Chapter 19
Inflation and Some Questions
Abstract Inflation involves an extremely rapid expansion of the universe, which
can be qualitatively described in terms of a de Sitter model universe. We will briefly
discuss the dominant current view of inflation, which is based on one (or several)
scalar fields that caused the early universe to expand exponentially much like a de
Sitter universe. Quantum fluctuations during the expansion may be used to explain
the subsequent structure we observe on the cosmological scale. Observational data on
the inflationary era however are sparse and many questions remain. Other questions
of note that we will briefly mention are the physical nature of dark matter and dark
energy, and the quantum properties of the universe in the earliest times.
19.1 Basic Ideas of Inflation
We saw in Sect. 17.3 that there is a puzzle as to how the universe could have been so
isotropic at the decoupling time. The cosmic background radiation is observed to be
isotropic to about 10
−5 over the whole sky, whereas the models we have discussed
predict that only a few degrees of the sky could have been causally connected and
thermalized at the time of the last scattering of the CMB. One might simply postulate
that the universe was initially very isotropic, but that is not a satisfying answer. One
favored approach to a solution is to appeal to a scenario called inflation, wherein
there is postulated to be a period of extremely rapid expansion before the radiation
era. This produces a horizon such that the entire observable universe was once in
causal contact and thus could have been thermalized (Freedman 2006; Peebles 1993;
Linde 2007; Liddle 2003).
At a conceptual level the solution to the horizon puzzle is quite simple. Instead
of the situation shown in Fig. 17.3 in which the coordinate distance σ 12 is small and
the angle θ is thus also small we ask instead that σ 12 be quite large so the coordinate
horizon distance is large enough to encompass our entire view of the big bang fireball.
This obviously means that the scale factor a must be such that the integral in (17.17)
for σ 12 is larger than the coordinate distance from the source to us in (17.18). It is
also obvious that there are many ways we could choose a so that this is true; indeed
it is easy to choose the scale factor a so the integral is divergent and σ 12 is infinite.
© 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_19
281
Inflation and Some Questions
Abstract Inflation involves an extremely rapid expansion of the universe, which
can be qualitatively described in terms of a de Sitter model universe. We will briefly
discuss the dominant current view of inflation, which is based on one (or several)
scalar fields that caused the early universe to expand exponentially much like a de
Sitter universe. Quantum fluctuations during the expansion may be used to explain
the subsequent structure we observe on the cosmological scale. Observational data on
the inflationary era however are sparse and many questions remain. Other questions
of note that we will briefly mention are the physical nature of dark matter and dark
energy, and the quantum properties of the universe in the earliest times.
19.1 Basic Ideas of Inflation
We saw in Sect. 17.3 that there is a puzzle as to how the universe could have been so
isotropic at the decoupling time. The cosmic background radiation is observed to be
isotropic to about 10
−5 over the whole sky, whereas the models we have discussed
predict that only a few degrees of the sky could have been causally connected and
thermalized at the time of the last scattering of the CMB. One might simply postulate
that the universe was initially very isotropic, but that is not a satisfying answer. One
favored approach to a solution is to appeal to a scenario called inflation, wherein
there is postulated to be a period of extremely rapid expansion before the radiation
era. This produces a horizon such that the entire observable universe was once in
causal contact and thus could have been thermalized (Freedman 2006; Peebles 1993;
Linde 2007; Liddle 2003).
At a conceptual level the solution to the horizon puzzle is quite simple. Instead
of the situation shown in Fig. 17.3 in which the coordinate distance σ 12 is small and
the angle θ is thus also small we ask instead that σ 12 be quite large so the coordinate
horizon distance is large enough to encompass our entire view of the big bang fireball.
This obviously means that the scale factor a must be such that the integral in (17.17)
for σ 12 is larger than the coordinate distance from the source to us in (17.18). It is
also obvious that there are many ways we could choose a so that this is true; indeed
it is easy to choose the scale factor a so the integral is divergent and σ 12 is infinite.
© 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_19
281