Can we bypass no-go theorem for Ricci-inverse Gravity?
  Recently, Amendola et al. proposed a geometrical theory of gravity containing
higher-order derivative terms. The authors introduced anticurvature scalar
$(A)$, which is the trace of the inverse of the Ricci tensor ($A^{\mu\nu} =
R_{\mu\nu}^{-1}$). In this work, we consider two classes of Ricci-inverse --
Class I and Class II -- models. Class I models are of the form $f(R, A)$ where
$f$ is a function of Ricci and anticurvature scalars. Class II models are of
the form ${\cal F}(R, A^{\mu\nu}A_{\mu\nu})$ where ${\cal F}$ is a function of
Ricci scalar and square of anticurvature tensor. For both these classes of
models, we numerically solve the modified Friedmann equations in the redshift
range $1500 < z < 0$. We show that the late-time evolution of the Universe,
i.e., evolution from matter-dominated epoch to accelerated expansion epoch, can
not be explained by these two classes of models. Using the reduced action
approach, we show why we can not bypass the no-go theorem for Ricci-inverse
gravity models. Finally, we discuss the implications of our analysis for the
early-Universe cosmology.
