids in distant galaxies allow a
determination of the distance to supernovas and the supernovas in turn serve
as standard candles for greater distances (Weinberg 1972; Ohanian 1994).
The objects first studied by Hubble and other early workers were galaxies,
but supernovas and red giant stars have allowed much larger distances to be
measured. This has allowed researches to determine the age of the universe and
to discover the acceleration of the universe that implies the existence of dark
energy. We will say more about these concepts later in this chapter.
2. Velocity measurements of galaxies in clusters and of stars in outer portions of
galaxies: We discussed this type of measurement briefly in Sect. 14.3. The earliest
evidence for dark matter was in the random velocities of galaxies in galactic
clusters. Such velocities are directly related to the gravitational potential in their
region; already in the 1930s Zwicky realized that there must be much more matter
in many such clusters than was indicated from the luminous matter (Zwicky
1933). Several decades later Rubin used measurements of the velocities of stars
in the outer regions of individual galaxies to reach a similar conclusion (Rubin
1995). Since galactic clusters are so much larger than galaxies such measurements
on both scales are very important; they are probably the simplest evidence for
the existence and universality of dark matter.
3. Gravitational lensing by dark matter: In Chap. 10 we discussed the bending of
light in a gravitational field. In fact density distributions of matter can be analyzed
by detecting the light that passes by them or through them, much as the shape of
a magnifying glass can be determined by the way it focuses light. Einstein was
the first to point out the existence of such lensing; he thought in terms of lensing
by stellar size objects, whereas gravitational lensing as currently used makes use
of light lensed by galaxy size distributions of matter, and in particular the dark
matter that we mentioned in Chap. 14 (Schneider 1992).
Another application of gravitational lensing is in measuring cosmological
distances and parameters, called cosmography. Consider a source galaxy whose
light passes by and is deflected by a galaxy that is closer to us. In general we
will see several images of the source galaxy, and the angles between the images
will give us information on the distances involved (Narayan 1997; Schneider
1992). If the light from the source galaxy varies we will see those variations at
different times. The combination of the angles between the images and the time
delay of the variations can give us information on the distance to the source and
cosmological parameters, in particular the Hubble constant (Chen 2019).
4. Spectrum of the cosmic microwave background: We have already mentioned the
CMB in Chap. 13; it is interpreted as the dim afterglow of the radiation fireball of
the early universe. In the next chapter we will discuss how the temperature and
spectrum of the fireball and its present afterglow are determined; the spectrum is
16 Some Properties of the LCDM Universe
We have already discussed the measured values of the Hubble constant in
Appendix 1 in Chap. 13. In short summary the primary measurements involve a
“distance ladder," in which the distance to relatively nearby objects, in particular
Cepheid variable stars, is measured using parallax; the Cepheids then provide a
standard candle for larger distances since their periodicity is related to their
brightness in a known way; finally the Cepheids in distant galaxies allow a
determination of the distance to supernovas and the supernovas in turn serve
as standard candles for greater distances (Weinberg 1972; Ohanian 1994).
The objects first studied by Hubble and other early workers were galaxies,
but supernovas and red giant stars have allowed much larger distances to be
measured. This has allowed researches to determine the age of the universe and
to discover the acceleration of the universe that implies the existence of dark
energy. We will say more about these concepts later in this chapter.
2. Velocity measurements of galaxies in clusters and of stars in outer portions of
galaxies: We discussed this type of measurement briefly in Sect. 14.3. The earliest
evidence for dark matter was in the random velocities of galaxies in galactic
clusters. Such velocities are directly related to the gravitational potential in their
region; already in the 1930s Zwicky realized that there must be much more matter
in many such clusters than was indicated from the luminous matter (Zwicky
1933). Several decades later Rubin used measurements of the velocities of stars
in the outer regions of individual galaxies to reach a similar conclusion (Rubin
1995). Since galactic clusters are so much larger than galaxies such measurements
on both scales are very important; they are probably the simplest evidence for
the existence and universality of dark matter.
3. Gravitational lensing by dark matter: In Chap. 10 we discussed the bending of
light in a gravitational field. In fact density distributions of matter can be analyzed
by detecting the light that passes by them or through them, much as the shape of
a magnifying glass can be determined by the way it focuses light. Einstein was
the first to point out the existence of such lensing; he thought in terms of lensing
by stellar size objects, whereas gravitational lensing as currently used makes use
of light lensed by galaxy size distributions of matter, and in particular the dark
matter that we mentioned in Chap. 14 (Schneider 1992).
Another application of gravitational lensing is in measuring cosmological
distances and parameters, called cosmography. Consider a source galaxy whose
light passes by and is deflected by a galaxy that is closer to us. In general we
will see several images of the source galaxy, and the angles between the images
will give us information on the distances involved (Narayan 1997; Schneider
1992). If the light from the source galaxy varies we will see those variations at
different times. The combination of the angles between the images and the time
delay of the variations can give us information on the distance to the source and
cosmological parameters, in particular the Hubble constant (Chen 2019).
4. Spectrum of the cosmic microwave background: We have already mentioned the
CMB in Chap. 13; it is interpreted as the dim afterglow of the radiation fireball of
the early universe. In the next chapter we will discuss how the temperature and
spectrum of the fireball and its present afterglow are determined; the spectrum is