Non-singular modified gravity unifying inflation with late-time
  acceleration and universality of viscous ratio bound in F(R) theory
  The review of basic cosmological properties of four-dimensional F(R)-gravity,
including FRW equations of motion and its accelerating solutions, generalized
fluid and scalar-tensor representation of the theory is done. Cosmological
reconstruction equation is written and conditions for stability of cosmological
solution are discussed. The overview of realistic F(R)-models unifying
inflation with dark energy epoch is made. The avoidance of finite-time future
singularities in such theories via the introduction of R^2-term is studied. New
realistic non-singular F(R)-gravity unifying early-time inflation with
late-time acceleration is presented. The exit from inflationary era in such
model may be caused by the gravitational scenario. It is demonstrated that
five-dimensional F(R)-gravity considered as non-perturbative stringy effective
action leads to universal relation for viscous bound ratio.
