Modified theories of Gravity: Why, How and What?

Abstract

General Relativity (GR) was proven via the direct detection of gravitational waves from the mergers of the binary black holes and binary neutron stars by the Advanced LIGO and Advanced Virgo detectors. These detections confirmed the prediction of GR and provided the first direct evidence of the existence of stellar-mass black holes (BHs). However, the occurrence of singularities at the centers of BHs suggests that GR is inapplicable because of the breakdown of the equivalence principle at the singularities. The fact that these singularities exist indicates that GR cannot be a universal theory of space-time. In the low-energy limit, the theoretical and observational challenges faced by the $\Lambda$CDM model also indicate that we might have to look beyond GR as the underlying theory of gravity. Unlike GR, whose field equations contain only up to second-order derivatives, the modified theories with higher derivative Ricci/Riemann tensor gravity models include higher derivatives. Therefore, one expects significant differences between GR and modified theories. Since there are many ways of modifying GR in the strong-gravity and cosmological distances, each model has unique features. This leads to the following crucial question: Are there a set of unique signatures that distinguish GR from modified gravity (MG) theories? This review discusses three aspects of MG theories: (1) Why do we need to consider MG theories? (2) How to modify GR? and (3) What are the observational consequences? The review is written in a pedagogical style with the expectation that it will serve as a useful reference for theorists and observers and those interested in bridging the divide between theory and observations.

arXiv comment44 pages, 4 figures; Review article accepted in the special issue of General Relativity and Gravitation, dedicated to the memory of Professor Thanu Padmanabhan

References in corpus (92)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Dynamics of dark energy
• The Cosmological Constant and Dark Energy
• f(R) Theories Of Gravity
• Modified Gravity and Cosmology
• The Confrontation between General Relativity and Experiment
• f(R) theories
• Extended Theories of Gravity
• Cosmological Constant - the Weight of the Vacuum
• The Case for a Positive Cosmological Lambda-term
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• The Standard Model Higgs boson as the inflaton
• Quasi-Normal Modes of Stars and Black Holes
• In the Realm of the Hubble tension $-$ a Review of Solutions
• k-Inflation
• The galileon as a local modification of gravity
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Quasinormal modes of black holes: from astrophysics to string theory
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• Testing General Relativity with Present and Future Astrophysical Observations
• Kinetically Driven Quintessence
• Disappearing cosmological constant in f(R) gravity
• Exploring the Sensitivity of Next Generation Gravitational Wave Detectors
• Beyond the Cosmological Standard Model
• Tensions between the Early and the Late Universe
• Massive Gravity
• Theoretical Aspects of Massive Gravity
• Physics, Astrophysics and Cosmology with Gravitational Waves
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Test of the Equivalence Principle Using a Rotating Torsion Balance
• KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics
• Chern-Simons Modification of General Relativity
• The Thermodynamics of Black Holes
• Can modified gravity explain accelerated cosmic expansion?
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Black holes, gravitational waves and fundamental physics: a roadmap
• Chern-Simons Modified General Relativity
• Scaling solutions in general non-minimal coupling theories
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Gravitational Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing Arrays
• Hawking Radiation and Black Hole Thermodynamics
• Tests of Lorentz invariance: a 2013 update
• Dark Energy vs. Modified Gravity
• New Limits to the Drift of Fundamental Constants from Laboratory Measurements
• Testing General Relativity with Pulsar Timing
• Testing the no-hair theorem with GW150914
• Strong coupling in Horava gravity
• Dynamical Chern-Simons Modified Gravity I: Spinning Black Holes in the Slow-Rotation Approximation
• Gravitational Test Beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole
• Leptogenesis from Gravity Waves in Models of Inflation
• Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
• A Lower Growth Rate from Recent Redshift Space Distortion Measurements than Expected from Planck
• Introduction to Effective Field Theory
• Lanczos-Lovelock models of gravity
• Solar System tests DO rule out 1/R gravity
• Fourth order gravity: equations, history, and applications to cosmology
• Review of short-range gravity experiments in the LHC era
• The effects of Chern-Simons gravity on bodies orbiting the Earth
• Vainshtein mechanism after GW170817
• Hubble Space Telescope Spectroscopy of the Balmer lines in Sirius B
• The basic physics of the binary black hole merger GW150914
• Causality and Hyperbolicity of Lovelock Theories
• Effective Field Theory of Gravity to All Orders
• Non-perturbative spinning black holes in dynamical Chern-Simons gravity
• Analytical computation of quasi-normal modes of slowly-rotating black-holes in dCS gravity
• Falsifying $\Lambda$CDM: Model-independent tests of the concordance model with eBOSS DR14Q and Pantheon
• Low Energy Theorems of Quantum Gravity from Effective Field Theory
• Characterization of the Lovelock gravity by Bianchi derivative
• On Noncommutative Geometric Regularisation
• Ricci-inverse gravity: a novel alternative gravity, its flaws, and how to cure them
• Possible golden events for ringdown gravitational waves
• Quasinormal modes as a distinguisher between general relativity and f(R) gravity
• Black Hole Thermodynamics and Statistical Mechanics
• Discovery of a Quadruple Lens in CANDELS with a Record Lens Redshift z=1.53
• Black Hole Thermodynamics: General Relativity and Beyond
• Gravitationally induced uncertainty relations in curved backgrounds
• Maximal momentum GUP leads to quadratic gravity
• Causality in 3D Massive Gravity Theories
• Testing the"no-hair" nature of binary black holes using the consistency of multipolar gravitational radiation
• Quasinormal modes as a distinguisher between general relativity and f(R) gravity: Charged black-holes
• Helical magnetic fields from Riemann coupling
• Distinguishing general relativity from Chern-Simons gravity using gravitational wave polarizations
• Relativistic Extended Uncertainty Principle from Spacetime Curvature
• Black Hole Entropy and the Problem of Universality
• Strong gravity signatures in the polarization of gravitational waves
• Helical magnetic fields from Riemann coupling lead to baryogenesis
• Infinitely degenerate exact Ricci-flat solutions in f(R) gravity
• Low-energy modified gravity signatures on the large-scale structures
• Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants

