Testing General Relativity in Cosmology

Abstract

We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy associated with it. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, gravitational screening mechanisms, and computer codes developed for these tests. We then provide summaries of recent cosmological constraints on MG parameters and selected MG models. We supplement these cosmological constraints with a summary of implications from the recent binary neutron star merger event. Next, we summarize some results on MG parameter forecasts with and without astrophysical systematics that will dominate the uncertainties. The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field. It can also serve as a quick reference to recent results and constraints on testing gravity at cosmological scales.

Invited review article for Living Reviews in Relativity. 201 pages, 17 figures. Matches published version

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• Cosmology in generalized Proca theories
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• Non-Local Modification of Gravity and the Cosmological Constant Problem
• hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System
• Generalized Proca action for an Abelian vector field
• Testing Landau gauge OPE on the Lattice with a $<A^2>$ Condensate
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• Observational constraints on self-accelerating cosmology
• Gauge-invariant gravitational perturbations of maximally symmetric spacetimes
• On the growth of linear perturbations
• Dynamics of Nonlocal Cosmology
• How to optimally parametrize deviations from General Relativity in the evolution of cosmological perturbations
• Cascading DGP
• Nonlocal gravity. Conceptual aspects and cosmological predictions
• Planck 2013 results. XIX. The integrated Sachs-Wolfe effect
• Modified-Source Gravity and Cosmological Structure Formation
• Ghosts, Instabilities, and Superluminal Propagation in Modified Gravity Models
• Ghosts in the self-accelerating universe
• Constructing stabilized brane world models in five-dimensional Brans-Dicke theory
• Large-scale cosmological perturbations on the brane
• Cosmological perturbations in Horava-Lifshitz theory without detailed balance
• Observables and unobservables in dark energy cosmologies
• Limits on the number of spacetime dimensions from GW170817
• A Trouble with Hořava-Lifshitz Gravity
• A practical approach to cosmological perturbations in modified gravity
• Generalized Gravity and a Ghost
• Einstein gravity on the codimension 2 brane?
• Challenges to the DGP Model from Horizon-Scale Growth and Geometry
• No-Go Theorems for Generalized Chameleon Field Theories
• Probing modifications of General Relativity using current cosmological observations
• Limits of Quasi-Static Approximation in Modified-Gravity Cosmologies
• Cascading Gravity and Degravitation
• Nonlinear Cosmological Power Spectra in Real and Redshift--Space
• Modified Gravity N-body Code Comparison Project
• Self-Consistent Cosmological Simulations of DGP Braneworld Gravity
• Growth of Cosmic Structure: Probing Dark Energy Beyond Expansion
• Vainshtein mechanism after GW170817
• Median statistics and the Hubble constant
• Can Cosmic Structure form without Dark Matter?
• Horndeski: beyond, or not beyond?
• Constraints on a New Post-General Relativity Cosmological Parameter
• Relativistic Stars in Beyond Horndeski Theories
• Non-linear Evolution of Matter Power Spectrum in Modified Theory of Gravity
• Brane-world extra dimensions in light of GW170817
• Beyond generalized Proca theories
• Constraints on Einstein-aether theory after GW170817
• The impact of intrinsic alignment on current and future cosmic shear surveys
• Large-Scale Tests of the DGP Model
• An algorithm for the direct reconstruction of the dark matter correlation function from weak lensing and galaxy clustering
• Phantom dark energy from non-local infrared modifications of General Relativity
• Can codimension-two branes solve the cosmological constant problem?
• Stable and unstable cosmological models in bimetric massive gravity
• Probing Gravity with Spacetime Sirens
• Brane cosmological perturbations
• The Observational Future of Cosmological Scalar-Tensor Theories
• Cosmology of codimension-two braneworlds
• Horava-Lifshitz Dark Energy
• Measurements of H(z) and D_A(z) from the Two-Dimensional Two-Point Correlation Function of Sloan Digital Sky Survey Luminous Red Galaxies
• Piercing the Vainshtein screen with anomalous gravitational wave speed: Constraints on modified gravity from binary pulsars
• Can We See Lorentz-Violating Vector Fields in the CMB?
