16.1 Diverse Cosmological Observations
249
very nearly that of an isothermal black body, but with small and very important
variations. The spectrum was first measured by the Cosmic Background Explorer
(COBE) satellite and found to fit the black body spectrum extremely well, to about
a part in 10
5 (Boggess 1992). That alone was very strong evidence for the big bang
paradigm. Since then the small variations in the spectrum have been accurately
measured by the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck
satellites and used as tests of theories of the present and early universe—and also
the very early universe (Bennet 2003; Planck 2018).
The detailed shape of the CMB spectrum depends on a small number of
cosmological parameters, such as the Hubble constant, as well as the constituents
and dynamics of the universe at about the time of emission. In particular the
position and spacing of some peaks in the spectrum can be understood in terms
of density oscillations or standing “acoustic” waves at the time of emission.
Combined with a theoretical calculation of the speed of sound in the material
this translates to information on the wavelength of such oscillations. Putting this
information together we can determine the values of the parameters by fitting the
theoretical CMB spectrum to the observed spectrum. (The fitting of the spectrum
can be done using openly available programs such as CMBFAST.) One important
result is that the Hubble constant may be accurately determined from the CMB
spectrum as we discussed in Appendix 1 in Chap. 13 (Planck 2018). See also
Sect. 17.4.
The dominant theories of the very early universe involve a very large and rapid
expansion of the universe called inflation, which ended when the radiation era
began. Processes during inflation also affect the CMB spectrum in interesting
ways. We will discuss the motivation for such theories in Chaps. 17 and 18, and
give a rough sketch of how they work in Chap. 19.
5. Gravitational waves from black hole and neutron star mergers: We discussed
in Chap. 11 the gravitational waves from binary black holes and neutron stars
spiraling in to merge. The inverse distance dependence of the amplitudes of such
waves can be used to estimate their distance from us. The frequency and the
change in the frequency over the course of the merger also provide additional
information as we discussed in Sects. 11.5 and 11.6. As the binaries radiate energy
the orbit decays and the frequency increases in a predictable way, that is a chirp,
that depends on the binary masses, so the systems thus act as “standard sirens,”
analogous to the standard candles used for traditional distance measurements.
The amplitude and the dependence of frequency on time allow us to measure the
Hubble constant independently of any other measurements (Schutz 1986; Holz
2018).
Such measurements of the Hubble constant using the binary neutron star
merger GW170817 give a value that is consistent with those obtained in other
ways, in particular those using the distance ladder method discussed above
(Abbott 2019; Abbott 2017; Fischbach 2018). This was discussed in Appendix
1 in Chap. 13. The accuracy of such measurements at present is not comparable
to distance ladder and CMB methods, but is expected to increase as more events
are detected.
249
very nearly that of an isothermal black body, but with small and very important
variations. The spectrum was first measured by the Cosmic Background Explorer
(COBE) satellite and found to fit the black body spectrum extremely well, to about
a part in 10
5 (Boggess 1992). That alone was very strong evidence for the big bang
paradigm. Since then the small variations in the spectrum have been accurately
measured by the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck
satellites and used as tests of theories of the present and early universe—and also
the very early universe (Bennet 2003; Planck 2018).
The detailed shape of the CMB spectrum depends on a small number of
cosmological parameters, such as the Hubble constant, as well as the constituents
and dynamics of the universe at about the time of emission. In particular the
position and spacing of some peaks in the spectrum can be understood in terms
of density oscillations or standing “acoustic” waves at the time of emission.
Combined with a theoretical calculation of the speed of sound in the material
this translates to information on the wavelength of such oscillations. Putting this
information together we can determine the values of the parameters by fitting the
theoretical CMB spectrum to the observed spectrum. (The fitting of the spectrum
can be done using openly available programs such as CMBFAST.) One important
result is that the Hubble constant may be accurately determined from the CMB
spectrum as we discussed in Appendix 1 in Chap. 13 (Planck 2018). See also
Sect. 17.4.
The dominant theories of the very early universe involve a very large and rapid
expansion of the universe called inflation, which ended when the radiation era
began. Processes during inflation also affect the CMB spectrum in interesting
ways. We will discuss the motivation for such theories in Chaps. 17 and 18, and
give a rough sketch of how they work in Chap. 19.
5. Gravitational waves from black hole and neutron star mergers: We discussed
in Chap. 11 the gravitational waves from binary black holes and neutron stars
spiraling in to merge. The inverse distance dependence of the amplitudes of such
waves can be used to estimate their distance from us. The frequency and the
change in the frequency over the course of the merger also provide additional
information as we discussed in Sects. 11.5 and 11.6. As the binaries radiate energy
the orbit decays and the frequency increases in a predictable way, that is a chirp,
that depends on the binary masses, so the systems thus act as “standard sirens,”
analogous to the standard candles used for traditional distance measurements.
The amplitude and the dependence of frequency on time allow us to measure the
Hubble constant independently of any other measurements (Schutz 1986; Holz
2018).
Such measurements of the Hubble constant using the binary neutron star
merger GW170817 give a value that is consistent with those obtained in other
ways, in particular those using the distance ladder method discussed above
(Abbott 2019; Abbott 2017; Fischbach 2018). This was discussed in Appendix
1 in Chap. 13. The accuracy of such measurements at present is not comparable
to distance ladder and CMB methods, but is expected to increase as more events
are detected.