TDiff invariant field theories for cosmology

TL;DR

This paper explores scalar field theories invariant under transverse diffeomorphisms in cosmology, revealing their unique effects on particle motion, energy contributions, and potential for driving inflation and dark matter modeling.

Contribution

It introduces TDiff invariant scalar field theories and demonstrates their implications for cosmological dynamics, including inflation and dark matter, highlighting differences from standard Diff invariant theories.

Findings

Particles follow geodesics in geometric optics approximation.

Super-Hubble modes contribute differently to energy-momentum tensor.

A kinetic scalar field can drive inflation and produce scale-invariant fluctuations.

Abstract

We study scalar field theories invariant under transverse diffeomorphisms in cosmological contexts. We show that in the geometric optics approximation, the corresponding particles move along geodesics and contribute with the same active mass (energy) to the gravitational field as in Diff invariant theories. However, for low-frequency (super-Hubble) modes, the contributions to the energy-momentum tensor differ from that of Diff invariant theories. This opens up a wide range of possibilities for cosmological model building. As an example, we show that the simplest TDiff invariant scalar field theory with only kinetic term could drive inflation and generate a nearly scale invariant (red-tilted) spectrum of density fluctuations. We also present a detailed analysis of cosmological perturbations and show that the breaking of full Diff invariance generically induces new non-adiabatic pressure perturbations. A simple scalar field dark matter model based on a purely kinetic term that exhibits the same clustering properties as standard cold dark matter is also presented.