Effect of the Chameleon Scalar Field on Brane Cosmological Evolution

We have investigated a brane world model in which the gravitational field in the bulk is described both by a metric tensor and a minimally coupled scalar field. This scalar field is taken to be a chameleon with an appropriate potential function. The scalar field interacts with matter and there is an energy transfer between the two components. We find a late-time asymptotic solution which exhibits late-time accelerating expansion. We also show that the Universe recently crosses the phantom barrier without recourse to any exotic matter. We provide some thermodynamic arguments which constrain both the direction of energy transfer and dynamics of the extra dimension.Comment: 9 pages, 4 figures. To appear in Physics Letters

Scale transformation, modified gravity, and Brans-Dicke theory

A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless matter with non-vanishing modified terms together with dynamical cosmological and gravitational coupling terms. The obtained modified Einstein equations are neither those in $f(R)$ metric formalism nor the ones in $f({\cal R})$ Palatini formalism, whereas the modified source terms are {\it formally} equivalent to those of $f({\cal R})=\frac{1}{2}{\cal R}^2$ gravity in Palatini formalism. The correspondence between the present model, the modified gravity theory, and Brans-Dicke theory with $\omega=-\frac{3}{2}$ is explicitly shown, provided the dilaton field is condensated to its vacuum state.Comment: 14 pages, accepted for publication in IJT

Mach's Principle and Model for a Broken Symmetric Theory of Gravity

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that gravitational coupling may be the result of a spontaneous symmetry breaking. In this model matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. We show that after the spontaneous symmetry breaking the resulting theory is consistent with Mach's principle in the sense that inertial masses of particles have variable configurations in a cosmological context. Moreover, our analysis allows to construct a mechanism in which the resulting large vacuum energy density relaxes during evolution of the universe.Comment: 9 pages, no figure

Hadamard States and Two-dimensional Gravity

We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.Comment: 7 pages, no figur

The Coincidence Problem in Holographic f(R) Gravity

It is well-known that $f(R)$ gravity models formulated in Einstein conformal frame are equivalent to Einstein gravity together with a minimally coupled scalar field. In this case, the scalar field couples with the matter sector and the coupling term is given by the conformal factor. We apply the holographic principle to such interacting models. In a spatially flat universe, we show that the Einstein frame representation of $f(R)$ models leads to a constant ratio of energy densities of dark matter to dark energy.Comment: 10 pages, no figure

Mechanism for a Decaying Cosmological Constant

A mechanism is introduced to reduce a large cosmological constant to a sufficiently small value consistent with observational upper limit. The basic ingradient in this mechanism is a distinction which has been made between the two unit systems used on cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of the large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this manner a cancellation mechanism is presented in which the conformal factor plays a key role to relax the large effective cosmological constant.Comment: 6 pages, no figur

Cosmic Acceleration in Brans-Dicke Cosmology

We consider Brans-Dicke theory with a self-interacting potential in Einstein conformal frame. We show that an accelerating expansion is possible in a spatially flat universe for large values of the Brans-Dicke parameter consistent with local gravity experiments.Comment: 10 Pages, 3 figures, To appear in General Relativity and Gravitatio