Quantum fluctuations in the DGP model and the size of the cross-over scale

Abstract

The Dvali-Gabadadze-Porrati model introduces a parameter, the cross-over scale $r_c$, setting the scale where higher dimensional effects are important. In order to agree with observations and to explain the current acceleration of the Universe, $r_c$ must be of the order of the present Hubble radius. We discuss a mechanism to generate a large $r_c$, assuming that it is determined by a dynamical field and exploiting the quantum effects of the graviton. For simplicity, we consider a scalar field $\Psi$ with a kinetic term on the brane instead of the full metric perturbations. We compute the Green function and the 1-loop expectation value of the stress tensor of $\Psi$ on the background defined by a flat bulk and an inflating brane (self-accelerated or not). We also include the flat brane limit. The quantum fluctuations of the bulk field $\Psi$ provide an effective potential for $r_c$. For a flat brane, the 1-loop effective potential is of the Coleman-Weinberg form, and admits a minimum for large $r_c$ without fine tuning. When we take into account the brane curvature, a sizeable contribution at the classical level changes this picture and the potential develops a (minimum) maximum for the (non-) self-accelerated branch.

arXiv comment16 pages, 2 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
• 4D Gravity on a Brane in 5D Minkowski Space
• Accelerated Universe from Gravity Leaking to Extra Dimensions
• Cosmology on a Brane in Minkowski Bulk
• Tests of the Gravitational Inverse-Square Law
• Strong Interactions and Stability in the DGP Model
• Classical and Quantum Consistency of the DGP Model
• The Phenomenology of Dvali-Gabadadze-Porrati Cosmologies
• More on ghosts in DGP model
• Supernovae, CMB, and Gravitational Leakage into Extra Dimensions
• The Power of Brane-Induced Gravity
• Casimir effect for scalar fields under Robin boundary conditions on plates
• Brane world: disappearing massive matter
• Scales of Gravity
• Quantum Stabilization of Compactified AdS_5
• Casimir Energy and Radius Stabilization in Five and Six Dimensional Orbifolds
• Radion effective potential in the Brane-World
• Are there ghosts in the self-accelerating brane universe?
• Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum
• Quantized bulk scalar fields in the Randall-Sundrum brane-model
• QCD uncertainties at the LHC and the implications of HERA
• Induced gravity with a non-minimally coupled scalar field on the brane
• Massive scalar states localized on a de Sitter brane
• Superconformal Quantum Mechanics of Small Black Holes
• Ultra-large distance modification of gravity from Lorentz symmetry breaking at the Planck scale
• Massless scalar fields and infrared divergences in the inflationary brane world
• Vacuum destabilization from Kaluza-Klein modes in an inflating brane

Cited by in corpus (4)

• Consistent Lorentz Violation in Flat and Curved Space
• The Schwinger-DeWitt technique for quantum effective action in brane induced gravity models
• A Model for Cosmic Self-Acceleration
• Effective action and heat kernel in a toy model of brane-induced gravity