Emergent cosmology from matrix theory

Abstract

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.

Limitations of an effective field theory treatment of early Universe cosmology

“…In this calculation, the starting point is the BFSS matrix model [99] (for which the leading term in the high temperature limit is given by the IKKT model), and leading correction terms to the pure IKKT result play an important role. The results obtained [96] in the context of the IKKT matrix model [97] are thus quite promising. In addition to obtaining emergent space and time, the model yields fluctuations which are similar in form to those obtained in SGC and hence in good agreement with current observations.…”

“…A very different approach to early Universe string cosmology has recently been suggested in [96]. The starting point of this analysis is the IKKT matrix model [97], a proposed non-perturbative definition of superstring theory.…”

“…Here, Φ is the the relativistic generalization of the Newtonian gravitational potential which describes the curvature perturbations, and h is the amplitude of a gravitational wave mode. The results of a detailed calculation [96] demonstrate that the spectra of both curvature fluctuations and gravitational waves are scale-invariant, with the curvature spectrum obtaining a thermal component with a Poisson spectrum which dominates on very short wavelengths. In this calculation, the starting point is the BFSS matrix model [99] (for which the leading term in the high temperature limit is given by the IKKT model), and leading correction terms to the pure IKKT result play an important role.…”

“…The results obtained [96] in the context of the IKKT matrix model [97] are thus quite promising. In addition to obtaining emergent space and time, the model yields fluctuations which are similar in form to those obtained in SGC and hence in good agreement with current observations.…”

Signature change of the emergent space-time in the IKKT matrix model

“…The mechanism for the appearance of the (1+1)D space-time may be understood from the bosonic action (5). Since the spatial direction expands exponentially, the Tr [ 𝐴 𝑖 , 𝐴 𝑗 ] 2 term becomes dominant.…”