• Nonlocal Gravity Simulates Dark Matter
• Cuscuton Cosmology: Dark Energy meets Modified Gravity
• Determining the Hubble constant from Hubble parameter measurements
• Astrophysical Probes of the Vainshtein Mechanism: Stars and Galaxies
• Recovering General Relativity from massive gravity
• Thermodynamics and classification of cosmological models in the Horava-Lifshitz theory of gravity
• The observational status of Galileon gravity after Planck
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• Redshift space distortions in f(R) gravity
• Nonlocal Models of Cosmic Acceleration
• Phenomenological Aspects of Horava-Lifshitz Cosmology
• Cosmological perturbations in Massive Gravity and the Higuchi bound
• Effective gravitational couplings for cosmological perturbations in generalized Proca theories
• CFHTLenS tomographic weak lensing: Quantifying accurate redshift distributions
• Cross-correlation of the CMB and radio galaxies in real, harmonic and wavelet spaces: detection of the integrated Sachs-Wolfe effect and dark energy constraints
• Consistent Spin-Two Coupling and Quadratic Gravitation
• Dynamical Scalar Degree of Freedom in Horava-Lifshitz Gravity
• Evolution of Cosmological Perturbations in the Brane World
• Cosmological Simulations of Normal-Branch Braneworld Gravity
• Measurements of Sub-degree B-mode Polarization in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data
• Self-accelerating Massive Gravity: Exact solutions for any isotropic matter distribution
• Cosmological constraints on Brans-Dicke theory
• Generalizing TeVeS Cosmology
• Cosmology in the Randall-Sundrum Brane World Scenario
• Nonsingular Black Hole
• Selftuning and its footprints
• Stability of spherically symmetric solutions in modified theories of gravity
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• Cosmic Acceleration and Modified Gravitational Models
• Observational Constraints on Dark Radiation in Brane Cosmology
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• Model Comparison tests of modified gravity from the Eöt-Wash experiment
• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• Generalized SU(2) Proca theory reconstructed and beyond
• Minimal theory of massive gravity in the light of CMB data and the $S_8$ tension
• Lensing with generalized symmetrons
• Large fluctuations and Primordial Black Holes
• New cosmological constraints on $f(T)$ gravity in light of full Planck-CMB and type Ia supernovae data
• A systematic procedure to build the beyond generalized Proca field theory
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Cosmological constraints on dark energy models using DESI BAO 2024
• Anisotropic massive Brans-Dicke gravity extension of the standard $\Lambda$CDM model
• Testing General Relativity on cosmological scales at redshift z ~ 1.5 with quasar and CMB lensing
• Comparison of different approaches to the quasi-static approximation in Horndeski models
• Observational Constraints on Dynamical Dark Energy Models
• Cosmological constraints on non-adiabatic dark energy perturbations
• Measuring the ringdown scalar polarization of gravitational waves in Einstein scalar Gauss-Bonnet gravity
• Hints for possible low redshift oscillation around the best fit $\Lambda$CDM model in the expansion history of the Universe
• Convolution Lagrangian perturbation theory for biased tracers beyond general relativity
• Current constraints on deviations from General Relativity using binning in redshift and scale
• Cosmological dynamical systems in modified gravity
• Constraints on field flows of quintessence dark energy
• Mapping the ${\Lambda }_{\mathrm{s}}$CDM scenario to $f(T)$ modified gravity: Effects on structure growth rate
• Methodological Reflections on the MOND/Dark Matter Debate
• Observational Constraints in Nonlocal Gravity: the Deser-Woodard Case
• Forecasted constraints on modified gravity from Sunyaev Zel'dovich tomography
• Semi-classical gravity in de Sitter spacetime and the cosmological constant
• Cosmological gravity on all scales: simple equations, required conditions, and a framework for modified gravity
• Viscous cosmology in $f(T)$ gravity
• Inherently stable effective field theory for dark energy and modified gravity
