p-adic Inflation

TL;DR

This paper develops inflationary solutions within p-adic string theory, demonstrating compatibility with CMB data, unique slow-roll conditions, and the theory's ultraviolet completeness, offering a novel approach to early universe cosmology.

Contribution

It introduces approximate inflationary solutions in p-adic string theory with unique slow-roll features and compatibility with observational data, highlighting the theory's UV completeness.

Findings

Existence of slow-roll solutions with large parameters

Compatibility with CMB observations under specific conditions

Prediction of a red-tilted spectrum and low tensor-to-scalar ratio

Abstract

We construct approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory, a nonlocal theory with derivatives of all orders. Novel features include the existence of slow-roll solutions even when the slow-roll parameters, as usually defined, are much greater than unity, as well as the need for the Hubble parameter to exceed the string mass scale m_s. We show that the theory can be compatible with CMB observations if g_s / \sqrt{p} ~ 10^{-7}, where g_s is the string coupling, and if m_s < 10^{-6} M_p. A red-tilted spectrum is predicted, and the scalar-to-tensor ratio is bounded from above as r < 0.006. The p-adic theory is shown to have identical inflationary predictions to a local theory with superPlanckian parameter values, but with the advantage that the p-adic theory is ultraviolet complete.