Cosmological dynamics and observational constraints: The f(Q) gravity, a brief review

24 May 2024

This paper is available on arxiv under CC 4.0 license.


(1) A. Oliveros, Programa de F´ısica, Universidad del Atl´antico;

(2) Mario A. Acero, Programa de F´ısica, Universidad del Atl´antico.

2. The f(Q) gravity: a brief review

In general, the action for an f(Q) gravity model in the presence of matter components is given by

with the Levi-Civita connection of the metric given by

the contortion tensor is

Considering the flat Friedman-Robertson-Walker (FRW) metric,

with a(t) representing the scale factor, the time and spatial components of Eq. (10) are given, respectively, by [9, 10]


It should be noted that in this scenario, the standard Friedmann equations of General Relativity (GR) plus the cosmological constant are recovered when assuming that f(Q) = Q + 2Λ.

If there is no interaction between non-relativistic matter and radiation, then these components obey separately the conservation laws

As usual in the literature, it is possible to rewrite the field equations (13) and (14) in the Einstein-Hilbert form:

In this case, we assume that the equation of state parameter for this effective dark energy satisfies the following relation: