Observational constraints on nonlinear matter extensions of general
  relativity
  We present a phenomenological analysis of current observational constraints
on classes of FLRW cosmological models in which the matter side of Einstein's
equations includes, in addition to the canonical term, a term proportional to
some function of the energy-momentum tensor
($T^2=T_{\alpha\beta}T^{\alpha\beta}=\rho^2+3p^2$), or of its trace
($T=\rho-3p$). Qualitatively, one may think of these models as extensions of
general relativity with a nonlinear matter Lagrangian. As such they are
somewhat different from the usual dynamical dark energy or modified gravity
models: in the former class of models one adds further dynamical degrees of
freedom to the Lagrangian (often in the form of scalar fields), while in the
latter the gravitational part of the Lagrangian is changed. We study both of
these models under two different scenarios: (1) as phenomenological
two-parameter or three-parameter extensions of the standard $\Lambda$CDM, in
which case the model still has a cosmological constant but the nonlinear matter
Lagrangian leads to additional terms in Einstein's equations, which
cosmological observations tightly constrain, and (2) as alternatives to
$\Lambda$CDM, where there is no cosmological constant, and the nonlinear matter
term would have to provide the acceleration (which would be somewhat closer in
spirit to the usual modified gravity models). A comparative analysis of the
observational constraints obtained in the various cases provides some insight
on the level of robustness of the $\Lambda$ model and on the parameter space
still available for phenomenological alternatives.
