Inflationary Cosmology after Planck 2013

TL;DR

Planck 2013 results reinforce inflation while motivating a unified framework of cosmological attractors that yield robust predictions for n_s and r across diverse models. The author surveys chaotic inflation, initial condition arguments, reheating, and perturbation theory, then introduces universal attractor classes including Starobinsky-like and α-attractors that converge to the same observational targets despite varied microphysics. The work also connects inflation to broader themes such as the string theory landscape, eternal inflation, and the multiverse, discussing how these ideas shape initial conditions and observable parameters like the cosmological constant and tensor modes. Overall, the paper argues that inflation remains viable and predictive, with a large and interconnected family of attractor models compatible with current data and with deep implications for high-energy theory and cosmology.

Abstract

I give a general review of inflationary cosmology and of its present status, in view of the 2013 data release by the Planck satellite. A specific emphasis is given to the new broad class of theories, the cosmological attractors, which have nearly model-independent predictions converging at the sweet spot of the Planck data in the (n_s,r) plane. I also discuss the problem of initial conditions for the theories favored by the Planck data.

Figures (23)

• 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. 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 these 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 elementary particles, and the universe becomes hot.
• Figure 2: Inflation of a tiny universe consisting of many different parts with different properties makes each of these parts exponentially large and uniform, while preserving distinct features of each of these parts. The universe becomes a multiverse consisting of exponentially large parts with different properties.
• Figure 3: 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 4: CMB data (Planck 2013) versus the predictions of one of the simplest inflationary models with $\Omega = 1$ (green line).
• Figure 5: Constraints on $n_{s}$ and $r$ according to Planck 2013.