Dark energy and cyclic universe from Arnowitt-Deser-Misner renormalizable group approach

Abstract

We discuss the generic features of the accelerated universe from Arnowitt-Deser-Misner renormalizable group approach applied for gravity models with variable gravitational coupling constant and cosmological constant. The universe undergoes an endless sequence of cosmic eras which starts inflating after a Big Bang and end contracting to a Big Crunch dominated by phantom energy. Presently, the universe found to be presently accelerating in time and is dominated by dark energy. Some important features and numerical results are revealed and discussed in some details.Keywords: Ddark energy; Phantom energy; ADM formalism, accelerated expansion; Cyclic universe; Bekenstein entropy Recent astronomical observation on the Cosmic Microwave Background (CMB) Anisotropy [1] and Supernova Type Ia (SNIa) [2] suggest that our Universe undergoes a phase of accelerated expansion tending to a flat de-Sitter space-time as predicted by inflation theory [3] and in accord with recent findings of BOOMERANG experiments [4]. In fact 70% of the total density results from a mysterious and unknown vacuum energy density or an effective equivalent, and weakly interacting dark matter [5][6][7][8][9]. The nature of the dark energy component represents one of the most profound and important tasks for modern cosmology, astrophysics and theoretical physics. This dark energy was important in the past as it is now. It might have played a part in limiting the formation of largest gravitationally bound structures. Several candidates to represent and explain dark energy have been postulated and confronted with observations: the Λ CDM (Λ-Cold-Dark-Matter) matter [10] consisting a mixture of cosmological constant Λ and cold dark matter (CDM) or WIMPS composed of weakly interacting massive particles which must be relics of a grand unified phase of the Universe, quintessence with a very shallow many-forms potential [11], K-essence [12], viscous fluid [13], Chaplygin gas [14,15], Generalized Chaplygin gas model (GCGM) which mimics both dark matter and dark energy [16,17], Brans-Dicke (BD) pressureless solutions [18] and so on.Most of these theories are problematic and faced many difficulties. For example, within the framework of the ΛCDM cosmological scenario, the vacuum energy is set to be constant with time while the matter energy density is a decreasing quantity, their ratio must be set to a specific infinitesimally small value 10 −120 in the early Universe so as to nearly coincide today, i.e. a huge vacuum energy which by about 120 orders of magnitude exceeds the experimental limit. This is the famous "cosmic coincidence" problem (CCP). Present astronomical observations indicate that the matter contribution Ω m to the present universe is such that 0.1 < Ω m < 0.4. One can model the dark energy by a cosmological constant (or a vacuum decaying energy). One interesting possibility is that the cosmological constant may be effective, and indeed could be varying with cosmic time. As we strongly believe that the effective cosmological constant is very close to ...