Alexei A. Starobinsky


Problems with constructing complete cosmological models in f(R)
gravity and their resolution


f(R) gravity, where R is the scalar curvature, is a phenomenological
macroscopic way to describe both types of dark energy which have
appeared during the Universe evolution: primordial dark energy
driving inflation in the early Universe and present dark energy
which has much smaller effective energy density. In the case of
inflation, the simplest R+R2 model proposed already in 1980 is
internally consistent, has a graceful exit to the radiation-dominated
FRW stage via the period of reheating in which all matter in the
Universe arises as a result of gravitational particle creation, and
remains in agreement with the most recent observational data. Moreover,
this form of f(R) may be justified by a number of microscopic models.
It is possible to construct models describing the present dark energy
in f(R) gravity which satisfy all present observational tests. However,
these models require a much more complicated form of f(R) and a very
low energy scale, so we don't have any reasonable microscopic
justification of them at present. More critical is that these models
generically cannot reproduce the correct evolution of the Universe in
the past due to formation of additional weak singularities and other
problems. Thus, to construct complete cosmological models of present
dark energy not destroying all previous achievements of the early
Universe cosmology including the recombination, the correct BBN and
inflation of any kind, one has to change the behaviour of f(R) at
large positive R and to extend f(R) to the region of negative R. I
shall describe correct ways to do it. Combined description of
primordial and present dark energy using one f(R) function is possible,
too, but it leads to completely different reheating after inflation
during which strongly non-linear oscillations of R occur.

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Last-modified: 2013-11-20 (水) 11:11:54 (2710d)