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by Cosmological thinking: time, space and universal causation May 24th, 2024

This paper is available on arxiv under CC 4.0 license.

**Authors:**

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

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

- Abstract and Intro
- The f(Q) gravity: a brief review
- Cosmological dynamics in late-time
- Parameter constraints
- Conclusions
- Acknowledgments and References

*Keywords*: Modified gravity, Dark energy, f(Q) gravity, parameter constraints.

*PACS*: 04.50.Kd, 98.80.-k

For over two decades, significant efforts have been dedicated to cosmological research in pursuit of an explanation of the observed late-time cosmic acceleration. The primary avenue of investigation involves the introduction of a novel energy component within the Universe, termed dark energy (DE), which is distinguished by its negative pressure. Nevertheless, as of the present time, a definitive and satisfactory resolution to the enigma of DE remains elusive; its incorporation into the framework of fundamental physics theories continues to challenge researchers (for a comprehensive review about this topic see Refs. [1, 2, 3]).

One of the intriguing approaches for elucidating the late-time cosmic acceleration, beyond the inclusion of either DE or novel forms of matter to account for this phenomenon, lies within the field of modified gravity theories (see e.g. Refs. [4, 5, 6] for a review). Usually, in this framework, the fundamental action is built assuming generalized functions of the scalar curvature (the so-called f(R) theories), general higher-order theories, scalar–tensor theories of gravitation, etc. Recently, a new proposal has emerged within the realm of modified theories of gravitation. These particular theories, in which gravitational interactions are governed by non-metricity, with curvature and torsion being rendered negligible, are known as f(Q) theories or f(Q) symmetric teleparallel gravity, where Q is the non-metricity scalar [7, 8, 9, 10, 11]. These theoretical frameworks hold the potential to provide fresh perspectives on the phenomenon of cosmic acceleration, stemming from the inherent consequences of an alternative geometry as opposed to the conventional Riemannian framework (see Ref. [12] for a recent and extensive review on this topic).

Although this proposal is very recent, there are numerous works in the literature that have been carried out using it [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]. Usually, owing to the presence of nonlinear elements within the field equations, one of the principal challenges inherent in these scenarios pertains to the task of deriving solutions, whether through analytical or numerical means. Although, commonly the field equations are solved numerically, it is also an usual try to propose a parametrization of either the Hubble parameter, the equation state parameter or f(Q) in terms of the redshift, among other strategies.

For instance, in Ref. [13] the authors performed an observational analysis of several modified f(Q) models using the redshift approach, where the f(Q) Lagrangian is reformulated as an explicit function of the redshift, f(z). Various different polynomial parameterizations of f(z) are proposed, including new terms which would allow for deviations from the ΛCDM model. In Ref. [27] a new parametrization of the Hubble parameter is proposed in a model-independent way and apply it to the Friedmann equations in the FLRW Universe. Also, the authors of Ref. [38] implemented a parametrization scheme for the Hubble parameter, obtaining an exact solution for the field equations in f(Q) cosmology.

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