Se p 20 08 Friedmann Equation for Brans Dicke Cosmology

In the context of Brans-Dicke scalar tensor theory of gravitation, the cosmological Friedmann equation which relates the expansion rate H of the universe to the various fractions of energy density is analyzed rigorously. It is shown that BransDicke scalar tensor theory of gravitation brings a negligible correction to the matter density component of Friedmann equation. Besides, in addition to ΩΛ and ΩM in standard Einstein cosmology, another density parameter, Ω ∆ , is expected by the theory inevitably. Some cosmological consequences of such non-familiar case are examined as far as recent observational results are concerned. Theory implies that if Ω ∆ is found to be nonzero, data can favor this model and hence this theory turns out to be the most powerful candidate in place of the standard Einstein cosmological model with cosmological constant. Such replacement will enable more accurate predictions for the rate of change of Newtonian gravitational constant in the future. Bog̃aziçi Univ., Dept. of Physics, Bebek, Istanbul, Turkey Dogus Univ., Dept. of Sciences, Acibadem, Zeamet Street No: 21 34722 Kadikoy, Istanbul, Turkey E-mail: [email protected], [email protected], [email protected] Recent observational data have strongly confirmed that we live in an accelerating universe [1] and have made it possible to determine the composition of the universe [2]-[4]. According to these observations, nearly seventy percent of the energy density in the universe is unclustered (dark energy) and has negative pressure by which it is driving an accelerated expansion [5]-[8]. Furthermore, the energy density of the vacuum is much smaller than the estimated values so far. By itself, acceleration seems to be much more understandable in the context of general relativity (cosmological constant) [9] and quantum field theory (quantum zero point energy); however, the very small and non-zero energy scale implied by the observations is not quite comprehensible. Because of these conceptual problems associated with the cosmological constant [10][13], alternative treatments to the problem have been produced and they are being used widely in the literature nowadays [14]-[17]. For more detailed explanation about a number of approaches proposed so far and recent progress made towards understanding the nature of this dark energy see [18]. In some of these treatments, mostly, a scalar field φ is considered together with a suitably chosen V (φ) to make the vacuum energy vary with time. To get a model in which the current value of the cosmological constant can be expressed in a more natural way; namely, without need of any fine tuning, in Friedmann Equation for Brans Dicke Cosmology 2 the literature, there exist a number of studies on accelerated models in Brans Dicke theory [19]-[25]. For example, Sen et al [26] have found the potential relevant to power law expansion in Brans-Dicke (BD) cosmology whereas Arık and Çalık [27] have shown that BD theory of gravity with the standard mass term potential (1/2)mφ is a beneficial theory in both explaining the rapid primordial and slow late-time inflation. In this regard, we have chosen the underlying theory as a scalar tensor theory, especially, BD scalar tensor theory of gravitation since scalar-tensor theories are the most serious alternative to standard general relativity. The theory is parameterized by a dimensionless constant ω, as ω → ∞ BD theory approaches the Einstein theory [28]. In BD model, Lagrangian is defined by as in the following form