In this work, we consider an extension of symmetric teleparallel gravity, namely, $f(Q)$ gravity, where the fundamental block to describe spacetime is the nonmetricity, $Q$. Within this formulation of gravitation, we perform 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 parametrizations of $f(z)$ are proposed, including new terms which would allow for deviations from the $\mathrm{\Lambda }$ Cold Dark Matter model. Given a variety of observational probes, such as the expansion rate data from early type galaxies, type Ia supernovae, quasars, gamma ray bursts, baryon acoustic oscillations data, and cosmic microwave background distance priors, we have checked the validity of these models at the background level in order to verify if this new formalism provides us with plausible alternative models to explain the late time acceleration of the Universe. Indeed, this novel approach provides a different perspective on the formulation of observationally reliable alternative models of gravity.

Dark energy and dark matter are the dominant sources in the evolution of the late universe. They are currently only indirectly detected via their gravitational effects, and there could be a coupling between them without violating observational constraints. We investigate the background dynamics when dark energy is modeled as exponential quintessence and is coupled to dark matter via simple models of energy exchange. We introduce a new form of dark sector coupling, which leads to a more complicated dynamical phase space and has a better physical motivation than previous mathematically similar couplings.

We illustrate how form-invariance transformations can be used for constructing phantom cosmologies from standard scalar field universes. First we discuss how to relate two flat Friedmann-Robertson-Walker cosmologies with different barotropic indexes $\gamma$ and $\overline{\gamma }$. Then we consider the particular case $\overline{\gamma }=-\gamma$, and we show that, if the matter content is interpreted in terms of self-interacting scalar fields, then the corresponding transformation provides the link between a standard and a phantom cosmology. After that, we illustrate the method by considering models with exponential potentials. Finally, we also show that the mentioned duality persists even if the typical brane-world modifications to the Friedmann equation are considered.

In this paper we analyze the effect of recently proposed classes of sudden future singularities on causal geodesics of FLRW spacetimes. Geodesics are shown to be extendible and just the equations for geodesic deviation are singular, although tidal forces are not strong enough to produce a Big Rip. For the sake of completeness, we compare with the typical sudden future singularities of phantom cosmologies.

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, $\mathrm{\Lambda }\mathrm{CDM}$.