Einstein's general relativity is the simplest plausible theory of gravity that can be based on just one symmetric tensor field (the metric tensor).
Others include: Starobinsky (R+R^2) gravity, Gauss–Bonnet gravity, f(R) gravity, and Lovelock theory of gravity..
Essentially, modified gravity assumes that on the largest and/or smallest scales, gravity acts in novel ways compared to the well-tested scales in the middle (including those ceaselessly probed by toddlers)..
The idea of modifying gravity on cosmological scales has really taken off over the past decade.
This has been triggered, in part, by theoretical developments involving higher dimensional theories, as well as new developments in constructing renormalizable theories of gravity.
By additionally factoring in a measurement of gravitational redshift, future surveys could have the power to distinguish between these possibilities.
The gravitational slip — or the difference in the way gravity is felt by matter and light — is widely accepted as a key cosmological signature of modified gravity 1.
[Submitted on 22 Jun 2020 ( v1 ), last revised 10 Feb 2021 (this version, v4)] A covariant modified gravity (MOG) is formulated by adding to general relativity two new degrees of freedom, a scalar field gravitational coupling strength G = 1/χ and a gravitational spin 1 vector field ϕμ.
The term ‘gravitational theory’ can then be functionally defined by the set of field equations obeyed by the rank-2 tensor, and any other non-matter fields it interacts with.
If these equations are anything other than Einstein’s equations, then we consider it to be a ‘modified theory of gravity’.
