A modified theory of gravity where gravity arises from spacetime non-metricity rather than curvature.F(Q) gravity is a modified theory of gravity that generalizes the concept of spacetime geometry. Instead of using curvature (as in Einstein's general relativity) or torsion (as in teleparallel gravity), F(Q) gravity is based on non-metricity, which measures how much the metric tensor changes as it is parallel transported. In this framework, gravity is not a curvature of spacetime but a manifestation of the non-metricity of the connection. The theory is named after the function F(Q), where Q is the non-metricity scalar, and different choices of F lead to different gravitational dynamics.
The concept of non-metricity in gravity has roots in early 20th-century geometry, but the specific F(Q) gravity theory was formulated in the late 2010s. A key paper by Jiménez, Heisenberg, and Koivisto in 2018 introduced the symmetric teleparallel framework and its connection to general relativity, and subsequent works generalized it to F(Q) gravity.
In F(Q) gravity, the gravitational action is a function of the non-metricity scalar Q, which is constructed from the non-metricity tensor. The field equations are derived by varying this action with respect to the metric, yielding modified Einstein equations. For the special case F(Q) = Q, the theory reduces to symmetric teleparallel gravity, which is equivalent to general relativity. Choosing a nonlinear F(Q) introduces extra degrees of freedom that can modify gravitational behavior, potentially explaining cosmic acceleration without dark energy or providing alternative models for galactic rotation curves.
F(Q) gravity is primarily a theoretical framework used in cosmology to model the accelerated expansion of the universe and in astrophysics to study gravitational phenomena beyond general relativity. It is also a testing ground for alternative theories of gravity in the context of observational data.
In F(Q) gravity, the gravitational interaction is not due to the bending of spacetime but due to the 'stretching' of the metric itself, which is a fundamentally different geometric interpretation than Einstein's curvature.














