UV sensitive one-loop matter power spectrum in degenerate higher-order scalar-tensor theories

TL;DR

This paper derives the one-loop matter power spectrum in degenerate higher-order scalar-tensor theories, revealing enhanced sensitivity to small-scale physics and more stringent convergence conditions than in general relativity.

Contribution

It provides the first systematic derivation of the one-loop matter power spectrum in DHOST theories, including third-order solutions and novel shape functions.

Findings

Convergence conditions are more stringent in DHOST theories than in GR.

The one-loop power spectrum is sensitive to short-wavelength linear spectrum.

New shape functions characterize third-order solutions in DHOST.

Abstract

We study matter density perturbations up to third order and the one-loop matter power spectrum in degenerate higher-order scalar-tensor (DHOST) theories beyond Horndeski. We systematically solve gravitational field equations and fluid equations order by order, and find three novel shape functions characterizing the third-order solution in DHOST theories. A complete form of the one-loop matter power spectrum is then obtained using the resultant second- and third-order solutions. We confirm the previous result that the convergence condition of the loop integrals in the infrared limit becomes more stringent than that of the standard one in general relativity. We show that also in the ultraviolet limit the convergence condition becomes more stringent and the one-loop matter power spectrum is thus sensitive to the short-wavelength behavior of the linear power spectrum.