Inflationary Cosmology: Progress and Problems

TL;DR

This work surveys inflationary cosmology as a framework that resolves key problems of standard cosmology by enabling a causal generation of structure during a period of accelerated expansion. It highlights two major advances: (i) a refined reheating paradigm, including parametric resonance and preheating, and (ii) a quantum-mechanical treatment of cosmological perturbations yielding a nearly scale-invariant spectrum consistent with COBE. The analysis also identifies principal challenges—fluctuation amplitudes, Planck-scale sensitivity, singularities, and the cosmological constant problem—and surveys promising directions such as condensate-driven inflation, nonsingular higher-derivative gravity, and perturbation back-reaction. Collectively, the discussion emphasizes that while inflation elegantly links fundamental physics to observations, a canonical, testable theory remains elusive, guiding future work toward models that address these core issues.

Abstract

These lecture notes intend to form a short pedagogical introduction to inflationary cosmology, highlighting selected areas of recent progress such as reheating and the theory of cosmological perturbations. Problems of principle for inflationary cosmology are pointed out, and some new attempts at solving them are indicated, including a nonsingular Universe construction by means of higher derivative terms in the gravitational action, and the study of back-reaction of cosmological perturbations.

Figures (8)

• Figure 1: A space-time diagram (physical distance $x_p$ versus time $t$) illustrating the homogeneity problem: the past light cone $\ell_p (t)$ at the time $t_{rec}$ of last scattering is much larger than the forward light cone $\ell_f (t)$ at $t_{rec}$.
• Figure 2: A sketch (conformal separation vs. time) of the formation of structure problem: the comoving separation $d_c$ between two clusters is larger than the forward light cone at time $t_{eq}$.
• Figure 3: The time line of an inflationary Universe. The times $t_i$ and $t_R$ denote the beginning and end of inflation, respectively. In some models of inflation, there is no initial radiation dominated FRW period. Rather, the classical space-time emerges directly in an inflationary state from some initial quantum gravity state.
• Figure 4: Sketch (physical coordinates vs. time) of the solution of the homogeneity problem. During inflation, the forward light cone $l_f(t)$ is expanded exponentially when measured in physical coordinates. Hence, it does not require many e-foldings of inflation in order that $l_f(t)$ becomes larger than the past light cone at the time of last scattering. The dashed line is the forward light cone without inflation.
• Figure 5: A sketch (physical coordinates vs. time) of the solution of the formation of structure problem. Provided that the period of inflation is sufficiently long, the separation $d_c$ between two galaxy clusters is at all times smaller than the forward light cone. The dashed line indicates the Hubble radius. Note that $d_c$ starts out smaller than the Hubble radius, crosses it during the de Sitter period, and then reenters it at late times.