Inflation

TL;DR

Inflation provides a mechanism for accelerated expansion driven by negative pressure from scalar fields, yielding an exponentially growing scale factor and addressing horizon, flatness, and monopole problems. It predicts a nearly scale-invariant, adiabatic perturbation spectrum linked to the inflaton potential via slow-roll parameters $\epsilon$ and $\eta$, with perturbation amplitude related to $V^{3/2}/(M_p^3 V')$ and a scalar index $n_s$ close to unity. The paper then analyzes eternal inflation in both new and chaotic models, showing self-reproduction of pockets and discussing the profound implications for initial conditions, predictions, and vacuum selection, while highlighting the past-boundary theorem and the persistent measure problem. It concludes that current observations—particularly CMB anisotropies and flatness—strongly support inflation, and that eternal inflation offers a path to robustly connect theory with a multiverse picture, though defining probabilities and the past boundary remains an area of active foundational work.

Abstract

The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. I describe the quantum origin of density perturbations, giving a heuristic derivation of the scale invariance of the spectrum and the leading corrections to scale invariance. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique.

Figures (4)

• Figure 1.1: Generic form of the potential for the new inflationary scenario.
• Figure 1.2: Generic form of the potential for the chaotic inflationary scenario.
• Figure 1.3: Power spectra of the cosmic background radiation as measured by WMAP (Bennett et al. 2003, courtesy of the NASA/WMAP Science Team). The top panel shows the temperature anisotropies, and the bottom panel shows the correlation between temperature fluctuations and E-mode polarization fluctuations. The solid line is a fit consistent with simple inflationary models.
• Figure 1.4: An observer measures the velocity of passing test particles to infer the Hubble parameter.