Dynamical system analysis of generalized energy-momentum-squared gravity

Understand

In this work we have investigated the dynamics of a recent modification to the general theory of relativity, the energy-momentum squared gravity model $f(R,\mathbf{T^2})$, where $R$ represents the scalar curvature and $\mathbf{T^2}$ the square of the energy-momentum tensor.

• By using dynamical system analysis for various types of gravity functions $f(R,\mathbf{T^2})$, 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 $f(R,\mathbf{T^2})=f_0 R^n(\mathbf{T^2})^m$, 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 with an accelerated expansion, or decelerated periods.