String Cosmology: from the Early Universe to Today

TL;DR

This article surveys how string theory informs cosmology from the earliest moments of the universe to the present-day acceleration. It reviews cosmological inflation, including single- and multi-field realizations, and details how moduli, compactifications, and nonperturbative effects shape inflationary dynamics and post-inflationary histories. The review then covers moduli stabilisation in various corners of string theory (notably IIB KKLT and LVS), their cosmological consequences, and prospects for de Sitter vacua versus quintessence within swampland constraints. A major portion discusses post-inflationary epochs (reheating, moduli domination, dark radiation, and non-thermal dark matter) and non-standard histories arising from branes and extra dimensions. Finally, it analyzes dark energy in string theory—both vacuum energy and dynamical quintessence—alongside landscape, swampland, and multi-field quintessence scenarios, highlighting observational connections and theoretical challenges.

Abstract

We review applications of string theory to cosmology, from primordial times to the present-day accelerated expansion. Starting with a brief overview of cosmology and string compactifications, we discuss in detail moduli stabilisation, inflation in string theory, the impact of string theory on post-inflationary dynamics (reheating, moduli domination, kination), dark energy (the cosmological constant from a string landscape and models of quintessence) and various alternative scenarios (string/brane gases, the pre big-bang scenario, rolling tachyons, ekpyrotic/cyclic cosmologies, bubbles of nothing, S-brane and holographic cosmologies). The state of the art in string constructions is described in each topic and, where relevant, connections to swampland conjectures are made. The possibilities for novel particles and excitations (axions, moduli, cosmic strings, branes, solitons, oscillons and boson stars) are emphasised. Implications for the physics of the CMB, gravitational waves, dark matter and dark radiation are discussed along with potential observational signatures.

Figures (37)

• Figure 1: Energy density evolution for radiation $\rho_r$, non-relativistic matter $\rho_m$, (constant) dark energy $\rho_\Lambda$ and the total energy density, $\rho_T$ as a function of the scale factor in Planck units with $a_0=1$ today.
• Figure 2: A schematic representation of the different epochs and their temperatures within the history of the universe in the standard $\Lambda$CDM cosmological model.
• Figure 3: An illustration of the standard picture of slow-roll inflation ending in fast roll of the inflation to a minimum and subsequent reheating of the universe.
• Figure 4: Horizon exit and re-entry of a density perturbation with wave number $k$.
• Figure 5: The power spectrum of the scalar fluctuations of the cosmic microwave background including error bars for the $\Lambda$CDM model. This is one of most impressive examples of the precision level ($\simeq 10^{-5}$) reached in cosmology so far, in which only a handful of parameters is enough to explain such a large number of data points (taken from Planck:2018vyg).