Particle Physics and Inflationary Cosmology

TL;DR

This work surveys the interplay between particle physics and inflationary cosmology, tracing how scalar fields and spontaneous symmetry breaking underpin unified theories and drive early-universe dynamics. It presents a progression from classical scalar-field models and quantum corrections to the inflationary paradigm (notably chaotic inflation), emphasizing how quasi-exponential expansion solves the hot Big Bang problems (flatness, horizon, monopole) and naturally seeds large-scale structure via quantum fluctuations that become adiabatic density perturbations. The text also analyzes phase transitions in hot and cold regimes, the reheating process, and the self-reproducing nature of the inflationary universe, including anthropic considerations and the possible existence of a multiverse of inflating domains. Overall, it demonstrates inflation as a robust framework reconciling high-energy particle theories with cosmological observations, while highlighting unresolved issues (vacuum energy, monopole abundances, and infrared problems) and the need for further theoretical refinement. The work underscores the pivotal role of de Sitter-like expansion, quantum fluctuations, and multi-field dynamics in shaping the observable universe and its large-scale structure.

Abstract

This is the LaTeX version of my book "Particle Physics and Inflationary Cosmology'' (Harwood, Chur, Switzerland, 1990). I decided to put it to hep-th, to make it easily available. Many things happened during the 15 years since the time when it was written. In particular, we have learned a lot about the high temperature behavior in the electroweak theory and about baryogenesis. A discovery of the acceleration of the universe has changed the way we are thinking about the problem of the vacuum energy: Instead of trying to explain why it is zero, we are trying to understand why it is anomalously small. Recent cosmological observations have shown that the universe is flat, or almost exactly flat, and confirmed many other predictions of inflationary theory. Many new versions of this theory have been developed, including hybrid inflation and inflationary models based on string theory. There was a substantial progress in the theory of reheating of the universe after inflation, and in the theory of eternal inflation. It's clear, therefore, that some parts of the book should be updated, which I might do sometimes in the future. I hope, however, that this book may be of some interest even in its original form. I am using it in my lectures on inflationary cosmology at Stanford, supplementing it with the discussion of the subjects mentioned above. I would suggest to read this book in parallel with the book by Liddle and Lyth "Cosmological Inflation and Large Scale Structure,'' with the book by Mukhanov "Physical Foundations of Cosmology,'' to be published soon, and with my review article hep-th/0503195, which contains a discussion of some (but certainly not all) of the recent developments in inflationary theory.

Figures (35)

• Figure 1: Effective potential ${\rm V}(\varphi)$ in the simplest theories of the scalar field $\varphi$. a) ${\rm V}(\varphi)$ in the theory (\ref{['1.1.1']}), and b) in the theory (\ref{['1.1.5']}).
• Figure 2: Effective potential ${\rm V}(\varphi, {\rm T})$ in the theory (\ref{['1.1.5']}) at finite temperature. A) ${\rm T} = 0$; B) $0<{\rm T}<{\rm T}_c$; C) ${\rm T}>{\rm T}_c$. As the temperature rises, the field $\varphi$ varies smoothly, corresponding to a second-order phase transition.
• Figure 3: Behavior of the effective potential ${\rm V}(\varphi, {\rm T})$ in theories in which phase transitions are first-order. Between ${\rm T}_{c_1}$ and ${\rm T}_{c_2}$, the effective potential has two minima; at ${\rm T}={\rm T}_c$, these minima have the same depth. A) ${\rm T} = 0$; B) ${\rm T}_{c_1} < {\rm T} < {\rm T}_c$; C) ${\rm T}_c < {\rm T} < {\rm T}_{c_2}$; D) ${\rm T} > {\rm T}_{c_2}$.
• Figure 4: Evolution of the scale factor $a(t)$ for three different versions of the Friedmann hot universe theory: open (O), flat (F), and closed (C).
• Figure 5: Evolution of a homogeneous classical scalar field $\varphi$ in a theory with ${\rm V}(\varphi)=\frac{\lambda}{4}\,\varphi^4$, neglecting quantum fluctuations of the field. When $\varphi>\lambda^{-1/4}\,{\rm M}_{\rm P}$, the energy density of the field $\varphi$ is greater than the Planck density, and the evolution of the universe cannot be described classically. When $\frac{{\rm M}_{\rm P}}{3}\ \hbox{$<$$\sim$}\ \varphi\ \hbox{$<$$\sim$}\ \lambda^{-1/4}\,{\rm M}_{\rm P}$, the field $\varphi$ slowly decreases, and the universe then expands quasiexponentially (inflates). When $\varphi\ \hbox{$<$$\sim$}\ \frac{{\rm M}_{\rm P}}{3}$, the field $\varphi$ oscillates rapidly about the minimum of ${\rm V}(\varphi)$, and transfers its energy to the particles produced thereby (reheating of the universe).