Symmetric Teleparallel Horndeski Gravity

Abstract

Horndeski gravity is the most general scalar-tensor theory with one scalar field leading to second-order Euler-Lagrange field equations for the metric and scalar field, and it is based on Riemannian geometry. In this paper, we formulate an analogue version of Horndeski gravity in a symmetric teleparallel geometry which assumes that both the curvature (general) and torsion are vanishing and gravity is only related to nonmetricity. Our setup requires that the Euler-Lagrange equations for not only metric and scalar field but also connection should be at most second order. We find that the theory can be always recast as a sum of the Riemannian Horndeski theory and new terms that are purely teleparallel. Due to the nature of nonmetricity, there are many more possible ways of constructing second-order theories of gravity. In this regard, up to some assumptions, we find the most general $k$-essence extension of Symmetric Teleparallel Horndeski gravity. We also formulate a novel theory containing higher-order derivatives acting on nonmetricity while still respecting the second-order conditions, which can be recast as an extension of Kinetic Gravity Braiding. We finish our study by presenting the FLRW cosmological equations for our model.

35 pages. Matches published version in PRD

References in corpus (18)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Dark torsion as the cosmic speed-up
• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Imperfect Dark Energy from Kinetic Gravity Braiding
• G-inflation: inflation driven by the Galileon field
• On Born-Infeld Gravity in Weitzenbock spacetime
• Testing $F(Q)$ gravity with redshift space distortions
• Signatures of $f(Q)$-gravity in cosmology
• Accelerated Expansion of the Universe in Non-minimally Coupled Gravity
• Cosmography in $f(Q)$ gravity
• Observational constraints on cosmological solutions of $f(Q)$ theories
• Post-Newtonian limit of generalized symmetric teleparallel gravity
• Coincident gauge for static spherical field configurations in symmetric teleparallel gravity
• ADM formulation and Hamiltonian analysis of $f(Q)$ gravity
• Causality Constraints on Black Holes beyond GR
• Black hole solutions in scalar-tensor symmetric teleparallel gravity

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• Data reconstruction of the dynamical connection function in $f(Q)$ cosmology
• Observational test for $f(Q)$ gravity with weak gravitational lensing
• Equivalence of $f(Q)$ cosmology with quintom-like scenario: the phantom field as effective realization of the non-trivial connection
• A class of ghost-free theories in symmetric teleparallel geometry
• Stability of $f(Q,B)$ Gravity via Dynamical System Approach: a Comprehensive Bayesian Statistical Analysis
• Holographic renormalization of Horndeski gravity
• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
• Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation
• Background-dependent and classical correspondences between $f(Q)$ and $f(T)$ gravity
• Healthy Horndeski cosmologies with torsion
• Field transformations and invariant quantities in scalar-teleparallel theories of gravity
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Spatial Dependence of the Growth Factor in Scalar-Tensor Cosmology
• Post-Newtonian limit of generalized scalar-teleparallel theories of gravity