272
17 Earlier Times and Radiation
ℓ
Fig. 17.5 A sketch of the CMB power spectrum obtained from an LCDM model
Calculation of the C power spectrum from theory is an interesting but formidable
task; it requires consideration of the physics of the materials in the universe during the
radiation era, which includes such things as photon electron interactions, the type
and density of neutrinos, etc. It also requires analysis of physics before and after
the radiation era. Most important it requires an understanding of the wavelength of
density fluctuations due to standing sound waves, called baryon acoustic oscillations
or BAOs (Knox 2019). We will give a brief conceptual discussion of some of these
issues in Chap. 19.
Because of the complexity of the problem the calculation of the CMB spectrum
is usually done using openly accessible computer programs that turn cosmological models into spectra quite rapidly; one useful reference is Tegmark (2019). An
illustrative example of such a theoretical spectrum is shown in Fig. 17.5.
One important aspect of comparing theory and CMB observation is to ascribe
specific features of the spectrum to various physical causes. The spacing of the
prominent peaks in Fig. 17.5 is particularly interesting; it allows us to measure
distances around the time of emission of the CMB, and from that estimate the Hubble
constant. We can see intuitively how this can be done: the peaks are due to standing
sound waves, the BAOs, at and before the time of emission; the waves correspond to
regions of high and low density. Combined with a theoretical understanding of the
speed of sound at that time this provides a distance scale, and that distance scale acts
as a meter stick in the sky (Knox 2019).
Thus, as we mentioned previously in Sect. 16.1 and Appendix 1 in Chap. 13 the
comparison of theory with the observed CMB spectrum provides a measurement of
important cosmological parameters. Indeed it is fair to say that the study of the CMB
spectrum is now one of the most important tools in early universe cosmology (NASA
2019).
Exercises
17.1 Why is the temperature 0.26 eV at which hydrogen atoms in the early universe
were largely ionized considerably less than the binding energy 13.6 eV? Give
a rough qualitative answer. It is possible to estimate the temperature accurately
as in Liddle (2003) and Peebles (1993).
17 Earlier Times and Radiation
ℓ
Fig. 17.5 A sketch of the CMB power spectrum obtained from an LCDM model
Calculation of the C power spectrum from theory is an interesting but formidable
task; it requires consideration of the physics of the materials in the universe during the
radiation era, which includes such things as photon electron interactions, the type
and density of neutrinos, etc. It also requires analysis of physics before and after
the radiation era. Most important it requires an understanding of the wavelength of
density fluctuations due to standing sound waves, called baryon acoustic oscillations
or BAOs (Knox 2019). We will give a brief conceptual discussion of some of these
issues in Chap. 19.
Because of the complexity of the problem the calculation of the CMB spectrum
is usually done using openly accessible computer programs that turn cosmological models into spectra quite rapidly; one useful reference is Tegmark (2019). An
illustrative example of such a theoretical spectrum is shown in Fig. 17.5.
One important aspect of comparing theory and CMB observation is to ascribe
specific features of the spectrum to various physical causes. The spacing of the
prominent peaks in Fig. 17.5 is particularly interesting; it allows us to measure
distances around the time of emission of the CMB, and from that estimate the Hubble
constant. We can see intuitively how this can be done: the peaks are due to standing
sound waves, the BAOs, at and before the time of emission; the waves correspond to
regions of high and low density. Combined with a theoretical understanding of the
speed of sound at that time this provides a distance scale, and that distance scale acts
as a meter stick in the sky (Knox 2019).
Thus, as we mentioned previously in Sect. 16.1 and Appendix 1 in Chap. 13 the
comparison of theory with the observed CMB spectrum provides a measurement of
important cosmological parameters. Indeed it is fair to say that the study of the CMB
spectrum is now one of the most important tools in early universe cosmology (NASA
2019).
Exercises
17.1 Why is the temperature 0.26 eV at which hydrogen atoms in the early universe
were largely ionized considerably less than the binding energy 13.6 eV? Give
a rough qualitative answer. It is possible to estimate the temperature accurately
as in Liddle (2003) and Peebles (1993).