We introduce a four-dimensional dilaton-BransDicke cosmological scenario corresponding to multiverse filled with dark energy or phantom energy having a positive cosmological constant and containing infinite singularities with eternally Big Rip. Many interesting consequences are revealed and discussed in some details.Keywords Generalized Chaplygin gas · Dilaton Brans-Dicke scalar field · Dynamical cosmological constant · Dark energy · Phantom energy · Big Rip · Multiverse Perhaps one of the greatest challenges in modern cosmology in the present day would be to comprehend the appearance and nature of the observed late-time universe acceleration and propose an answer to the so-called cosmic coincidence conundrum which concerns the enigma: why at the present epoch are the energy densities of dark energy and of dustlike dark matter of the same order of magnitude? Moreover, the addressed question: "why the universe starts to accelerate very recently after the completion of galaxies and clusters of galaxies" is not solved even if a positive cosmological constant is present. For instance, according to the Hubble diagram of supernovae type SNIa, the astronomical results of the WMAP satellite and the large scale structures of the universe seems to confirm that the universe is in an accelerated phase (discovery in observational cosmology in recent years. SNIa observations also provide the evidence of a decelerated universe in the recent past with transition from deceleration to acceleration occurring at redshift z(q = 0) ≈ 0.5 while the Cosmic Microwave Background (CMB) observations sustain a spatially flat universe as predicted by most of the inflationary scenarios. The universe energy density appears to consist of approximately 4% of that of Visible Matter, 21% of that of Dark Matter and 75% of that of Dark Energy (DE). In reality, the nature of DE is one of the most profound problems in high energy physics and astrophysics. Up to now, the most conservative candidate and natural explanation for the DE is the positive cosmological constant, however, the unusual large value of the cosmological constant arising out of the spontaneously broken field theoretic vacuum leads to the search for alternative dynamical dark energy models. Perhaps the most fashionable candidate with non-trivial dynamics is the quintessence (slowly-rolling scalar field) (Peebles and Ratra 2003). Both the cosmological constant and quintessence are also often termed vacuum energy. A lot of works has been done and a new class of cosmological models characterized by exotic type of scalar fields has been conjectured for modeling the DE in terms of sub-negative pressure to solve the quintessence trouble. These models include the K-essence, viscous fluid, Chaplygin gas with equation of state p = −Kρ −1 , ρ > 0, K ∈ R (p is the spatially homogeneous pressure and ρ the energy density) (Fabris et al. 2002), Generalized Chaplygin gas (GCG) model whose equation of state is p = −Kρ −a , ρ > 0, 0 < a ≤ 1 (Bento et al. 2002), exotic matters with generalized equation ...
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