How can we tell whether dark energy is composed by multiple fields?

TL;DR

This paper explores how multi-field scalar-tensor models of dark energy affect observable gravitational parameters, proposing a method to determine the number of scalar fields involved by analyzing their polynomial ratios in data.

Contribution

It introduces a general framework for expressing modified gravity parameters in multi-field models and demonstrates how to infer the number of scalar fields from observational data.

Findings

Observable parameters are ratios of polynomials in Fourier wavenumber k.

Number of scalar fields N determines polynomial order 2N.

Reducing polynomial order is generally not feasible in realistic models.

Abstract

Dark energy is often assumed to be composed by a single scalar field. The background cosmic expansion is not sufficient to determine whether this is true or not. We study multi-field scalar-tensor models with a general dark matter source and write the observable modified gravity parameters (effective gravitational constant and anisotropic stress) in the form of a ratio of polynomials in the Fourier wavenumber k of order 2N, where N is the number of scalar fields. By comparing these observables to real data it is in principle possible to determine the number of dark energy scalar fields coupled to gravity. We also show that there are no realistic non-trivial cases in which the order of the polynomials is reduced.