A systematic approach to generalisations of General Relativity and their cosmological implications

Abstract

A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious challenges of modern cosmology and of particle physics have motivated the exploration of further generalised theories of spacetime. Even though Einstein's interpretation of gravity in terms of the curvature of spacetime is commonly adopted, the assignment of geometrical concepts to gravity is ambiguous because General Relativity allows three entirely different, but equivalent approaches of which Einstein's interpretation is only one. From a field-theoretical perspective, however, the construction of a consistent theory for a Lorentz-invariant massless spin-2 particle uniquely leads to General Relativity. Keeping Lorentz invariance then implies that any modification of General Relativity will inevitably introduce additional propagating degrees of freedom into the gravity sector. Adopting this perspective, we will review the recent progress in constructing consistent field theories of gravity based on additional scalar, vector and tensor fields. Within this conceptual framework, we will discuss theories with Galileons, with Lagrange densities as constructed by Horndeski and beyond, extended to DHOST interactions, or containing generalized Proca fields and extensions thereof, or several Proca fields, as well as bigravity theories and scalar-vector-tensor theories. We will review the motivation of their inception, different formulations, and essential results obtained within these classes of theories together with their empirical viability.

193 pages, Review under press at Physics Reports

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Cited by in corpus (239)

• Horndeski theory and beyond: a review
• Cosmology in $f(Q)$ geometry
• Teleparallel Gravity: From Theory to Cosmology
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Stellar structure models in modified theories of gravity: lessons and challenges
• Black holes in $f(\mathbb{Q})$ Gravity
• Polarization of gravitational waves in symmetric teleparallel theories of gravity and their modifications
• Revisiting Cosmologies in Teleparallelism
• The Novel Probes Project -- Tests of Gravity on Astrophysical Scales
• FLRW solutions in $f(Q)$ theory: the effect of using different connections
• A new gauge-invariant double copy for heavy-mass effective theory
• Scale transformations in metric-affine geometry
• Isotropization of locally rotationally symmetric Bianchi-I universe in $f(Q)$-gravity
• Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology
• A class of static spherically symmetric solutions in $f(Q)$-gravity
• A new parametrization of Hubble parameter in $f(Q)$ gravity
• Modified gravity: a unified approach
• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• Anisotropic Strange Star Model Beyond Standard Maximum Mass Limit by Gravitational Decoupling in $f(Q)$ Gravity
• Non-linear extension of non-metricity scalar for MOND
• Parity-Violating Gravity and GW170817 in Non-Riemannian Cosmology
• Junction conditions in Palatini $f(R)$ gravity
• hi_class: Background Evolution, Initial Conditions and Approximation Schemes
• Dark energy beyond quintessence: Constraints from the swampland
• Quantifying the $S_8$ tension and evidence for interacting dark energy from redshift-space distortion measurements
• Torsion/non-metricity duality in f(R) gravity
• Formation and Evolution of Binary Neutron Stars: Mergers and Their Host Galaxies
• Sound speed resonance of the stochastic gravitational wave background
• Influence of three parameters on maximum mass and stability of strange star under linear $f(Q)-$action
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Current and future constraints on cosmology and modified gravitational wave friction from binary black holes
• ADM formulation and Hamiltonian analysis of $f(Q)$ gravity
• Minisuperspace quantum cosmology in $f(Q)$ gravity
• First-order thermodynamics of Horndeski gravity
• Homogeneous and isotropic cosmology in general teleparallel gravity
• Double shadows of reflection-asymmetric wormholes supported by positive energy thin-shells
• Exact Spherically Symmetric Solutions in Modified Teleparallel gravity
• Asymptotically locally flat and AdS higher-dimensional black holes of Einstein-Horndeski-Maxwell gravity in the light of EHT observations: shadow behavior and deflection angle
• The effective field theory approach to the strong coupling issue in $f(T)$ gravity
• Spin-dependent exotic interactions
• New Weyl-invariant vector-tensor theory for the cosmological constant
