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 (Amendola et al. in Phys Lett B 811:135923, 2020. https://doi.org/10.1016/j.physletb.2020.135923 , arXiv:2006.04209 ). The authors introduced anticurvature scalar ( A ), which is the trace of the inverse of the Ricci tensor ( A^μν = R_μν^-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 ℱ(R, A^μνA_μν) where 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 that 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.