Matrix theory is a proposed non-perturbative definition of superstring theory in which space is emergent. We begin a study of cosmology in the context of matrix theory. Specifically, we show that matrix theory can lead to an emergent non-singular cosmology which, at late times, can be described by an expanding phase of Standard Big Bang cosmology. The horizon problem of Standard Big Bang cosmology is automatically solved. We show that thermal fluctuations in the emergent phase source an approximately scale-invariant spectrum of cosmological perturbations and a scale-invariant spectrum of gravitational waves. Hence, it appears that matrix theory can lead to a successful scenario for the origin of perturbations responsible for the currently observed structure in the universe while providing a consistent UV-complete description.

In this paper, we study some aspects of moduli stabilization using string gases in the context of the Swampland. In the framework which we derive, the matter Lagrangian for string gases yields a potential for the size moduli which satisfies the de Sitter conjecture with the conditionMp , where p is the number of compactified dimensions. Moreover, the moduli find themselves stabilized at the self-dual radius, and gravity naturally emerges as the weakest force.

The IKKT matrix model yields an emergent space-time. We further develop these ideas and give a proposal for an emergent metric. Based on previous numerical studies of this model, we provide evidence that the emergent space-time is continuous and infinite in extent, both in space and in time, and that the metric is spatially flat. The time evolution describes the transition from a string-theoretic emergent phase to a phase in which the SO(9) symmetry of the model is spontaneously broken to SO(6) × SO(3), with three dimensions of space expanding, becoming classical and at later times evolving like in a radiation-dominated universe, and the remaining six dimensions of space stabilized at the string scale. We speculate on how this analysis can be extended to yield an early universe cosmology which, in addition to the above-mentioned properties, also leads to a roughly scale-invariant spectrum of cosmological fluctuations and gravitational waves.

Cosmic strings produce charged particles which, by emitting electromagnetic radiation, partially ionize neutral hydrogen during the dark ages. Corrections to the ionization fraction of neutral hydrogen induced by cosmic strings could lead to new observational effects and/or new constraints on the string tension around Gµ ∼ 10 −16 − 10 −22 for values of the primordial magnetic field in the range B0 ∼ 10 −11 − 10 −9 Gauss.

We review a proposal to obtain an emergent metric space-time and an emergent early universe cosmology from the Banks–Fischler–Shenker–Susskind (BFSS) matrix model. Some challenges and directions for future research are outlined.