• Gravitational wave memory beyond general relativity
• New class of Proca interactions
• On Black Hole Temperature in Horndeski Gravity
• New Graviton Mass Bound from Binary Pulsars
• On the Kuzmin model in fractional Newtonian gravity
• Noether charge and black hole entropy in teleparallel gravity
• Gravitational wave propagation in $f(R)$ models: New parametrizations and observational constraints
• The complete theory of Maxwell and Proca fields
• New scalar compact objects in Ricci-based gravity theories
• Dynamical analysis of cosmological models with non-Abelian gauge vector fields
• Proca in the sky
• Hamiltonian formulation of an effective modified gravity with nondynamical background fields
• The Maxwell-Proca theory: definition and construction
• Dirac-Bergmann analysis and Degrees of Freedom of Coincident $f(Q)$-gravity
• Multi-field Inflation in High-Slope Potentials
• Probing cosmological fields with gravitational wave oscillations
• Cosmic Structure Formation with Kinetic Field Theory
• Symmetric Teleparallel Horndeski Gravity
• First-order thermodynamics of scalar-tensor cosmology
• Spherically symmetric vacuum solutions in 1-Parameter New General Relativity and their phenomenology
• Eternal Inflation, Entropy Bounds and the Swampland
• Generalized SU(2) Proca theory reconstructed and beyond
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Horndeski in the Swampland
• Spontaneous scalarization of charged black holes in the Scalar-Vector-Tensor theory
• A systematic procedure to build the beyond generalized Proca field theory
• Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models
• Comparison of different approaches to the quasi-static approximation in Horndeski models
• An axiomatic purification of gravity
• Nonmetricity theories and aspects of gauge symmetry
• Torsion in string-inspired cosmologies and the universe dark sector
• AdS/BCFT correspondence and BTZ black hole thermodynamics within Horndeski gravity
• Transit String Dark Energy Models in $f(Q)$ Gravity
• Coupled Multi-Proca Vector Dark Energy
• Constant-roll inflation in the generalized SU(2) Proca theory
• Pregeometry and spontaneous time-space asymmetry
• Modified-gravity theories with nondynamical background fields
• Shear viscosity from black holes in generalized scalar-tensor theories in arbitrary dimensions
• Cosmology of Extended Proca-Nuevo
• The Non-Relativistic Geometric Trinity of Gravity
• Overcharging a Reissner-Nordström Taub-NUT regular black hole
• Generalized Proca and its Constraint Algebra
• Horndeski under the quantum loupe
• Cosmological Perturbation Theory in Metric-Affine Gravity
• Planck-PR4 anisotropy spectra show (better) consistency with General Relativity
• $f(Q,L_m)$ gravity, and its cosmological implications
• One-loop renormalization in Galileon effective field theory
• Conformally invariant proper time with general non-metricity
• Static spherically symmetric Einstein-Yang-Mills-dilaton black hole and its thermodynamics
• Parameterized non-relativistic limit of stellar structure equations in Ricci-based gravity theories
• Positive Energy Warp Drive from Hidden Geometric Structures
• Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative
• Rotating black hole with a probe string in Horndeski Gravity
• Quantum Stability of Generalized Proca Theories
• Peculiar thermal states in the first-order thermodynamics of gravity
• Stability of symmetric teleparallel scalar-tensor cosmologies with alternative connections
• Describing metric-affine theories anew: alternative frameworks, examples and solutions
• Addressing Cosmological Tensions by Non-Local Gravity
• Braneworlds in Horndeski gravity
• Horndeski stars
• Stability Conditions in the Generalized SU(2) Proca Theory
• Disformal map and Petrov classification in modified gravity
• Observational bounds on extended minimal theories of massive gravity: New limits on the graviton mass
• Geometrical Trinity of Unimodular Gravity
• Geometrized quantum Galileons
• Cosmology from pregeometry
• Tensor Perturbations from Bounce Inflation Scenario in f(Q) Gravity
• Gravitational-wave constraints on scalar-tensor gravity from a neutron star and black-hole binary GW200115
• Detecting Fundamental Vector Fields with LISA
• On the viability of the evolution of the universe with Geometric Inflation
• Pregeometry and euclidean quantum gravity
• Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity
• Cosmological stability in $f(\varphi ,\mathcal{G})$ gravity
• Einstein-Proca theory from the Einstein-Cartan formulation
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Influence of pressure anisotropy and non-metricity parameter on mass-radius relation and stability of millisecond pulsar in $f(Q)$ gravity
