Modified gravity

Modified gravity comprises theories that change general relativity’s equations or gravitational degrees of freedom to explain observations, including cosmic acceleration, without necessarily invoking dark energy.

Scalar–tensor theory: A gravity theory in which a scalar field supplements the metric and can alter the effective strength of gravity. It adds a dynamical scalar field to gravity, a common route beyond general relativity.
General relativity: Einstein’s theory describing gravity as the curvature of spacetime sourced by matter and energy. It is the baseline theory that modified-gravity proposals extend or replace.
Accelerating expansion of the universe: The observed increase over time in the rate at which the universe expands. Modified gravity is often proposed to account for this acceleration without a dark-energy component.
MOND: A phenomenological modification of Newtonian dynamics introduced to explain galaxy rotation without dark matter. It modifies low-acceleration dynamics, unlike relativistic modified-gravity theories built by changing general relativity.
f(R) gravity: A gravity theory that replaces the Ricci scalar in the Einstein–Hilbert action with a function of that scalar. Changing the curvature term can produce cosmic acceleration and an extra scalar degree of freedom.
Ricci scalar: A scalar measure of curvature obtained by contracting the Ricci curvature tensor. It appears directly in the Einstein–Hilbert action and in many modified curvature actions.
Dark matter: Matter inferred from gravitational effects that emits little or no detectable light. Some modified-gravity proposals also seek to explain phenomena attributed to dark matter.
ΛCDM model: The standard cosmological model combining general relativity, cold dark matter, and a cosmological constant. It explains cosmic acceleration and structure using dark components rather than altered gravitational laws.
Brans–Dicke theory: A scalar–tensor theory in which a scalar field determines the effective gravitational coupling. It is a foundational example of gravity modified by a field that changes gravitational strength.
Einstein–Hilbert action: The action whose variation with respect to the metric yields Einstein’s field equations in general relativity. Many modifications begin by changing this action’s curvature or matter terms.

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