1209.2695 (Plamen P. Fiziev)

Withholding Potentials, Absence of Ghosts and Relationship between
Minimal Dilatonic Gravity and f(R) Theories    [PDF]

Plamen P. Fiziev

We study the relation between Minimal Dilatonic Gravity (MDG) and f(R) theories of gravity and establish strict conditions for their equivalence. Such equivalence takes place only for a certain class of cosmological potentials, dubbed here withholding potentials, since they prevent change of the sign of dilaton $\Phi$. The withholding property ensures the attractive character of gravity, as well as absence of ghosts and a tachyon in the gravi-dilaton sector. Large classes of withholding cosmological potentials and functions $f(R)$ are found and described in detail. It is shown that the popular choices of $f(R)$ functions are not withholding ones. The particle content of the gravi-dilaton sector is found using perturbation theory around de Sitter vacuum of MDG. It is shown that the graviton acquires a very small mass $m_{g}\approx 3 \times 10^{-38} m_e$, $m_e$ being the mass of the electron. The mass of the dilaton is much larger: $m_{\Phi}\gtrapprox 10^{29} m_{g}$. Two new phenomena: scalaron waves and induction of gravitational waves by the scalaron field are discussed using the derived wave equations for scalaron and graviton. Thus, the MDG and f(R) theories are shown to predict physical deviations from GR. Seemingly, the MDG and f(R) theories, when equivalent, offer a unified description of dark energy and dark matter.

View original: http://arxiv.org/abs/1209.2695