Dark Energy Oscillations in Mimetic $F(R)$ Gravity
  In this paper we address the problem of dark energy oscillations in the
context of mimetic $F(R)$ gravity with potential. The issue of dark energy
oscillations can be a problem in some models of ordinary $F(R)$ gravity and a
remedy that can make the oscillations milder is to introduce additional
modifications in the functional form of the $F(R)$ gravity. As we demonstrate
the power-law modifications are not necessary in the mimetic $F(R)$ case, and
by appropriately choosing the mimetic potential and the Lagrange multiplier, it
is possible to make the oscillations almost to vanish at the end of the matter
domination era and during the late-time acceleration era. We examine the
behavior of the dark energy equation of state parameter and of the total
effective equation of state parameter as functions of the redshift and we
compare the resulting picture with the ordinary $F(R)$ gravity case. As we also
show, the present day values of the dark energy equation of state parameter and
of the total effective equation of state parameter are in better agreement with
the observational data, in comparison to the ordinary $F(R)$ gravity case.
Finally, we study the evolution of the growth factor as a function of the
redshift for all the mimetic models we shall use.
