In this work we have investigated the dynamics of a recent modification to the general theory of relativity, the energy-momentum squared gravity model $f(R,{\mathbf{T}}^{\mathbf{2}})$, where $R$ represents the scalar curvature and ${\mathbf{T}}^{\mathbf{2}}$ the square of the energy-momentum tensor. By using dynamical system analysis for various types of gravity functions $f(R,{\mathbf{T}}^{\mathbf{2}})$, we have studied the structure of the phase space and the physical implications of the energy–momentum squared coupling. In the first case of functional where $f(R,{\mathbf{T}}^{\mathbf{2}})=f_0{R}^n({\mathbf{T}}^{\mathbf{2}}{)}^m$, with $f_0$ constant, we have shown that the phase space structure has a reduced complexity, with a high sensitivity to the values of the $m$ and $n$ parameters. Depending on the values of the $m$ and $n$ parameters, the model exhibits various cosmological epochs, corresponding to matter eras, solutions associated to an accelerated expansion, or decelerated periods. The second model studied corresponds to the $f(R,{\mathbf{T}}^{\mathbf{2}})=\alpha R^n+\beta {({\mathbf{T}}^{\mathbf{2}})}^m$ form with $\alpha$, $\beta$ constant parameters. In this case a richer phase space structure is obtained which can recover different cosmological scenarios, associated to matter eras, de–Sitter solutions, and dark energy epochs. Hence, this model represent an interesting cosmological model which can explain the current evolution of the Universe and the emergence of the accelerated expansion as a geometrical consequence.

The paper studies the physical characteristics for the extended $f(P)$ cubic gravity from a transitive perspective based on dynamical system analysis, by considering the linear stability theory in two specific cases, corresponding to power–law $f(P)=f_0{P}^{\alpha }$ and exponential $f(P)=f_0{e}^{\alpha P}$ gravity types, where $f_0$ and $\alpha$ are constant parameters. In these cases we have analyzed the effects in the phase space complexity, revealing the cosmological solutions attached to the critical points. For the power–law and exponential gravity types, we have noticed the presence of two cosmological epochs associated to the critical points involved, corresponding to de Sitter eras and quintessencelike epochs, described by a constant effective equation of state. For all of these solutions we have studied the dynamical characteristics which are associated to the stability properties, determining possible constraints to various parameters from a transient perspective. The dynamical prospects asserted that the extended $f(P)$ cubic gravity can represent a promising modified theory of gravitation, leading to the manifestation of the accelerated expansion at late time evolution.

In this paper we propose a new dark energy model in the teleparallel alternative of general relativity, by considering a generalized non-minimal coupling of a tachyonic scalar field with the...

The paper studies a new type of dark energy, a scalar field with positive or negative kinetic energy, generically coupled to a term which is composed by specific contractions of the Riemann tensor. After presenting the resulting field equations, we have analyzed the physical characteristics of the corresponding model by implementing the linear stability theory. In the case of an exponential coupling function and exponential potential energy, we have deduced the phase space characteristics, analyzing the critical points obtained which can represent specific eras in the evolution of the Universe. The analytical study is showing that this model can represent a feasible cosmological setup, having various epochs which correspond to stiff-fluid, matter domination, and dark energy eras, pointing toward the emergence of the accelerated expansion as a geometrical effect.

In this work we have studied a cosmological model based on a quintom dark energy model non-minimally coupled with gravity, endowed with a specific potential energy of the exponential squared type. For this specific type of potential energy and non-minimal coupling, the dynamical properties are analyzed and the corresponding cosmological effects are discussed. Considering the linear stability method, we have investigated the dynamical properties of the phase space structure, determining the physically acceptable solutions. The analysis showed that in this model we can have various cosmological epochs, corresponding to radiation, matter domination, and de Sitter eras. Each solution is investigated from a physical and cosmological point of view, obtaining possible constraints of the model’s parameters. In principle the present cosmological setup represent a possible viable scalar tensor theory which can explain various transitional effects related to the behavior of the dark energy equation of state and the evolution of the Universe at large scales.