• Implications of axionic hair on shadow of M87*
• High Redshift Long Gamma-Ray Bursts Hubble Diagram as a Test of Basic Cosmological Relations
• Cosmological discordances III: more on measure properties, Large-Scale-Structure constraints, the Hubble constant and Planck
• Overcharging a Reissner-Nordström Taub-NUT regular black hole
• A general study of chameleon fifth force in gravity space experiments
• Enhanced Forman curvature and its relation to Ollivier curvature
• Planck-PR4 anisotropy spectra show (better) consistency with General Relativity
• Modelling the matter bispectrum at small scales in modified gravity
• Observational Constraints on Growth Index with Cosmography
• MG-MAMPOSSt: A code to test modifications of gravity with the dynamics of galaxy clusters
• $f(Q,L_m)$ gravity, and its cosmological implications
• Big Bang Nucleosynthesis constraints on $f(T,T_G)$ gravity
• The matter density PDF for modified gravity and dark energy with Large Deviations Theory
• General Effective Field Theory of Teleparallel Gravity
• Underdetermination in Classic and Modern Tests of General Relativity
• Searching for modified gravity in the astrophysical gravitational wave background: Application to ground-based interferometers
• Noether Symmetry Approach in Scalar-Torsion $f(T,\varphi )$ Gravity
• Ghost and Laplacian Instabilities in the Teleparallel Horndeski Gravity
• Constraining the cosmological evolution of scalar-tensor theories with local measurements of the time variation of G
• Unified $f(R)$ gravity at local scales
• Modified gravity in the interior of population II stars
• Observational bounds on extended minimal theories of massive gravity: New limits on the graviton mass
• Parametrizations for tests of gravity
• Exploring the Redshift-Space Peculiar Velocity Field and its Power Spectrum
• Testing non-local gravity by clusters of galaxies
• Constraining modified gravity from tidal phenomena in binary stars
• Cosmological Probes of Structure Growth and Tests of Gravity
• Constraints on $f(R)$ and nDGP Modified Gravity Model Parameters with Cluster Abundances and Galaxy Clustering
• Constraining gravity with a new precision $E_G$ estimator using Planck + SDSS BOSS
• Constraining extended cosmologies with GW$\times$LSS cross-correlations
• Limited Modified Gravity
• Constraint on the minimally extended varying speed of light using time dilations in type Ia supernovae
• Negative Temperature Pressure in Black Holes
• Cosmological dynamics of multifield dark energy
• Gaussian-process reconstructions and model building of quintom dark energy from latest cosmological observations
• Testing gravity with gravitational waves $\times$ electromagnetic probes cross-correlations
• Growth of structures and redshift-space distortion data in scale-dependent gravity
• Gravitational-wave constraints on scalar-tensor gravity from a neutron star and black-hole binary GW200115
• Forecast Analysis on Interacting Dark Energy Models from Future Generation PICO and DESI Missions
• Parameterised post-Newtonian formalism for the effective field theory of dark energy via screened reconstructed Horndeski theories
• The Probability Distribution of Astrophysical Gravitational-Wave Background Fluctuations
• Small Anisotropy in Stellar Objects in Modified Theories of Gravity
• Mathematical General Relativity
• Quantum-enhanced screened dark energy detection
• Dark Matter Halo Sparsity of Modified Gravity Scenarios
• Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity
• Cosmologically viable generalized Einstein-Aether theories
• Noether Symmetries in $f(T,T_G)$ Cosmology
• Quantum simulation of dark energy candidates
• Two new approaches to the anomalous limit of Brans-Dicke to Einstein gravity
• Growth of non-linear structures and spherical collapse in the Galileon Ghost Condensate model
• Multi-component DHOST analysis in galaxy clusters
• Is gravity getting weaker at low z? Observational evidence and theoretical implications
• Naked singularity in 4D Einstein-Gauss-Bonnet novel gravity: Echoes and (in)-stability
• Cluster counts. II. Tensions, massive neutrinos, and modified gravity
• Global properties of the growth index of matter inhomogeneities in the universe
