FRW cosmology from five dimensional vacuum Brans–Dicke theory

Abstract

We follow the approach of induced-matter theory for a five-dimensional (5D) vacuum Brans-Dicke theory and introduce induced-matter and induced potential in four dimensional (4D) hypersurfaces, and then employ a generalized FRW type solution. We confine ourselves to the scalar field and scale factors be functions of the cosmic time. This makes the induced potential, by its definition, vanishes, but the model is capable to expose variety of states for the universe. In general situations, in which the scale factor of the fifth dimension and scalar field are not constants, the 5D equations, for any kind of geometry, admit a power-law relation between the scalar field and scale factor of the fifth dimension. Hence, the procedure exhibits that 5D vacuum FRW-like equations are equivalent, in general, to the corresponding 4D vacuum ones with the same spatial scale factor but a new scalar field and a new coupling constant,ω. We show that the 5D vacuum FRW-like equations, or its equivalent 4D vacuum ones, admit accelerated solutions. For a constant scalar field, the equations reduce to the usual FRW equations with a typical radiation dominated universe. For this situation, we obtain dynamics of scale factors of the ordinary and extra dimensions for any kind of geometry without any priori assumption among them. For nonconstant scalar fields and spatially flat geometries, solutions are found to be in the form of power-law and exponential ones. We also employ the weak energy condition for the induced-matter, that gives two constraints with negative or positive pressures. All types of solutions fulfill the weak energy condition in different ranges. The 123 848 A. F. Bahrehbakhsh et al.power-law solutions with either negative or positive pressures admit both decelerating and accelerating ones. Some solutions accept a shrinking extra dimension. By considering non-ghost scalar fields and appealing the recent observational measurements, the solutions are more restricted. We illustrate that the accelerating power-law solutions, which satisfy the weak energy condition and have non-ghost scalar fields, are compatible with the recent observations in ranges −4/3 < ω ≤ −1.3151 for the coupling constant and 1.5208 ≤ n < 1.9583 for dependence of the fifth dimension scale factor with the usual scale factor. These ranges also fulfill the conditionω > −3/2 which prevents ghost scalar fields in the equivalent 4D vacuum Brans-Dicke equations. The results are presented in a few tables and figures.

Chameleon field dynamics during inflation

“…[64], the chameleon is slow rolling along the minimum of the effective potential and hence, follows the attractor solution φ ≈ φ min as long as m φ H. Such a condition, using equation (21) and definition m 2 φ = V eff (φ min ), leads to η 1 1. 1 Hence, by considering it into relation (30), one can neglect with respect to η 1 , and in turn, neglects the termφ with respect to η 1 Hφ term due to condition (19). Therefore, relation (30) reads…”

Cosmological and solar system consequences off(R,T)gravity models

“…For this purpose, the first-order Taylor expansion of the field equation (5.1) yields 20) of which the tt, rr, and θθ equations, for a pressureless fluid, are approximated to give 23) where the prime indicates differentiation with respect to r. By considering solution (5.15), one does expect that Ψ(r) and Φ(r) will have similar functionality to r, which implies that the terms R (s) Ψ and R (s) Φ are of second-order, and hence we have neglected them in obtaining the filed equations (5.21)-(5.23). Therefore, the most general form of the potential Ψ(r), outside the body, using (5.14), (5.15), and (5.21), can be obtained as 24) where C 1Ψ and C 2Ψ are the integral constants and we have assumed F (b) = 0. One can set C 2Ψ = 0 as usually done in the Newtonian limit.…”

“…Other theories of this type are loop quantum gravity/cosmology [6][7][8], theories based on the Ads/CFT correspondence [9,10] and the holographic gravity/cosmology [11,12]. In addition, there are higher-order gravities including the special case f (R) gravity [13][14][15][16][17][18][19], the induced gravity [20,21], the scalar-tensor theories with the special case of Brans-Dicke theory [22][23][24][25][26][27][28], higher-dimensional theories, e.g., the Kaluza-Klein theories [29] and the braneworld scenarios [30]. Also, there are theories that introduce some modifications in the matter component [31,32] or change the geometrical structure, e.g., the non-commutative theories [33][34][35][36][37][38].…”

Interacting Induced Dark Energy Model

“…where we consider T (X) αβ as dark energy component of the energy-momentum tensor that analogous to the IM theory [42] and [43], defined by…”