Cosmology in nonlinear multidimensional gravity and the Casimir effect
  We study the possible cosmological models in Kaluza-Klein-type
multidimensional gravity with a curvature-nonlinear Lagrangian and a spherical
extra space, taking into account the Casimir energy. First, we find a minimum
of the effective potential of extra dimensions, leading to a physically
reasonable value of the effective cosmological constant in our 4D space-time.
In this model, the huge Casimir energy density is compensated by a fine-tuned
contribution of the curvature-nonlinear terms in the original action. Second,
we present a viable model with slowly evolving extra dimensions and power-law
inflation in our space-time. In both models, the results formulated in Einstein
and Jordan frames are compared.
