Yuri Shtanov, Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
Facets of f(R) gravity: inflation, dark matter, scale symmetry breaking
We discuss several facets of the metric f(R) gravity theory coupled to the Standard Model. The theory contains an extra scalar degree of freedom (the scalaron), which can be employed in several interesting ways. Firstly, if the scalaron is very heavy, it can play the role of an inflaton. In this case, a typical f(R) theory is equivalent to scalar-field models with hilltop or tabletop potentials in the Einstein frame. Inflationary evolution in such models can proceed in two alternative directions: towards the stable point at small scalar curvature describing the observable universe, or towards the asymptotic region at large scalar curvature. A universe evolving towards this asymptotically free gravity region will either run into a "Big-Rip" singularity or inflate eternally. Secondly, the scalaron in metric f(R) gravity can be a dark-matter candidate if its mass lies in the range between around 4 meV and 1.2 MeV. The scalaron manifests itself as an almost sterile cold dark matter, and one of its possible observational verifications consists in measuring specific Yukawa gravitational forces on submillimeter spatial scales. We will discuss initial conditions for the scalaron in the early universe and the role played by the Higgs field and electroweak crossover in the formation of these initial conditions. Thirdly, the scalaron in scale-invariant R^2 gravity theory can play the role of a massless dilaton breaking the scale (and electroweak) symmetry and generating the mass scale in quantum field theory. We briefly discuss this model and its fine-tuning.