Modified gravity: A unified approach

Abstract

Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in other popular modified gravity models. Using a more general setting the theory gives fourth order equations. This model is based on the metric alone and does not require more general geometries. It is possible to show that our new theory and the recently proposed fðQÞ gravity models are equivalent at the level of the action and at the level of the field equations, provided that appropriate boundary terms are taken into account. Our theory can also reproduce fðRÞ gravity, which is an expected result. Perhaps more surprisingly, we show that this equivalence extends to fðTÞ gravity at the level of the action and its field equations, provided that appropriate boundary terms are taken in account. While these three theories are conceptually different and are based on different geometrical settings, we can establish the necessary conditions under which their field equations are the same. The final part requires matter to couple minimally to gravity. Through this work we emphasize the importance played by boundary terms which are at the heart of our approach.

Post-Newtonian limit of generalized scalar-torsion theories of gravity

“…If we assume curvature and torsion as being zero and simultaneously nonmetricity as nonvanishing, we can construct the Symmetric Teleparallel Equivalent of General Relativity (STEGR) [4][5][6][7][8][9][10][11]. Another possibility invokes both torsion and nonmetricity [12,13]. However, even though all of these formulations are equivalent, generalization thereof differ from each other.…”

Cosmological dynamical systems in modified gravity

“…Matter is coupled minimally in GR, which means it might also be of interest to consider non-minimal couplings. The vast majority of modified gravity models being considered fall somewhere in the above description [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

“…In the following, we deal with three classes of modified gravity theories which are generally known as f (G), f (T ) and f (Q) gravity, all of which can be found in [30,31,[40][41][42] and the previously mentioned overview papers. All these models have in common that the cosmological field equations are compatible with the choice N = 1 for the lapse function.…”

“…The reason for this equivalence can be understood by carefully studying the various terms which connect these theories which are all defined in different geometrical settings. The relevant terms were identified in [30] where equivalence for more general spacetimes was also discussed. For all three models, the energy-momentum conservation equation is automatically satisfied and does not yield additional conditions to be satisfied.…”

Stability of motion and thermodynamics in charged black holes in $f(T)$ gravity

“…The usual approach in the construction of gravitational modifications is to start from the Einstein-Hilbert action and extend it in various ways [3]. Nevertheless, one can start from the equivalent torsional formulation of gravity, and in particular from the Teleparallel Equivalent of General Relativity (TEGR) [4][5][6], and modify it accordingly, obtaining f (T ) gravity [7][8][9], f (T, T G ) gravity [10], f (T, B) gravity [11][12][13], scalar-torsion theories [14][15][16], etc. Torsional gravity, can lead to interesting cosmological phenomenology and hence it has attracted a large amount of research [7,.…”