On exponential modified gravity
  A modified theory of gravity with the function $F(R) = R\exp(\alpha R)$
instead of Ricci scalar $R$ in the Einstein$-$Hilbert action is considered and
analyzed. The action of the model is converted into Einstein$-$Hilbert action
at small value of the parameter $\alpha$. From local tests we obtain a bound on
the parameter $\alpha\leq 10^{-6}$ cm$^2$. The Jordan and Einstein frames are
investigated and the potential of the scalar field in Einstein's frame is
found. The mass of a scalar degree of freedom as a function of curvature is
obtained. The static solutions of the model are found corresponding to the
Schwarzschild$-$de Sitter space. We show that the de Sitter space is unstable
but a solution with zero curvature is stable. The cosmological parameters of
the model are calculated. It was demonstrated that the model passes the matter
stability test.
