Weak field limit of higher dimensional massive Brans-Dicke gravity: Observational constraints

Abstract

We consider higher-dimensional massive Brans-Dicke theory with Ricci-flat internal space. The background model is perturbed by a massive gravitating source which is pressureless in the external (our space) but has an arbitrary equation-of-state parameter $\Omega$ in the internal space. We obtain the exact solution of the system of linearized equations for the perturbations of the metric coefficients and scalar field. For a massless scalar field, relying on the fine-tuning between the Brans-Dicke parameter $\omega$ and $\Omega$, we demonstrate that (i) the model does not contradict gravitational tests relevant to the parameterized post-Newtonian parameter $\gamma$, and (ii) the scalar field is not ghost in the case of nonzero $|\Omega |\sim O(1)$ along with the natural value $|\omega |\sim O(1)$. In the general case of a massive scalar field, the metric coefficients acquire the Yukawa correction terms, where the Yukawa mass scale $m$ is defined by the mass of the scalar field. For the natural value $\omega \sim O(1)$, the inverse-square-law experiments impose the following restriction on the lower bound of the mass: $m\gtrsim 10^{-11}$GeV. The experimental constraints on $\gamma$ requires that $\Omega$ must be extremely close to $-1/2$.

arXiv comment8 pages, no figures and tables; matches the version published in Physical Review D

References in corpus (23)

• The Hierarchy Problem and New Dimensions at a Millimeter
• Modified Gravity and Cosmology
• Extended Theories of Gravity
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Kaluza-Klein Dark Matter
• On the Unification Problem in Physics
• PPN Parameter $\gamma$ and Solar System Constraints of Massive Brans-Dicke Theories
• The first law of black brane mechanics
• General Definition of Gravitational Tension
• Tension Perturbations of Black Brane Spacetimes
• Multidimensional cosmological models: cosmological and astrophysical implications and constraints
• Classical tests of multidimensional gravity: negative result
• Kaluza-Klein models: can we construct a viable example?
• Latent solitons, black strings, black branes, and equations of state in Kaluza-Klein models
• Remarks on gravitational interaction in Kaluza-Klein models
• Kaluza-Klein models with spherical compactification: observational constraints and possible examples
• Kaluza-Klein multidimensional models with Ricci-flat internal spaces: the absence of the KK particles
• Problematic aspects of Kaluza-Klein excitations in multidimensional models with Einstein internal spaces
• Black branes and black strings in the astrophysical and cosmological context
• Many-body problem in Kaluza-Klein models with toroidal compactification
• Significance of tension for gravitating masses in Kaluza-Klein models
• Weak-field limit of Kaluza-Klein model with non-linear perfect fluid
• Weak-field limit of Kaluza-Klein models with spherically symmetric static scalar field: observational constraints

Cited by in corpus (2)

• Anisotropic massive Brans-Dicke gravity extension of the standard $\Lambda$CDM model
• $\Lambda$CDM cosmology with a quiescent anisotropy in a higher dimensional steady state universe