CMB spectrum in unified EFT of dark energy: scalar-tensor and vector-tensor theories

TL;DR

This paper explores how a unified effective field theory framework for dark energy, encompassing scalar-tensor and vector-tensor theories, impacts the cosmic microwave background spectrum, revealing that vectorial features generally do not modify the spectrum.

Contribution

It introduces a new EFT parameter $oldsymbol{ extalpha_V}$ to unify scalar and vector dark energy theories and analyzes their effects on the CMB spectrum using a Boltzmann code.

Findings

Vectorial nature typically prevents modifications to the CMB spectrum.

Shift symmetry influences perturbations mainly near $oldsymbol{ extLambda CDM}$.

Phantom dark energy ($w_{DE}<-1$) is favored unless the background is close to $oldsymbol{ extLambda CDM}$.

Abstract

We study the cosmic microwave background (CMB) radiation in the unified description of the effective field theory (EFT) of dark energy that accommodates both scalar-tensor and vector-tensor theories. The boundaries of different classes of theories are universally parameterised by a new EFT parameter $\alpha_V$ characterising the vectorial nature of dark energy and a set of consistency relations associated with the global/local shift symmetry. After implementing the equations of motion in a Boltzmann code, as a demonstration, we compute the CMB power spectrum based on the $w$CDM background with the EFT parameterisation of perturbations and a concrete Horndeski/generalised Proca theory. We show that the vectorial nature generically prevents modifications of gravity in the CMB spectrum. On the other hand, while the shift symmetry is less significant in the perturbation equations unless the background is close to the $\Lambda$CDM, it requires that the effective equation of state of dark energy is in the phantom region $w_{\rm DE}<-1$. The latter is particularly interesting in light of the latest result of the DESI+CMB combination as the observational verification of $w_{\rm DE}>-1$ can rule out shift-symmetric theories including vector-tensor theories in one shot.