Realisation of de Sitter space as an excited state in string theory

Abstract

String theory is widely regarded as the only plausible candidate for a consistent UV-complete theory of quantum gravity. Cosmological observations suggest that our universe is undergoing accelerated expansion, pointing towards the presence of a small positive cosmological constant. Since de Sitter space is the maximally symmetric solution of Einstein's equations with a positive cosmological constant, understanding whether four-dimensional de Sitter space can be realized within string theory has become one of the central questions. Following a series of works that realize de Sitter space as an excited state---namely, as a Glauber--Sudarshan (GS) state in type IIB string theory---our goal has been to extend such a construction to heterotic string theories. Realizing de Sitter space as an excited state over a time-independent supersymmetric Minkowski background provides a mechanism for evading the vacuum-based no-go theorems that obstruct de Sitter solutions in string theory. Starting from a generic M-theory configuration, we obtain four-dimensional de Sitter space in the late-time limit of flat-slicing coordinates in both heterotic $SO(32)$ and heterotic $E_8 \times E_8$ theories through appropriate dynamical duality sequences. The corresponding GS state is constructed by evaluating the expectation value of the metric operator in M-theory using path-integral techniques. We analyse the conditions required for the existence of a well-defined effective field theory description of the setup and find that these conditions are equivalent to satisfying the null energy condition in a 3+1-dimensional FLRW cosmology. Furthermore, the de Sitter GS states are found to lie well within the temporal bound imposed by the Trans-Planckian Censorship Conjecture, rendering them as transient states. In the case of $E_8\times E_8$ theory, we also investigate implications arising from axion cosmology.