Einstein and Brans–Dicke Frames in Multidimensional Cosmology

Abstract

Inhomogeneous multidimensional cosmological models with a higher dimen-are investigated under dimensional reduction to a D 0 -dimensional effective non-minimally coupled σ-model which generalizes the familiar Brans-Dicke model. It is argued that the Einstein frame should be considered as the physical one. The general prescription for the Einstein frame reformulation of known solutions in the Brans-Dicke frame is given. As an example, the reformulation is demonstrated explicitly for the generalized Kasner solutions where it is shown that in the Einstein frame there are no solutions with inflation of the external space. 04.50.+h, 98.80.Hw

On Observational Predictions from Multidimensional Gravity

“…A feature of interest is the universal prediction of β > 1 in (53) for both frames (42) and (43). This conclusion does not depend on the system integrability and rests solely on the positivity of energy required.…”

“…The choice of a physical CF in non-Einsteinian theories of gravity is widely discussed, but the discussion is mostly restricted to the 4-dimensional metric -see e.g. [41,42,43] and numerous references therein. There are arguments in favour of the Einstein frame, and the most important ones, applicable to higher order and scalar-tensor theories (and many multiscalar-tensor theories obtainable from multidimensional gravity) are connected with the positivity of scalar field energy and the existence of a classically stable ground state [41,42]; though, these requirements are violated if quantum effects are taken into account [4].…”

Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein–Gauss–Bonnet model with a $$\Lambda $$ Λ -term

“…The evolution of the l-dimensional internal factor space is described by the Hubble-like parameter h. It is widely known that the 4d effective gravitational constant G = G e f f in the Brans-Dicke-Jordan (or simply Jordan) frame [35] (see also [36]) is proportional to the inverse volume scale factor of the internal space, see [37,39] and references therein.…”

“…We also consider a subclass of solutions which correspond to a small enough variation of the effective gravitational constant G in the Jordan frame [35,36] (see also [37][38][39] and Refs. therein).…”

Problem of inflation in nonlinear multidimensional cosmological models

“…They are geometrical moduli (radions, gravexcitons) which are related to the shape of internal spaces (to scale factors of the internal spaces). After dimensional reduction to four dimensions, scalar field potential is completely defined by the topology and matter content of original higherdimensional model [2,3]. Thus, it is of undoubted interest to realize inflation in these models (see e.g.…”