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.
Highlights
Our starting point will be the BFSS matrix model [18]
In this paper we have suggested a concrete realization of a non-singular emergent cosmology based a matrix theory, a proposed non-perturbative definition of superstring theory in which space is emergent
We have used results of numerical and analytical studies of matrix theory to show that a spontaneous breaking of the SO(9) spatial symmetry takes place, and that exactly three dimensions of space become large
Summary
Our starting point will be the BFSS matrix model [18]. The basic objects in this model are d = 9 bosonic N × N Hermitian matrices Xai,b and their sixteen fermionic superpartners θa,b which transform as spinors under the SO(9) group of spatial rotations. Taking the results from the analysis of the IKKT model described above back to the BFSS side, we argue that in the high temperature limit (which is relevant for our discussion of the emergent phase) the background which minimizes the free energy will experience spontaneous symmetry breaking in which three of the spatial dimensions (given by the quantum expectation values of eigenvalue distribution of the matrices Xi) become large compared to the other six. Note that this symmetry breaking occurs during the emergent phase, and at the end of it. We turn to the computation of these fluctuations
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