f(R,T) Gravity Theories and Cosmological Models

f(R,T) gravity represents a class of extended gravitational theories in which the standard Einstein–Hilbert action is generalised to include an arbitrary function of the Ricci scalar R and the trace T of the energy–momentum tensor. By introducing this non-minimal coupling between matter and geometry, the theory naturally generates extra terms in the field equations that act as an effective source of dark energy, potentially driving cosmic acceleration without invoking a separate exotic component. The modified field equations exhibit non-conservation of the energy–momentum tensor, leading to an additional force term that influences both cosmological evolution and astrophysical structure. In cosmology, particular choices of f(R,T) functions yield generalised Friedmann equations capable of describing early-time inflation, a subsequent matter-dominated deceleration, and a late-time accelerated expansion in a unified framework. On astrophysical scales, f(R,T) gravity has been applied to compact objects—neutron stars, white dwarfs and strange stars—to explore how matter–geometry coupling alters equilibrium configurations, mass–radius relations and stability criteria. Across these applications, the theory offers a rich phenomenology that bridges fundamental modifications to gravity with observable signatures in high-density environments and the large-scale dynamics of the Universe.

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f(R,T) Gravity Theories and Cosmological Models publication trend

The graph below shows the total number of articles in f(r,t) gravity theories and cosmological models across all publications each year (not limited to Nature Index journals).

Technical terms

f(R,T) gravity: A modified theory of gravity in which the action depends on the Ricci scalar R and the trace T of the energy–momentum tensor, introducing non-minimal coupling between matter and geometry.

Ricci scalar: A scalar curvature invariant obtained by contracting the Ricci tensor, measuring the degree to which matter curves spacetime at a point.

Energy–momentum tensor: A tensor describing the density and flux of energy and momentum in spacetime, serving as the source of gravitational fields.

Palatini formulation: A variational approach in which the metric and affine connection are treated as independent variables when deriving field equations.

Compactness: A dimensionless parameter C=2GM/(Rc²) quantifying how strongly mass M is concentrated within radius R, relevant to the stability and gravitational redshift of compact objects.

Equation of state: A relation between pressure and energy density of a fluid or matter distribution, essential for closing the system of field equations in astrophysical models.

References

1. The Effect of f(R, T) Modified Gravity on the Mass and Radius of Pulsar HerX1. The Astrophysical Journal (2023).
2. Confront f(R,T)=R+βT modified gravity with the massive pulsar PSR J0740+6620. European Physical Journal C (2023).
3. Palatini formulation of f(R, T) gravity theory, and its cosmological implications. European Physical Journal C (2018).
4. The simplest non-minimal matter–geometry coupling in the f(R, T) cosmology. European Physical Journal C (2017).
5. Compact stars in f(R,T) gravity. European Physical Journal C (2016).