Cited by in corpus (75)

• Quasinormal Modes and GUP-Corrected Hawking Radiation of BTZ Black Holes within Modified Gravity Frameworks
• Gravitational Lensing Phenomena of Ellis-Bronnikov-Morris-Thorne Wormhole with Global Monopole and Cosmic String
• Radiative losses and radiation-reaction effects at the first post-Newtonian order in Einstein-Cartan theory
• Can high-redshift Hubble diagrams rule out the standard model of cosmology in the context of cosmographic method?
• Gauge Invariant Perturbations of General Spherically Symmetric Spacetimes
• Quasinormal modes, temperatures and greybody factors of black holes in a generalized Rastall gravity theory
• Cosmological constant Petrov type-N space-time in Ricci-inverse gravity
• Gravitational atoms in the braneworld scenario
• Moment of inertia and compactness of quark stars within the context of $f(R,T,L_m)$ gravity
• Normal oscillation modes and radial stability of neutron stars with a dark-energy core from the Chaplygin gas
• Prospects of constraining $f(T)$ gravity with the third-generation gravitational-wave detectors
• White dwarfs in regularized 4D Einstein-Gauss-Bonnet gravity
• Circular geodesics in the field of double-charged dilatonic black holes
• Frequency-dependent squeezing for gravitational-wave detection through quantum teleportation
• Cosmological implications of the Weyl geometric gravity theory
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Hamilton's equations in the covariant teleparallel equivalent of general relativity
• Interacting Models of Dark Energy and Dark Matter in Einstein scalar Gauss Bonnet Gravity
• Stationary BTZ space-time in Ricci-Inverse and $f(\mathcal{R})$ gravity theories
• Generic EFT-motivated beyond General Relativity gravitational wave tests and their curvature dependence: from observation to interpretation
• Fundamental Physics and Cosmology with TianQin
• The dominating mode of two competing massive modes of quadratic gravity
• Particle-like solutions in the generalized SU(2) Proca theory
• Heat kernel coefficients for massive gravity
• Exploring the presence of a fifth force at the Galactic Center
• The curvature dependence of gravitational-wave tests of General Relativity
• Field redefinition invariant Lagrange multiplier formalism
• Probing a scale dependent gravitational slip with galaxy strong lensing systems
• Time-Machines Construct in $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ and $f(\mathcal{R})$ Modified Gravity Theories
• Mass Modeling and Kinematics of Galaxy Clusters in Modified Gravity
• Non-minimally coupled electromagnetic fields and observable implications for primordial black holes
• Dark energy effects on realistic neutron stars
• Electromagnetic memory in arbitrary curved space-times
• Recent Developments in Degenerate Higher Order Scalar Tensor Theories
• Gödel-type universes in energy-momentum-squared gravity
• Dynamical Oscillations in Dark Energy: Joint Constraints on the $w_{sin}$CDM Model from DESI, OHD, and Supernova Samples
• BBN to Late-Time Acceleration in $f(T,{\mathcal{L}}_m)$ Gravity