• ISiTGR: Testing deviations from GR at cosmological scales including dynamical dark energy, massive neutrinos, functional or binned parametrizations, and spatial curvature
• Cosmological fluids in the equivalence between Rastall and Einstein gravity
• Geometric and topological corrections to Schwarzschild black hole
• Probing gravity with redshift-space distortions: effects of tracer bias and sample selection
• A local self-tuning mechanism for the cosmological constant
• General Teleparallel Modifications of Schwarzschild Geometry
• Constraining modified gravity theories with scalar fields using black-hole images
• Post-Newtonian $\gamma$-like parameters and the gravitational slip in scalar-tensor and $f(R)$ theories
• Dark sector evolution in Horndeski models
• Inverse-Chirp Imprint of Gravitational Wave Signals in Scalar Tensor Theory
• Screening the Higgs portal
• The local dark sector. Probing gravitation's low-acceleration frontier and dark matter in the Solar System neighborhood
• Black String in Massive Gravity
• Accurate Computation of the Screening of Scalar Fifth Forces in Galaxies
• The Shape Dependence of Vainshtein Screening in the Cosmic Matter Bispectrum
• UV sensitive one-loop matter power spectrum in degenerate higher-order scalar-tensor theories
• Low-energy modified gravity signatures on the large-scale structures
• A study on Cubic Galileon Gravity Using N-body Simulations
• Accretion flows around exotic tidal wormholes I. Ray-tracing
• No Run Gravity
• Global properties of the growth index: mathematical aspects and physical relevance
• Cosmological Tests of Gravity: A Future Perspective
• $f(T,B)$ gravity in a Friedmann-Lema\^ıtre-Robertson-Walker universe with nonzero spatial curvature
• Observational constraints on interactions between dark energy and dark matter with momentum and energy transfers
• Bulk viscous matter in $f(T)$ gravity: A path to cosmic acceleration
• Coupled dark energy model inspired from general conformal transformation
• Bounds on the Horndeski Gauge-Gravity Coupling
• Non-local gravity in bouncing cosmology scenarios
• Cosmological framework for renormalization group extended gravity at the action level
• Primordial Black Hole-Neutron Star Merger Rate in Modified Gravity
• The Effective Fluid approach for Modified Gravity and its applications
• The full-sky Spherical Fourier-Bessel power spectrum in general relativity
• Towards unveiling the large-scale nature of gravity with the wavelet scattering transform
• Interacting Models of Dark Energy and Dark Matter in Einstein scalar Gauss Bonnet Gravity
• Data-driven and Almost Model-independent Reconstruction of Modified Gravity
• Pole Dark Energy
• A representation learning approach to probe for dynamical dark energy in matter power spectra
• Aether-quasi-dilaton massive gravity
• Effective Potential of Scalar-Tensor Gravity
• Perturbation Spectra of Warm Inflation in $f(Q,T)$ Gravity
• Gravitational Radiation from Eccentric Binary Black Hole System in Dynamical Chern-Simons Gravity
• Fast numerical method to generate halo catalogs in modified gravity (part I): second-order Lagrangian Perturbation Theory
• Cosmological fluids with boundary term couplings
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• Multi-horizons black hole solutions, photon sphere and perihelion shift in weak ghost-free Gauss-Bonnet theory of gravity
• Study on the mapping of halo clustering from real space to redshift space
• Scale-Dependent Gravitational Couplings in Parameterised Post-Newtonian Cosmology
• Exploring Modified Gravity: Constraints on the $\mu$ and $\Sigma$ Parametrization with WMAP, ACT, and SPT
• Reconstruction of the dark energy scalar field potential by Gaussian process
• Towards an optimal marked correlation function analysis for the detection of modified gravity
• Singling out modified gravity parameters and datasets reveals a dichotomy between Planck and lensing
• Reproducing the asymptotic behaviour of galaxy rotation curves by a novel constraint in general relativity
• Galileon scalar electrodynamics
• Scalar field as a null dust
• Constraining modified gravity scenarios with the 6dFGS and SDSS galaxy peculiar velocity datasets
