Coupling of gravity to matter, spectral action and cosmic topology

TL;DR

This paper explores a modified gravity model using spectral action on spherical space forms, revealing how matter coupling influences cosmic power spectra, with implications for inflation and fermion contributions.

Contribution

It introduces a nonperturbative method to compute the impact of matter coupling on cosmic spectra within a spectral action framework for spherical topologies.

Findings

Coupling to matter causes a multiplicative shift in power spectra amplitude.

The shift factor equals the total number of fermions in the matter sector.

Explicit spectral computations are performed using Poisson summation and heat-kernel methods.

Abstract

We consider a model of modified gravity based on the spectral action functional, for a cosmic topology given by a spherical space form, and the associated slow-roll inflation scenario. We consider then the coupling of gravity to matter determined by an almost commutative geometry over the spherical space form. We show that this produces a multiplicative shift of the amplitude of the power spectra for the density fluctuations and the gravitational waves, by a multiplicative factor equal to the total number of fermions in the matter sector of the model. We obtain the result by an explicit nonperturbative computation, based on the Poisson summation formula and the spectra of twisted Dirac operators on spherical space forms, as well as by a heat-kernel computation.