Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity

Abstract

We generalize and unify the $f(R,T)$ and $f(R,L_m)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$, of the trace of the energy-momentum tensor $T$, and of the matter Lagrangian $L_m$, so that $L_{grav}=f(R,L_m,T)$. We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy-momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov-Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $f(R,L_m,T)$ of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

21 pages, 3 figures, accepted for publication in EPJC; references added

References in corpus (39)

• f(R,T) gravity
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Disappearing cosmological constant in f(R) gravity
• Beyond the Cosmological Standard Model
• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• Extra force in $f(R)$ modified theories of gravity
• The Radial Acceleration Relation in Rotationally Supported Galaxies
• f(R,L_m) gravity
• Early dark energy, the Hubble-parameter tension, and the string axiverse
• One Law To Rule Them All: The Radial Acceleration Relation of Galaxies
• The Megamaser Cosmology Project. XIII. Combined Hubble constant constraints
• Modified gravity with arbitrary coupling between matter and geometry
• Thermodynamic interpretation of the generalized gravity models with geometry - matter coupling
• Dark matter as a geometric effect in f(R) gravity
• Modelling wormholes in $f(R,T)$ gravity
• Static Spherically Symmetric Wormholes in $f(R,T)$ Gravity
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• Energy-Momentum Squared Gravity
• Causal Limit of Neutron Star Maximum Mass in $f(R)$ Gravity in View of GW190814
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• Thin accretion disks in f(R) modified gravity models
• Unifying of Inflation with Early and Late Dark Energy Epochs in Axion $F(R)$ Gravity
• Wormholes in $R^2$-gravity within the $f(R,T)$ formalism
• Cosmology of hybrid metric-Palatini f(X)-gravity
• Generalized virial theorem in f(R) gravity
• Dark energy as a massive vector field
• Extended $f(R,L_m)$ gravity with generalized scalar field and kinetic term dependences
• New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state
• Geodesic deviation, Raychaudhuri equation, and tidal forces in modified gravity with an arbitrary curvature-matter coupling
• Quantum Cosmology of $f(R,T)$ gravity
• Radial oscillations and stability of compact stars in $f(R,T)=R+2\beta T$ gravity
• Gauge Structure of Teleparallel Gravity
• To conserve, or not to conserve: A review of nonconservative theories of gravity
• Late time cosmological approach in mimetic $f(R,T)$ gravity
• Matter may matter
• Unimodular $f(R,T)$ Gravity
• Lessons from $f(R,R_c^2,R_m^2,L_m)$ gravity: Smooth Gauss-Bonnet limit, energy-momentum conservation and nonminimal coupling

Cited by in corpus (6)

• Existence of Non-singular Stellar Solutions within the context of Electromagnetic Field: A Comparison between Minimal and Non-minimal Gravity Models
• Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity
• Thermodynamics and Perturbative Analysis of Some Newly Developed $\mathcal{F}(R,L_m,T)$ Theories Under the Scenario of Conserved Energy-momentum Tensor
• Moment of inertia and compactness of quark stars within the context of $f(R,T,L_m)$ gravity
• Relativistic structure of charged quark stars in energy-momentum squared gravity
• Non-Singular Collapse Scenario From Matter-Curvature Coupling