• Euclid preparation LXXI. Simulations and nonlinearities beyond $\mathsf{\Lambda }$CDM. 3. Constraints on $f(R)$ models from the photometric primary probes
• Spectral lines of dirty wormholes
• Testing $f(T)$ Gravity with Cosmological Observations: Confronting the Hubble Tension and Implications for the Late-Time Universe
• Uncalibrated Cosmic Standards as a Robust Test on Late-Time Cosmological Models
• Toward a more stringent test of gravity with redshift space power spectrum: simultaneous probe of growth and amplitude of large-scale structure
• Testing modified gravity scenarios with direct peculiar velocities
• Dark Energy in the DESI Era: A Brief Review of Evidence, Beyond-$\Lambda$CDM Interpretations, and Tensions
• Imprint of f(R) gravity in the cosmic magnification
• The momentum constraint equation in Parameterised Post-Newtonian Cosmology
• Probing the Spin-Induced Quadrupole Moment of Massive Black Holes with the Inspiral of Binary Black Holes
• Energy-momentum squared symmetric Teleparallel gravity: $f(Q,T_{\mu \nu }{T}^{\mu \nu })$ gravity
• Cosmological test of an extended quintessence model
• Compact Binary Merger Rate with Modified Gravity in Dark-Matter Spikes
• Weak-lensing tunnel voids in simulated light cones: A new pipeline to investigate modified gravity and massive neutrinos signatures
• Thermodynamic phase transition and Joule-Thomson expansion of a quantum corrected black hole in AdS spacetime
• Constraints on higher curvature gravity from time delay between GW170817 and GRB 170817A
• On variations of $G$ in the geometric scalar theory of gravity
• The Impact of ${\Omega }_{m0}$ Prior Bias on Cosmological Parameter Estimation: Reconciling DESI DR2 BAO and Pantheon+ SNe Data Combination Results
• Quantization of Einstein-aether Scalar field Cosmology
• Ricci-Determinant Gravity: Dynamical Aspects and Astrophysical Implications
• Dynamics of holographic dark energy with apparent-horizon cutoff and non-minimal derivative coupling gravity in non-flat FLRW universe
• Special Issue on Modified Gravity Approaches to the Tensions of $\Lambda$CDM: Goals and Highlights
• Cosmological constraints from the EFT power spectrum and tree-level bispectrum of 21cm intensity maps
• Teleparallel dark energy in a nonflat universe
• The scalar-torsion gravity corrections in the first-order inflationary models
• Constrain the linear scalar perturbation theory of Cotton gravity
• The Schönberg-Chandrasekhar limit in presence of small anisotropy and modified gravity
• In-in correlators and scattering amplitudes on a causal set
• THESEUS$-$BTA cosmological tests using Multimessenger Gamma-Ray Bursts observations
• Numerical implementation of the Cubic Galileon model in PINOCCHIO
• New method of exponential potentials reconstruction based on given scale factor in phantonical two-field models
• Cosmological Solutions of Chameleon Scalar Field Model
• The quantization of Proca fields on globally hyperbolic spacetimes: Hadamard states and Møller operators
• Universal expansion with spatially varying $G$
• Probing General Relativity in galactic scales at z $\sim 0.3$
• Tidal Love Numbers of Neutron Stars in Horndeski Theories
• Einstein's Geometrical Versus Feynman's Quantum-Field Approaches to Gravity Physics: Testing by Modern Multimessenger Astronomy
• A Post-Newtonian Analysis of Regularized 4D-EGB Theory: Complete Set of PPN Parameters and Observational Constraints
• Clusternets: A deep learning approach to probe clustering dark energy
• Cosmology in holographic non-minimal derivative coupling theory: constraints from inflation and variation of gravitational constant
• Kinetic recoupling of dark matter
• Probing Fundamental Physics with Gravitational Waves
• Principal Components for Model-Agnostic Modified Gravity with 3x2pt
• Observational constraints on the Kerr and its several single-parameter modified spacetimes using quasi-periodic oscillation data
• Epicyclic oscillations and accretion disk around a special Buchdahl-inspired spacetime
• Testing beyond-Kerr spacetimes with GWTC-3
• Compact scalar field solutions in EiBI gravity
• Innermost stable circular orbits of neutron stars in dilatonic-Einstein-Gauss-Bonnet theory
• Classical and quantum cosmology of $K$-essentially modified $R^2$ and pure $R^p$ gravity
• Testing Gauss-Bonnet Gravity with DESI BAO Data