• Polarization modes of gravitational waves in generalized Proca theory
• Positivity Bounds on Massive Vectors
• General Teleparallel Modifications of Schwarzschild Geometry
• Dark sector evolution in Horndeski models
• Positivity bounds in vector theories
• The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms
• Model Independent Analysis of Supernova Data, Dark Energy, Trans-Planckian Censorship and the Swampland
• Polarized gravitational waves in the parity violating scalar-nonmetricity theory
• Gibbons-Hawking-York boundary terms and the generalized geometrical trinity of gravity
• Maxwell-$f(Q)$ theory
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
• Anisotropic Scalar Field Dark Energy with a Disformally Coupled Yang-Mills Field
• Unveiling the Galileon in a three-body system : scalar and gravitational wave production
• Instability of hairy black holes in regularized 4-dimensional Einstein-Gauss-Bonnet gravity
• UV sensitive one-loop matter power spectrum in degenerate higher-order scalar-tensor theories
• Some Recent Results on Ricci-Based Gravity Theories
• Observational constraints on interactions between dark energy and dark matter with momentum and energy transfers
• Generalized no-hair theorems without horizons
• New Non-Abelian Reissner-Nordström Black Hole Solutions in the Generalized SU(2) Proca Theory And Some Astrophysical Implications
• Maxwell extension of $f(R)$ gravity
• Quantum stability of Proca-Nuevo
• The cosmological principle in theories with torsion: The case of Einstein-Cartan-Dirac-Maxwell gravity
• First-order thermodynamics of Horndeski cosmology
• Generalised Proca Theories in Teleparallel Gravity
• Towards the extended SU(2) Proca theory
• Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein-Cartan Theory with Background Fields
• The effect of screening mechanisms on black hole binary inspiral waveforms
• Generalization of the 2-form interactions
• Bounds on the Horndeski Gauge-Gravity Coupling
• Wald's entropy in Coincident General Relativity
• Spin precession as a new window into disformal scalar fields
• Aether scalar tensor theory: Hamiltonian Formalism
• Cosmological constraints on $f(Q)$ gravity models in the non-coincident formalism
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Particle-like solutions in the generalized SU(2) Proca theory
• Stability of neutron stars in Horndeski theories with Gauss-Bonnet couplings
• To Half--Be or Not To Be?
• Topological mass generation and $2-$forms
• Exploring Modified Gravity: Constraints on the $\mu$ and $\Sigma$ Parametrization with WMAP, ACT, and SPT
• From fundamental physics to tests with compact objects in metric-affine theories of gravity
• Static spherically symmetric black hole's solution in Einstein-Maxwell-Yang-Mills-dilaton theory
• Quadratic and cubic spherically symmetric black holes in the modified teleparallel equivalent of general relativity: Energy and thermodynamics
• Gravitational waves in massive gravity: Waveforms generated by a particle plunging into a black hole and the excitation of quasinormal modes and quasibound states
• Decoupling-limit consistency of the generalized SU(2) Proca theory
• Towards a unified interpretation of the early Universe in $R^2$-corrected dark energy model of $F(R)$ gravity
• Causality and Stability from Acoustic Geometry
• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
• Constraints on dark energy from the CSST galaxy clusters
• Proca-stinated Cosmology I: A N-body code for the vector Galileon
• Dipolar dark matter simulations on galaxy scales with the RAMSES code
• Black holes in the quadratic-order extended vector-tensor theories
• First-order formulation of teleparallel gravity and dual loop gravity
• General analysis of Noether symmetries in Horndeski gravity
• Holographic Boundary Conformal Field Theory within Horndeski Gravity
• Domain walls in Horndeski gravity
• The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity
• Background-dependent and classical correspondences between $f(Q)$ and $f(T)$ gravity
• $f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom
• Black branes in asymptotically Lifshitz spacetimes in $\kappa$-deformed Horndeski gravity
• New model of spontaneous scalarization of black holes induced by curvature and matter
• Ricci-Determinant Gravity: Dynamical Aspects and Astrophysical Implications
• An Expansion of Well Tempered Gravity
• Static topological black hole with nonminimal derivative coupling and nonlinear electromagnetic field of Born-Infeld type
• Kantowski-Sachs cosmology in scalar-torsion theory
