Non-archimedean quantum cosmology and tachyonic inflation

TL;DR

This paper explores quantum cosmology models involving tachyon fields, calculating exact propagators and vacuum states, and discusses their implications for inflation in both archimedean and nonarchimedean frameworks.

Contribution

It introduces a detailed quantum analysis of tachyon-driven inflation models, including exact propagators and adelic generalizations, expanding the understanding of non-archimedean quantum cosmology.

Findings

Exact quantum propagator for the tachyon model was derived.

Vacuum states and conditions for adelic generalization were identified.

Overview of cosmological models on archimedean and nonarchimedean spaces provided.

Abstract

We review the relevance of quantum rolling tachyons and corresponding inflation scenario in the frame of the standard, $p$-adic and adelic minisuperspace quantum cosmology. The field theory of tachyon matter proposed by Sen in a zero-dimensional version suggested by Kar leads to a model of a particle moving in a constant external field with quadratic damping. We calculate the exact quantum propagator of the model, as well as, the vacuum states and conditions necessary to construct an adelic generalization. In addition we present an overview on several important cosmological models on archimedean and nonarchimedean spaces.