Are Scalar and Tensor Deviations Related in Modified Gravity?

Abstract

Modified gravity theories on cosmic scales have three key deviations from general relativity. They can cause cosmic acceleration without a physical, highly negative pressure fluid, can cause a gravitational slip between the two metric potentials, and can cause gravitational waves to propagate differently, e.g. with a speed different from the speed of light. We examine whether the deviations in the metric potentials as observable through modified Poisson equations for scalar density perturbations are related to or independent from deviations in the tensor gravitational waves. We show analytically they are independent instantaneously in covariant Galileon gravity -- e.g. at some time one of them can have the general relativity value while the other deviates -- though related globally -- if one deviates over a finite period, the other at some point shows a deviation. We present expressions for the early time and late time de Sitter limits, and numerically illustrate their full evolution. This in(ter)dependence of the scalar and tensor deviations highlights complementarity between cosmic structure surveys and future gravitational wave measurements.

6 pages, 3 figures; v2 minor changes to match PRD version

References in corpus (18)

• The galileon as a local modification of gravity
• Generalized G-inflation: Inflation with the most general second-order field equations
• From k-essence to generalised Galileons
• Covariant Galileon
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
• The Relation between Physical and Gravitational Geometry
• General second order scalar-tensor theory, self tuning, and the Fab Four
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• Cosmology with Nonminimal Derivative Couplings
• Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models
• Effective gravitational couplings for cosmological perturbations in the most general scalar-tensor theories with second-order field equations
• Observables and unobservables in dark energy cosmologies
• DBI Galileons in the Einstein Frame: Local Gravity and Cosmology
• The Paths of Gravity in Galileon Cosmology
• Purely Kinetic Coupled Gravity
• Fab 5: Noncanonical Kinetic Gravity, Self Tuning, and Cosmic Acceleration
• One Gravitational Potential or Two? Forecasts and Tests

Cited by in corpus (13)

• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Testing General Relativity in Cosmology
• Cosmological parameter constraints for Horndeski scalar-tensor gravity
• No Slip Gravity
• Is the Effective Field Theory of Dark Energy Effective?
• Challenges in Connecting Modified Gravity Theory and Observations
• Cosmological constraints on dark energy in light of gravitational wave bounds
• Non-standard gravitational waves imply gravitational slip: on the difficulty of partially hiding new gravitational degrees of freedom
• Probing the speed of gravity with LVK, LISA, and joint observations
• Testing the Speed of Gravity with Black Hole Ringdown
• Gravitational Waves: A Test for Modified Gravity
• Radiative stability and observational constraints on dark energy and modified gravity
• On tachyonic stability priors for dark energy