A Computational Companion to Transient de Sitter and Quasi de Sitter States in SO(32) and E_8 X E_8 Heterotic String Theories I: Formalisms

TL;DR

This paper constructs de Sitter space as an excited state in string theories, providing a new approach to evade no-go theorems and analyzing conditions for effective field theory validity.

Contribution

It introduces a framework to realize de Sitter states as excited states in string theories using duality sequences and path-integral techniques, advancing the understanding of de Sitter solutions.

Findings

De Sitter space constructed as an excited state in string theories.

Conditions for effective field theory are shown to be equivalent to the null energy condition.

Constraints from axionic cosmology are analyzed with experimental bounds considered.

Abstract

We construct four-dimensional de Sitter space as an excited state, rather than as a vacuum configuration, in type IIB, heterotic SO(32), and heterotic E_8 \times E_8 string theories. This framework provides a mechanism to evade vacuum-based no-go theorems for de Sitter solutions in string theory. Starting from a generic M-theory configuration, we obtain de Sitter isometry in the dual string theories through appropriate dynamical duality sequences in the late-time limit. The excited state, identified as a Glauber-Sudarshan state, is constructed as the expectation value of the metric operator in M-theory using path-integral techniques. We further analyze the conditions required for the existence of a well-defined effective field theory description and show that these conditions are equivalent to the null energy condition for a (3+1)-dimensional FLRW cosmology. Finally, we investigate constraints arising from axionic cosmology and demonstrate how the time-dependent solutions are modified when experimental bounds on the axionic coupling constant are taken into account. This article serves as a computational companion to sections 3 and 4 of the paper arXiv:2511.03798 [hep-th].