Inflation and String Cosmology

TL;DR

The paper surveys the evolution of inflationary cosmology from early models (Starobinsky, Guth, and New/New2) to chaotic and hybrid scenarios, detailing how quantum fluctuations generate density perturbations and how eternal inflation leads to a self-reproducing multiverse. It then discusses reheating dynamics and the observational status of inflation, including predictions for a flat, adiabatic, nearly scale-invariant, Gaussian spectrum with potential tensor modes. The latter part of the work explores embedding inflation in string theory via KKLT stabilization, modular and brane inflation, and the role of the string landscape and eternal inflation in shaping initial conditions and low-energy physics. Overall, the article argues that inflation remains the leading framework and outlines plausible string-theory realizations that connect high-energy theory with cosmological observations, while highlighting challenges such as scale hierarchies and moduli stabilization. The discussion emphasizes the potential compatibility of slow-roll, eternal inflation, and a vast landscape of vacua in shaping the early universe and its low-energy manifestations.

Abstract

After 25 years of its existence, inflationary theory gradually becomes the standard cosmological paradigm. However, we still do not know which of the many versions of inflationary cosmology will be favored by the future observational data. Moreover, it may be quite nontrivial to obtain a natural realization of inflationary theory in the context of the ever changing theory of all fundamental interactions. In this paper I will describe the history and the present status of inflationary cosmology, including recent attempts to implement inflation in the context of string theory.

Figures (9)

• 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 $M_p^4$, 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 (region A: $m M_p^3 < V(\phi) < M_p^4$) 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 $V(\phi)$ (region B: $m^2 M_p^2 < V(\phi) < m M_p^3$ ) fluctuations of the field $\phi$ are small; it slowly moves down as a ball in a viscous liquid. Inflation occurs both in the region A and region B. Finally, near the minimum of $V(\phi)$ (region C) 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 black in those parts of the universe where the scalar field $\Phi$ is in the first minimum of its effective potential, and white where it is in the second minimum. 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.
• Figure 3: CMB data versus the predictions of one of the simplest inflationary models (thick yellow line), according to Tegmark.
• Figure 4: KKLT potential as a function of $\sigma = {\rm Re}\,\rho$. Thin green line corresponds to AdS stabilized potential for $W_0 =- 10^{{-4}}$, $A=1$, $a =0.1$. Dashed line shows the additional term, which appears either due to the contribution of a $\overline{D3}$ brane or of a D7 brane. Thick black line shows the resulting potential with a very small but positive value of $V$ in the minimum. All potentials are shown multiplied by $10^{15}$.
• Figure 5: Plot for the potential in the racetrack model (rescaled by $10^{16}$). Here X stays for $\sigma = {\rm Re }\, \rho$ and Y stays for $\alpha = {\rm Im }\, \rho$. Inflation begins in a vicinity of the saddle point at $X_{\rm saddle}=123.22$, $Y_{\rm saddle}=0$. Units are $M_p=1$.