f(T) teleparallel gravity and cosmology.

Over recent decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f (T) gravity, where f (T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f (T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f (T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, alternative to a cosmological constant, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, for a certain class of f (T) models, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations-or, alternatively, the Big Bang singularity can be avoided at even earlier moments due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f (T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f (T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f (R) gravity, trying to illuminate the subject of which formulation, or combination of formulations, might be more suitable for quantization ventures and cosmological applications.

Quintom cosmology and modified gravity after DESI 2024.

We reconstruct the cosmological background evolution under the scenario of dynamical dark energy through the Gaussian process approach, using the latest Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillations (BAO) combined with other observations. Our results reveal that the reconstructed dark-energy equation-of-state (EoS) parameter w(z) exhibits the so-called quintom-B behavior, crossing -1 from phantom to quintessence regime as the universe expands. We investigate under what situation this type of evolution could be achieved from the perspectives of field theories and modified gravity. In particular, we reconstruct the corresponding actions for f(R),f(T), and f(Q) gravity, respectively. We explicitly show that, certain modified gravity can exhibit the quintom dynamics and fit the recent DESI data efficiently, and for all cases the quadratic deviation from the ΛCDM scenario is mildly favored.

Modified cosmology through nonextensive horizon thermodynamics.

We construct modified cosmological scenarios through the application of the first law of thermodynamics on the universe horizon, but using the generalized, nonextensive Tsallis entropy instead of the usual Bekenstein-Hawking one. We result to modified cosmological equations that possess the usual ones as a particular limit, but which in the general case contain extra terms that appear for the first time, that constitute an effective dark energy sector quantified by the nonextensive parameter δ . When the matter sector is dust, we extract analytical expressions for the dark energy density and equation-of-state parameters, and we extend these solutions to the case where radiation is present too. We show that the universe exhibits the usual thermal history, with the sequence of matter and dark-energy eras, and according to the value of δ the dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or experience the phantom-divide crossing during the evolution. Even in the case where the explicit cosmological constant is absent, the scenario at hand can very efficiently mimic Λ CDM cosmology, and is in excellent agreement with Supernovae type Ia observational data.