Table of contents

String cosmology is a grand opportunity. The field involves elements of a promising framework, string theory, that brings together gravity and quantum mechanics and attempts to unify all the interactions. Confirming the concepts of string theory is presently beyond the reach of ground-based laboratories but the heavens may provide a setting for testing the string theoretic framework. Specifically, as cosmology develops into a rigorous, data-driven scientific discipline, windows into earlier epochs and higher energies are becoming available. If string theory controlled the evolution of the very early universe it is conceivable that it might have left imprints that are still detectable today.

With this possibility in mind, this focus issue of Classical and Quantum Gravity appraises recent applications of string-theoretic and string-inspired ideas to the cosmos. The contents of this issue span the following areas:

(1) Inflationary scenarios within different kinds of string-theoretic sectors (C P Burgess and L McAllister; M Cicoli and F Quevedo)

(2) Alternatives to conventional inflation and dark matter/energy models with novel dynamics or matter content (J-L Lehners; M Trodden and K Hinterbichler)

(3) Cosmic scenarios arising from the landscape of string vacua (M Kleban; B Freivogel)

(4) Dynamical mechanisms determining the number of dimensions and resolving cosmic singularities (R H Brandenberger; B Craps and O Evnin)

(5) Possible subsequent consequences of an early stringy phase (E J Copeland, L Pogosian and T Vachaspati; A Mazumdar)

(6) Whether an observational `window' might be accessible (D J Mulryne and J Ward).

The articles in this issue also survey a number of potentially promising directions for the future.

We present an overview of inflationary models derived from string theory focusing mostly on closed string moduli as inflatons. After a detailed discussion of the η-problem and different approaches to address it, we describe possible ways to obtain a de Sitter vacuum with all closed string moduli stabilized. We then look for inflationary directions and present some of the most promising scenarios where the inflatons are either the real or the imaginary part of Kähler moduli. We pay particular attention on extracting potential observable implications, showing how most of the scenarios predict negligible gravitational waves and could therefore be ruled out by the Planck satellite. We conclude by briefly mentioning some open challenges in string cosmology beyond deriving just inflation.

We critically assess the twin prospects of describing the observed universe in string theory, and using cosmological experiments to probe string theory. For the purposes of this short review, we focus on the limitations imposed by our incomplete understanding of string theory. After presenting an array of significant obstacles, we indicate a few areas that may admit theoretical progress in the near future.

The Galileons are a set of terms within four-dimensional effective field theories, obeying symmetries that can be derived from the dynamics of a (3 + 1)-dimensional flat brane embedded in a 5-dimensional Minkowski bulk. These theories have some intriguing properties, including freedom from ghosts and a non-renormalization theorem that hints at possible applications in both particle physics and cosmology. In this brief paper, we will summarize our attempts over the last year to extend the Galileon idea in two important ways. We will discuss the effective field theory construction arising from flat branes, of co-dimension greater than 1, embedded in a flat background—the multi-Galileons—and we will then describe symmetric covariant versions of the Galileons, more suitable for general cosmological applications. While all these Galileons can be thought of as interesting four-dimensional field theories in their own rights, the work described here may also make it easier to embed them into string theory, with its multiple extra dimensions and more general gravitational backgrounds.

Cosmological models involving a bounce from a contracting to an expanding universe can address the standard cosmological puzzles and generate 'primordial' density perturbations without the need for inflation. Some such models, in particular the ekpyrotic and cyclic models that we focus on, fit rather naturally into string theory. We discuss a number of topics related to these models: the reasoning that leads to the ekpyrotic phase, the predictions for upcoming observations, the differences between singular and non-singular models of the bounce as well as the predictive and explanatory power offered by these models.

String gas cosmology is a model of the evolution of the very early universe based on fundamental principles and key new degrees of freedom of string theory which are different from those of point particle field theories. In string gas cosmology the universe starts in a quasi-static Hagedorn phase during which space is filled with a gas of highly excited string states. Thermal fluctuations of this string gas lead to an almost scale-invariant spectrum of curvature fluctuations. Thus, string gas cosmology is an alternative to cosmological inflation as a theory for the origin of structure in the universe. This short review focuses on the building blocks of the model, the predictions for late time cosmology, and the main problems which the model faces.

Important open questions in cosmology require a better understanding of the big bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like big bang models, presenting both solved and open problems.

I describe reasons to think we are living in an eternally inflating multiverse where the observable 'constants' of nature vary from place to place. The major obstacle to making predictions in this context is that we must regulate the infinities of eternal inflation. I review a number of proposed regulators, or measures. Recent work has ruled out a number of measures by showing that they conflict with observation, and focused attention on a few proposals. Further, several different measures have been shown to be equivalent. I describe some of the many nontrivial tests these measures will face as we learn more from theory, experiment and observation.

I briefly review the physics of cosmic bubble collisions in false-vacuum eternal inflation. My purpose is to provide an introduction to the subject for readers unfamiliar with it, focussing on recent work related to the prospects for observing the effects of bubble collisions in cosmology. I will attempt to explain the essential physical points as simply and concisely as possible, leaving most technical details to the references. I make no attempt to be comprehensive or complete. I also present a new solution to Einstein's equations that represents a bubble universe after a collision, containing vacuum energy and ingoing null radiation with an arbitrary density profile.

We review the existence, formation and properties of cosmic strings in string theory, the wide variety of observational techniques that are being employed to detect them, and the constraints that current observations impose on string theory models.

We review the current observational status of string cosmology when confronted with experimental datasets. We begin by defining common observational parameters and discuss how they are determined for a given model. Then we review the observable footprints of several string theoretic models, discussing the significance of various potential signals. Throughout we comment on present and future prospects of finding evidence for string theory in cosmology and on significant issues for the future.