Modified Gravity

Modified gravity refers to theories that alter Einstein's field equations or the gravitational action to produce cosmological effects without invoking invisible matter or energy components. Rather than explaining cosmic acceleration through a cosmological constant or dark energy, modified gravity theories change how gravity itself behaves on large scales, potentially mimicking dark phenomena through geometric or dynamical modifications.

Prominent examples include f(R) gravity, which replaces the Ricci scalar R in the Einstein-Hilbert action with an arbitrary function f(R); TeVeS, a relativistic extension of Modified Newtonian Dynamics (MOND) that attempts to explain galaxy rotation curves without dark matter; and DGP braneworld models, in which gravity leaks into extra dimensions at large distances, weakening its strength and altering expansion history.

Modified gravity is often framed as a competitor to the Lambda-CDM paradigm, but the two are not symmetric alternatives. Lambda-CDM adds new fields to the stress-energy tensor; modified gravity changes the tensor itself. The distinction is subtle but profound: dark energy is a matter hypothesis, modified gravity is a geometry hypothesis. The Hubble tension has revived interest in modified gravity because some models can alter the expansion history in ways that bridge the gap between early and late measurements — though most such models predict other observational signatures that have not been detected.