• Realizing the phantom-divide crossing with vector and scalar fields
• On constrained analysis and diffeomorphism invariance of generalised Proca theories
• Non-perturbative quantum Galileon in the exact renormalization group
• Tidal Love Numbers of Neutron Stars in Horndeski Theories
• Field transformations and invariant quantities in scalar-teleparallel theories of gravity
• Conventionalism, cosmology and teleparallel gravity
• Cosmology in theories with spontaneous scalarization of neutron stars
• Testing beyond-Kerr spacetimes with GWTC-3
• A Post-Newtonian Analysis of Regularized 4D-EGB Theory: Complete Set of PPN Parameters and Observational Constraints
• On sufficient conditions for degrees of freedom counting of multi-field generalised Proca theories
• Dynamical aspects of asymmetric Eddington gravity with scalar fields
• Compact scalar field solutions in EiBI gravity
• Principal Components for Model-Agnostic Modified Gravity with 3x2pt
• Contemplating the fate of modified gravity
• Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling
• Neutron stars in the generalized SU(2) Proca theory
• PPN meets EFT of dark energy: Post-Newtonian approximation in higher-order scalar-tensor theories
• Inflation in a scalar-vector-tensor theory
• Logarithmic and Strong Coupling Models in Weyl-Type $f(Q,T)$ Gravity
• Thermodynamic phase transition of Anti-de Sitter Reissner-Nordström black holes with exotic Einstein-Maxwell gravities
• Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8
• Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions
• Nonminimal Derivative Coupling Cosmology and the Speed of Gravitational Waves
• Can an Extra Degree of Freedom in Scalar-Tensor Non-Metricity Gravity Account for the Evolution of the Universe?
• Wald Entropy in Extended Modified Myrzakulov Gravity Theories: \(f(R, T, Q, R_{μν}T^{μν}, R_{μν}Q^{μν}, \dots)\)
• Dynamical Shortcomings in the Generalized SU(2) Proca Theory: Challenges for Cosmic Acceleration
• Dynamical 4-D Gauss-Bonnet action from matter-graviton interaction at one-loop
• Infrared Sensitivity of Cosmological Probes in Horndeski Theory
• Post-Newtonian limit of generalized scalar-teleparallel theories of gravity
• Cosmological scalar perturbations in Horndeski-like gravity
• Quintessence dark energy model in non-linear $f(Q)$ theory with bulk-viscosity
• Extremal cosmological black holes in Horndeski gravity and the anti-evaporation regime
• An ostentatious model of cosmological scalar-tensor theory
• Higgs-Induced Screening Mechanisms in Scalar-Tensor Theories
• Black hole solutions in gravity with nonminimal derivative coupling and nonlinear material fields
• Reconstruction of Tsallis Holographic Dark Energy via Modified Non-Metric Gravity: An $f(Q,C)$ Approach
• Is it possible to separate baryonic from dark matter within the $\Lambda$-CDM formalism?
• Absence of gravitational polarization mechanism in the canonical bimetric theory
• Gravity from the Determinant of the Energy-Momentum: Astrophysical Implications
• A note on higher rank descriptions of massless and massive spin-1 particles
• Constraining Scalar Charge in Neutron Stars through Gravitational Wave Signals from NSBH Mergers
• Neutron stars in $f(\mathbb{Q})$ gravity
• Effective $\Lambda$CDM model emerging from $f(Q,T)$ under a special EOS limit in symmetric cosmology with Bayesian and ANN observational constraints
• A Modified Gravitational Theory of the Matter Sector of the Type $\varphi (R,T){\mathcal{L}}_m$
• The ghost of vector fields in compact stars
• Cosmology in the presence of diffeomorphism-violating, nondynamical background fields
• Generalized Second Law and Thermodynamical Aspects of $f(Q,\mathcal{T})$ Gravity
• Kinetic gases in static spherically symmetric modified dispersion relations
• Emergent quantum field theories on curved spacetimes in spinor Bose-Einstein condensates: from scalar to Proca fields
• Non-minimal non-Abelian quantum vector fields in curved spacetime
• Linearized transverse diffeomorphism invariant spin-2 theories via gauge invariants
• Spacetime symmetries and the qubit Bloch ball: a physical derivation of finite dimensional quantum theory and the number of spatial dimensions
• Insights in $f(Q)$ cosmology: the relevance of the connection
• Linear perturbations of dyonic black holes in the lowest-order $U(1)$ gauge-invariant scalar-vector-tensor theories
• Covariant single-field formulation of effective cosmological bounces
• LHC constraints on hidden gravitons
• Vector Field Dynamics: Field Equations and Energy Tensor
• Symmetric teleparallel gravitational effects on solar neutrino oscillations