The conformal status of $\omega =-3/2$ Brans-Dicke cosmology

Abstract

Following recent fit of supernovae data to Brans-Dicke theory which favours the model with $\omega =-3/2$ \cite{fabris} we discuss the status of this special case of Brans-Dicke cosmology in both isotropic and anisotropic framework. It emerges that the limit $\omega =-3/2$ is consistent only with the vacuum field equations and it makes such a Brans-Dicke theory conformally invariant. Then it is an example of the conformal relativity theory which allows the invariance with respect to conformal transformations of the metric. Besides, Brans-Dicke theory with $\omega =-3/2$ gives a border between a standard scalar field model and a ghost/phantom model. In this paper we show that in $\omega =-3/2$ Brans-Dicke theory, i.e., in the conformal relativity there are no isotropic Friedmann solutions of non-zero spatial curvature except for $k=-1$ case. Further we show that this $k=-1$ case, after the conformal transformation into the Einstein frame, is just the Milne universe and, as such, it is equivalent to Minkowski spacetime. It generally means that only flat models are fully consistent with the field equations. On the other hand, it is shown explicitly that the anisotropic non-zero spatial curvature models of Kantowski-Sachs type are admissible in $\omega =-3/2$ Brans-Dicke theory. It then seems that an additional scale factor which appears in anisotropic models gives an extra deegre of freedom and makes it less restrictive than in an isotropic Friedmann case.

arXiv commentREVTEX4, 19 pages, 8 figures, references added

References in corpus (29)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Cosmological parameters from SDSS and WMAP
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Phantom Energy and Cosmic Doomsday
• Cosmological Results from High-z Supernovae
• The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang
• Quantum deSitter cosmology and phantom matter
• Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
• Cosmic Evolution in a Cyclic Universe
• From Big Crunch to Big Bang
• Constraining dark energy with SNe Ia and large-scale structure
• Study of the anomalous acceleration of Pioneer 10 and 11
• Superstring Cosmology
• Scalar-tensor gravity in an accelerating universe
• The conformal frame freedom in theories of gravitation
• Phantom cosmologies
• Designing Cyclic Universe Models
• Low energy effective string cosmology
• How to Test Stringy Dark Energy?
• Brans-Dicke Theory as a Unified Model for Dark Matter - Dark Energy
• Kantowski-Sachs String Cosmologies
• Description of Supernova Data in Conformal Cosmology without Cosmological Constant
• Triality between Inflation, Cyclic and Phantom Cosmologies
• Visible Branes with Negative Tension in Heterotic M-Theory
• Quantum Relaxation of the Cosmological Constant
• Cosmological Evolution of Black Holes in Brans-Dicke Gravity
• Conformal Transformations and Accelerated Cosmologies

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• From Brans-Dicke gravity to a geometrical scalar-tensor theory
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