Dynamical system analysis of generalized energy-momentum-squared gravity
  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. The second model studied corresponds to the
$f(R,\mathbf{T^2})=\alpha R^n+\beta\mathbf{(T^2)}^m$ 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 represents an
interesting cosmological model which can explain the current evolution of the
Universe and the emergence of the accelerated expansion as a geometrical
consequence.