• Non-Singular Bouncing cosmology from Phantom Scalar-Gauss-Bonnet Coupling: Reconstruction with Observational Insights
• Cylindrical black hole solutions in $f(\mathcal{R})$ and $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ modified gravity
• The scalar-torsion gravity corrections in the first-order inflationary models
• Effective field theory of magnetogenesis identify necessary and sufficient conditions
• White dwarf structure in $f(R,T,L_m)$ gravity: beyond the Chandrasekhar mass limit
• Slow-roll inflation in $f\left(R,T,R_{ab}{T}^{ab}\right)$ gravity
• Velocity dispersion of dark matter deficient ultra-diffuse galaxies: A case for modified gravity
• Testing Refracted Gravity with kinematics of galaxy clusters
• Variable Brane Tension and Dark Energy
• Generation of effective massive Spin-2 fields through spontaneous symmetry breaking of scalar field
• Galactic dynamics in the presence of scalaron: A perspective from $\mathbf{f}(\mathbf{R})$ gravity
• Analysis of Pantheon+ supernova data suggests evidence of sign-changing pressure of the cosmological fluid
• Relativistic stars in $f(Q)$-gravity: Exact analytic solution for the power-law case $f(Q)=Q+b{Q}^{\nu }$
• Quantum-Corrected Thermodynamics of Conformal Weyl Gravity Black Holes: GUP Effects and Phase Transitions
• Analog charged black hole formation via percolation: Exploring cosmic censorship and Hoop conjecture
• Exploring Cosmological Implications of the Modified Raychaudhuri Equation in Non-Gravitating Vacuum Energy Theory
• Eikonal gravitational-wave lensing in Einstein-aether theory
• Dynamical 4-D Gauss-Bonnet action from matter-graviton interaction at one-loop
• Dust stars in the minimal exponential measure model
• Is it possible to separate baryonic from dark matter within the $\Lambda$-CDM formalism?
• Geodesic dynamics and multi-inclination images of a non-minimally coupled black hole with a thin accretion disk
• Charged anisotropic white dwarfs in $f\left(R,T\right)$ gravity
• Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity
• Linearized Gravity in the Starobinsky Model: Perturbative Deviations from General Relativity
• First Order Axial Perturbation of the Reissner-Nordström Metric in a Possible Parity-Violating Gravity Background
• Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology
• Semiclassical Gravity Beyond General Relativity: Insights from Torsion
• Straight and Wiggly Cosmic Strings in Horndeski Theory
• Inflationary models in a minimally coupled $f(R,T)$ gravity: Constraints from $Planck$, BICEP/$Keck$, and ACT
• Cosmology in the presence of diffeomorphism-violating, nondynamical background fields
• Gravitational Collapse of an Inhomogeneous Fluid in Rastall Theory
• Primordial Black Holes: A Review of Formation and Evolution
• On the unexpected geometrical origin of the algebra of symmetries
• Structure formation in a non-canonical scalar field model of clustering dark energy
• Constraints on the Modified Emergent Dark Energy Model Using DESI DR2 BAO
• Discrimination of metric theories
• An Anti-halo Void Catalogue of the Local Super-Volume
• Comparison of Quasinormal Modes of Black Holes in $f(\mathbb{T})$ and $f(\mathbb{Q})$ Gravity