Effective gravitational couplings for cosmological perturbations in generalized Proca theories

Abstract

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to non-trivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling $G_{\mathrm{eff}}$ with matter density perturbations under a quasi-static approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing $G_{\mathrm{eff}}$. In fact, within the parameter space, $G_{\mathrm{eff}}$ can be even smaller than the Newton gravitational constant $G$ at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter $\eta$ and the evolution of growth rate $f{\sigma }_8$ are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the $\Lambda$CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

23 pages, 3 figures

References in corpus (25)

• Dynamics of dark energy
• Cosmology and the Fate of Dilatation Symmetry
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Beyond the Cosmological Standard Model
• Covariant Galileon
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• Measuring the dark side (with weak lensing)
• Approaches to Understanding Cosmic Acceleration
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• On couplings to matter in massive (bi-)gravity
• Constraints on scalar-tensor models of dark energy from observational and local gravity tests
• Observables and unobservables in dark energy cosmologies
• Matter perturbations in Galileon cosmology
• Ghosts & Matter Couplings in Massive (bi-&multi-)Gravity
• Density perturbations in general modified gravitational theories
• Phantom boundary crossing and anomalous growth index of fluctuations in viable f(R) models of cosmic acceleration
• Cosmology of the proxy theory to massive gravity
• A small cosmological constant from Abelian symmetry breaking
• Chameleon dark energy models with characteristic signatures
• Quantum corrections in massive bigravity and new effective composite metrics
• Cosmologies in Horndeski's second-order vector-tensor theory
• On the stability and causality of scalar-vector theories

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