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Kobayashi, Horndeski theory and beyond: a review, Rept

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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.

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2026 15 2025 8

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representative citing papers

Gravitational Memory from Hairy Binary Black Hole Mergers

gr-qc · 2026-04-10 · unverdicted · novelty 8.0

Gravitational memory from hairy binary black hole mergers in scalar-Gauss-Bonnet gravity differs from GR by a few percent due to altered nonlinear dynamics, with direct scalar contributions suppressed, and including memory increases GR-sGB mismatch by more than an order of magnitude.

Testing Dark Energy with Black Hole Ringdown

gr-qc · 2026-03-24 · unverdicted · novelty 7.0

Dynamical dark energy imprints O(1) shifts on black hole quasi-normal modes via cosmological hair, enabling constraints at 10^{-2} (LVK) to 10^{-4} (LISA) precision using the cubic Galileon as example.

Stable black hole solutions with cosmological hair

gr-qc · 2026-03-23 · unverdicted · novelty 7.0

Stable black hole solutions with cosmological scalar hair are explicitly derived in the cubic Galileon theory, recovering cosmological behavior at large distances and regular short-range dynamics.

All $2D$ generalised dilaton theories from $d\geq 4$ gravities

hep-th · 2026-03-06 · conditional · novelty 7.0

Generic 2D Horndeski theories arise from dimensional reduction of d≥4 gravities, yielding a Birkhoff theorem for quasi-topological gravities where static spherically symmetric solutions satisfy g_tt g_rr = -1 and are determined algebraically.

Regular Vaidya solutions of effective gravitational theories

gr-qc · 2025-06-17 · unverdicted · novelty 7.0

Regular Vaidya solutions exist in effective gravitational theories that dynamically describe radiation-driven formation of regular black holes or mimickers without curvature singularities.

Scalar memory from compact binary coalescences

gr-qc · 2026-05-08 · conditional · novelty 7.0

In Ricci-coupled scalar-Gauss-Bonnet gravity, the change in scalar charge during binary black hole mergers generates a scalar memory contribution that modifies the total memory signal on observable timescales.

A Master Equation for Screening in Luminal Horndeski Gravity

gr-qc · 2026-05-05 · unverdicted · novelty 7.0

A master screening equation is derived for luminal Horndeski gravity that recovers Vainshtein and Chameleon mechanisms and introduces Phaedrus screening with screening radius scaling linearly with source mass.

Frame invariant diffusive formulation of scalar-tensor gravity

gr-qc · 2026-04-17 · unverdicted · novelty 7.0

Scalar-tensor gravity admits a frame-invariant perfect-fluid description with zero temperature, so that general relativity corresponds to diffusive equilibrium for both minimal and nonminimal theories.

Cosmological Dynamics of a Non-Canonical Generalised Brans-Dicke Theory

gr-qc · 2026-05-07 · unverdicted · novelty 5.0

A non-canonical generalized Brans-Dicke theory admits background cosmological solutions matching Lambda CDM characteristics for constant, power-law, and exponential potentials, with dynamics distinct from other scalar-tensor models.

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