Alexei A. Starobinsky

Title:

Problems with constructing complete cosmological models in f(R)

gravity and their resolution

Abstract:

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.