Over the last years some interest has been gathered by $f(Q)$ theories, which are new candidates to replace Einstein’s prescription for gravity. The nonmetricity tensor $Q$ allows to put forward the assumption of a free torsionless connection and, consequently, new degrees of freedom in the action are taken into account. This work focuses on a class of $f(Q)$ theories, characterized by the presence of a general power-law term which adds up to the standard (linear in) $Q$ term in the action, and on new cosmological scenarios arising from them. Using the Markov chain Monte Carlo method, we carry out statistical tests relying upon background data such as Type Ia supernovae luminosities and direct Hubble data (from cosmic clocks), along with cosmic microwave background shift and baryon acoustic oscillations data. This allows us to perform a multifaceted comparison between these new cosmologies and the (concordance) $\mathrm{\Lambda }\mathrm{CDM}$ setup. We conclude that, at the current precision level, the best fits of our $f(Q)$ models correspond to values of their specific parameters which make them hardly distinguishable from our general relativity “échantillon,” that is, $\mathrm{\Lambda }\mathrm{CDM}$.

In this work we explore and test new formulations of cosmological scenarios in $f(Q)$ theories. In these settings, the nonmetricity scalar ($Q$) is the main source of gravity and Friedmann equations are modified to account for the associated degrees of freedom. This work focuses first on the derivation, and then theoretical and observational analysis of two such (new) exact cosmological models; they both display a nonstandard behavior in which an additional parameter encoding nonmetricity effects acts in the fashion of a screened cosmological constant. One of the new settings has the same background evolution as the well know DGP cosmological model, while the other resembles the former considerably, although its origin is purely phenomenological. We use the Markov Chain Montecarlo method combined with standard statistical techniques to perform observational astrophysical tests relying upon background data, specifically these are type Ia supernovae luminosities and direct Hubble data (from cosmic clocks), along with cosmic microwave background shift and baryon acoustic oscillations data. In addition, we compute some of the cosmographic parameters and other discriminators with the purpose of refining our knowledge about these models in the light of their theoretical and observational signatures, and this allows for a better comparison with the (concordance) $\mathrm{\Lambda }\mathrm{CDM}$ setup. We conclude that these scenarios do not show signatures indicating a departure from the $\mathrm{\Lambda }\mathrm{CDM}$ behavior.

We explore the role of the affine connection in f ( Q ) gravity, a modified theory where gravity is governed by non-metricity within the symmetric teleparallel framework. Although the connection is constrained to be flat and torsionless, it is not uniquely determined by the metric, allowing for multiple physically distinct formulations. We analyze three such connections compatible with a homogeneous and isotropic universe to show that they yield markedly different cosmological dynamics, even under the same functional form of f ( Q ). Using both analytical and numerical methods, including a Born-Infeld type model of f ( Q ), we demonstrate that specific connections can resolve cosmological singularities like the Big Bang and Big Rip, replacing them with smooth de Sitter phases. Others retain singularities but with notable modifications in their behavior. These findings highlight the physical relevance of connection choice in f ( Q ) gravity and its potential to address fundamental cosmological questions.

In this work, we explore wormhole geometries in a recently proposed modified gravity theory arising from a nonconservative gravitational theory, tentatively denoted action-dependent Lagrangian theories. The generalized gravitational field equation essentially depends on a background four-vector ${\lambda }^{\mu }$, that plays the role of a coupling parameter associated with the dependence of the gravitational Lagrangian upon the action, and may generically depend on the spacetime coordinates. Considering wormhole configurations, by using “Buchdahl coordinates,” we find that the four-vector is given by ${\lambda }_{\mu }=(0,0,{\lambda }_{\theta },0)$ and that the spacetime geometry is severely restricted by the condition $g_{tt}{g}_{uu}=-1$, where $u$ is the radial coordinate. We find a plethora of specific asymptotically flat, symmetric, and asymmetric solutions with power law choices for the function $\lambda$, by generalizing the Ellis-Bronnikov solutions and the recently proposed black-bounce geometries, among others. We show that these compact objects possess a far richer geometrical structure than their general relativistic counterparts.

In this work, we seek a cosmological mechanism that may define the sign of the effective gravitational coupling constant, G. To this end, we consider general scalar-tensor gravity theories as they provide the field theory natural framework for the variation of the gravitational coupling. We find that models with a quadratic potential naturally stabilize the value of G into the positive branch of the evolution and further, that de Sitter inflation and a relaxation to General Relativity is easily attained.