Disappearing cosmological constant in **f(R)** gravity

A. A. Starobinsky

Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia

Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

PACS: 04.50.+h, 95.36.+x, 98.80.-k

**Abstract**

For higher-derivative f(R) gravity where R is the Ricci scalar,
a class of models is proposed which produce viable cosmology different
from the LambdaCDM one at recent times and satisfy cosmological, Solar
system and laboratory tests. These models have both flat and de Sitter
space-times as particular solutions in the absence of matter. Thus,
a cosmological constant is zero in flat space-time, but appears
effectively in a curved one for sufficiently large R. A 'smoking gun'
for these models would be small discrepancy in values of the slope of
the primordial perturbation power spectrum determined from galaxy
surveys and
CMB fluctuations. On the other hand, a new problem for dark energy
models based on f(R) gravity is pointed which is
connected with possible overproduction of new massive scalar particles
(scalarons) arising in this theory in the very early Universe.