Inflationary Cosmology

TL;DR

Inflationary Cosmology surveys the historical development and core mechanisms of inflation, emphasizing chaotic inflation as a robust, generic route to exponential expansion without thermal initial conditions. It outlines how quantum fluctuations during slow-roll generate nearly scale-invariant density perturbations and discusses reheating, eternal inflation, and observational constraints, including the tensor-to-scalar ratio. The paper then surveys extensions to high-energy theories, notably supergravity and string theory, detailing how moduli stabilization (KKLT) and brane dynamics can realize inflation, while predicting typically small gravitational waves. It concludes by exploring the inflationary multiverse, anthropic considerations, and the status of alternatives, arguing that inflation remains the most viable framework for solving the standard cosmological problems while highlighting open questions testable by future observations.

Abstract

I give a general review of the history of inflationary cosmology and of its present status.

Figures (10)

• Figure 1: Motion of the scalar field in the theory with $V(\phi) = {m^2\over 2} \phi^2$. Several different regimes are possible, depending on the value of the field $\phi$. If the potential energy density of the field is greater than the Planck density $M_p^4 = 1$, $\phi \gtrsim m^{-1}$, quantum fluctuations of space-time are so strong that one cannot describe it in usual terms. Such a state is called space-time foam. At a somewhat smaller energy density (for $m \lesssim V(\phi) \lesssim 1$, $m^{-1/2} \lesssim \phi \lesssim m^{-1}$) quantum fluctuations of space-time are small, but quantum fluctuations of the scalar field $\phi$ may be large. Jumps of the scalar field due to quantum fluctuations lead to a process of eternal self-reproduction of inflationary universe which we are going to discuss later. At even smaller values of $V(\phi)$ (for $m^2 \lesssim V(\phi) \lesssim m$, $1 \lesssim \phi \lesssim m^{-1/2}$) fluctuations of the field $\phi$ are small; it slowly moves down as a ball in a viscous liquid. Inflation occurs for $1 \lesssim \phi \lesssim m^{-1}$. Finally, near the minimum of $V(\phi)$ (for $\phi \lesssim 1$) the scalar field rapidly oscillates, creates pairs of elementary particles, and the universe becomes hot.
• Figure 2: Evolution of scalar fields $\phi$ and $\Phi$ during the process of self-reproduction of the universe. The height of the distribution shows the value of the field $\phi$ which drives inflation. The surface is painted red, green or blue corresponding to three different minima of the potential of the field $\Phi$. Laws of low-energy physics are different in the regions of different color. The peaks of the "mountains" correspond to places where quantum fluctuations bring the scalar fields back to the Planck density. Each of such places in a certain sense can be considered as a beginning of a new Big Bang. At the end of inflation, each such part becomes exponentially large. The universe becomes a multiverse, a huge eternally growing fractal consisting of different exponentially large locally homogeneous parts with different laws of low-energy physics operating in each of them.
• Figure 3: CMB data (WMAP3, BOOMERANG03, ACBAR) versus the predictions of one of the simplest inflationary models with $\Omega = 1$ (red line), according to Kuo:2006ya.
• Figure 4: Possible values of $r$ and $n_{s}$ in the theory ${\lambda\over 4}(\phi^{2}-v^{2})^{2}$ for different initial conditions and different $v$, for $N = 60$. In the small $v$ limit, the model has the same predictions as the theory $\lambda\phi^{4}/4$. In the large $v$ limit it has the same predictions as the theory $m^{2}\phi^{2}$. The upper branch, above the first star from below (marked as $\phi^{2}$), corresponds to inflation which occurs while the field rolls down from large $\phi$; the lower branch corresponds to the motion from $\phi = 0$.
• Figure 5: Possible values of $r$ and $n_{s}$ for chaotic inflation with a potential including terms $\phi^{2}$, $\phi^{3}$ and $\phi^{4}$ for N = 50, according to Destri:2007pv. The color-filled areas correspond to 12%, 27%, 45%, 68% and 95% confidence levels according to the WMAP3 and SDSS data.