Horndeski theory and beyond: a review

Abstract

This article is intended to review the recent developments in the Horndeski theory and its generalization, which provide us with a systematic understanding of scalar-tensor theories of gravity as well as a powerful tool to explore astrophysics and cosmology beyond general relativity. This review covers the generalized Galileons, (the rediscovery of) the Horndeski theory, cosmological perturbations in the Horndeski theory, cosmology with a violation of the null energy condition, degenerate higher-order scalar-tensor theories and their status after GW170817, the Vainshtein mechanism in the Horndeski theory and beyond, and hairy black hole solutions.

Review paper. 54 pages, no figure v2: published version

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• Investigating shadow images and rings of the charged Horndeski black hole illuminated by various thin accretions
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• Numerical relativity for Horndeski gravity
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• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Nanohertz gravitational waves from NEC violation in the early universe
• Impact of compactlike and asymmetric configurations of thick branes on the scalar-tensor representation of $f\left(R,T\right)$ gravity
• Higher derivative scalar-tensor theory and spatially covariant gravity: the correspondence
• Primordial black holes and gravitational waves in teleparallel Gravity
• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• 50 Years of Horndeski Gravity: Past, Present and Future
• Solar System tests and chameleon effect in f (R) gravity
• Exploring the Small Mass Limit of Stationary Black Holes in Theories with Gauss-Bonnet Terms
• Disforming to Conformal Symmetry
• Stealth black holes in shift symmetric kinetic gravity braiding
• Cosmological implications of Rastall-$f(R)$ theory
• Revisiting slow-roll dynamics and the tensor tilt in general single-field inflation
• Superluminality in DHOST theory with extra scalar
• Noncommutativity, Saez-Ballester theory and kinetic inflation
• Mapping Poincaré gauge cosmology to Horndeski theory for emergent dark energy
• Emergent Modified Gravity
• Superluminality in beyond Horndeski theory with extra scalar field
• Weak gravity on a $\Lambda$CDM background
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• Self-tuning kinetic gravity braiding: Cosmological dynamics, shift symmetry, and the tadpole
• Scalar-Connection Gravity and Spontaneous Scalarization
• On the Coupling of Generalized Proca Fields to Degenerate Scalar-Tensor Theories
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• Healthy Horndeski cosmologies with torsion
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• Extended Gravity Constraints at Different Scales
• Gauge invariant perturbations in teleparallel Horndeski gravity
• Neutron stars as extreme gravity probes
• Cosmic acceleration from string induced Galileons
• Kaluza-Klein Bubble With Massive Scalar Field