A Computational Companion to Transient de Sitter and Quasi de Sitter States in SO(32) and E ₈ × E ₈ Heterotic String Theories I: Formalisms

We construct 4D de Sitter space as an excited state, rather than as a vacuum configuration, in type IIB, heterotic , and heterotic 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 4D Friedmann‐Lemaitre‐Robertson‐Walker 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], where we present the detailed intermediate steps underlying the analysis in those sections.