• Chameleon Gravity as an Alternative to Dark Matter
• Cosmological perturbations in the energy-momentum squared gravity theory: constraints from gravitational wave standard sirens and redshift space distortions
• Using Elliptical Galaxy Kinematics to Compare of the Strength of Gravity in Cosmological Regions of Differing Gravitational Potential -- A First Look
• Novel black holes with scalar hair in the Einstein-Maxwell-Scalar Theory with positive coupling
• On the KG-constrained general disformal transformation of the Einstein-Hilbert action
• Thermal channels of scalar and tensor waves in Jordan-frame scalar--tensor gravity
• Emergent Lorentzian dispersion relations from a Euclidean scalar-tensor theory
• Exploring Scalarized Einstein-Gauss-Bonnet Theories Through the Lens of Parametrized Post-Newtonian Formalism
• Propagation of anisotropic gravitational and electromagnetic waves at very high energies
• Recent bounds on graviton mass using galaxy clusters
• Astro- and Quantum Physical Tests of Screened Scalar Fields
• Quasilocal mass and multipole expansion in scalar-tensor gravity
• Probing gravity with the DES-CMASS sample and BOSS spectroscopy
• Analytical coordinate time at the second post-Newtonian order
• Gravity from the Determinant of the Energy-Momentum: Astrophysical Implications
• Illuminating the Dark Sector: Understanding Modified Gravity Signatures with Cross-Correlations of Gravitational Waves and Large-Scale Structure
• Compact binary system dynamics at the second post-Newtonian order: analytical formula of the coordinate time for eccentric and circular orbits
• Cosmological dynamical systems of non-minimally coupled fluids and scalar fields
• Correlation of structure growth index with current cosmic acceleration: constraints on dark energy models
• A New Paradigm for Testing Gravity: Theory-Independent Constraints Using Data From All Astrophysical and Cosmological Scales
• Cosmological dynamics of holographic dark energy with non-minimally coupled scalar field
• Shadow constraints of charged black hole with scalar hair and gravitational waves from extreme mass ratio inspirals
• Hybrid metric-Palatini gravity: Regular stringlike configurations
• Testing weakest force with coldest spot
• Exploring the self-tuning of the cosmological constant from Planck mass variation
• The Cosmological Impact of Brane-Chern-Simons Massive Gravity
• Damping of cosmological tensor modes in Horndeski theories after GW170817
• Dark energy with oscillatory tracking potential: Observational Constraints and Perturbative effects
• Higgs-Induced Screening Mechanisms in Scalar-Tensor Theories
• An ostentatious model of cosmological scalar-tensor theory
• Probing dynamical embeddings in a five-dimensional spacetime in light of DESI BAO
• gr-Orbit-Toolkit: A Python-Based Software for Simulating and Visualizing Relativistic Orbits
• Hamilton-Jacobi analysis of noncanonical inflation in $f(R,T)$ gravity: Constraints from Planck/ACT data, and theoretical bounds
• Regularized Black Hole Solution from a New String Cloud Source
• Propagation and emission of gravitational waves in the weak-field limit within the Palatini formalism
• Metric Field as Emergence of Hilbert Space
• Viscous effect in the late time evolution of phantom universe
• Constraining beyond $\Lambda$CDM models with 21cm intensity mapping forecast observations combined with latest CMB data
• Evolution of matter perturbations in the context of cosmic slowing down
• Origin & evolution of the Universe
• Cosmic magnification in beyond-Horndeski gravity
• Constraining Scalar Charge in Neutron Stars through Gravitational Wave Signals from NSBH Mergers
• Cosmology with the Roman Space Telescope -- Synergies with CMB lensing
• Hybrid $P_{\ell }(k)$: general, unified, non-linear matter power spectrum in redshift space
• First Light: Switching on Stars at the Dawn of Time
• Revisiting the equation of state of dark energy from DESI BAO with SNe Ia and CMB
• The initial value problem for gravitational waves in conformal gravity
• Cavendish experiment with fast radio bursts on cosmological scales
• Probing beyond-Horndeski gravity on ultra-large scales
• Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)