Basic Principles of 4D Dilatonic Gravity and Some of Their Consequences for Cosmology, Astrophysics and Cosmological Constant Problem

Abstract

We present a class of simple scalar-tensor models of gravity with one scalar field (dilaton $\Phi$) and only one unknown function (cosmological potential $U(\Phi )$). These models might be considered as a stringy inspired ones with broken SUSY. They have the following basic properties: 1) Positive dilaton mass, $m_{\Phi }$, and positive cosmological constant $\Lambda$, define two extremely different scales. The models under consideration are consistent with the known experimental facts if $m_{\Phi }>10^{-3}eV$ and $\Lambda ={\Lambda }^{obs}\sim 10^{-56}c{m}^{-2}$. 2) Einstein week equivalence principle is strictly satisfied and extended to scalar-tensor theories of gravity using a novel form of principle of "constancy of fundamental constants". 3) The dilaton plays simultaneously role of inflation field and quintessence field and yields a sequential hyper-inflation with graceful exit to asymptotic de Sitter space-time which is an attractor, and is approached as $\exp (-\sqrt{3{\Lambda }^{obs}}ct/2)$. The time duration of inflation is $\Delta t_{infl}\sim m_{\Phi }^{-1}$. 4) Ultra-high frequency (${\omega }_{\Phi }\sim m_{\Phi }$) dilatonic oscillations take place in asymptotic regime. 5) No fine tuning. (The Robertson-Walker solutions of general type have the above properties.) 6) A novel adjustment mechanism for cosmological constant problem seems to be possible: the huge value of cosmological constant in the stringy frame is re-scaled to its observed value by dilaton after transition to phenomenological frame.

Comments: 34 pages, 5 figures, LaTeX file, added references, corrected typos