Diffusion in quantum geometry

The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is controlled by a multiscale fractional diffusion equation, and physically interpreted as a composite stochastic process. The simplest example is a fractional telegraph process, describing quantum spacetimes with a spectral dimension equal to 2 in the ultraviolet and monotonically rising to 4 towards the infrared. The general profile of the spectral dimension of the recently introduced multifractional spaces is constructed for the first time.Comment: 5 pages, 1 figure. v2: title slightly changed, discussion improve

Stability of multi-field cosmological solutions

We explore the stability properties of multi-field solutions of assisted inflation type, where several fields collectively evolve to the same configuration. In the case of noninteracting fields, we show that the condition for such solutions to be stable is less restrictive than that required for tracking in quintessence models. Our results, which do not rely on the slow-roll approximation, further indicate that to linear order in homogeneous perturbations the fields are in fact unaware of each other's existence. We end by generalizing our results to some cases of interacting fields and to other background solutions and dynamics, including the high-energy braneworld.Comment: 6 pages; v2: typos corrected, version accepted by PR

2-point functions in quantum cosmology

We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories, with particular reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, deriving vertex expansions and composition laws they satisfy. We clarify the tie between definitions using a group averaging procedure and those in a deparametrised framework. We draw some conclusions about the physics of a single quantum universe and multiverse field theories where the role of these sectors and the inner product are reinterpreted.Comment: 4 pages, based on a talk given at Loops '11, Madrid, to appear in Journal of Physics: Conference Series (JPCS

2-point functions in quantum cosmology

We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories, with particular reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, deriving vertex expansions and composition laws they satisfy. We clarify the tie between definitions using a group averaging procedure and those in a deparametrised framework. We draw some conclusions about the physics of a single quantum universe and multiverse field theories where the role of these sectors and the inner product are reinterpreted.Comment: 4 pages, based on a talk given at Loops '11, Madrid, to appear in Journal of Physics: Conference Series (JPCS

2-point functions in quantum cosmology

We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories, with particular reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, deriving vertex expansions and composition laws they satisfy. We clarify the tie between definitions using a group averaging procedure and those in a deparametrised framework. We draw some conclusions about the physics of a single quantum universe and multiverse field theories where the role of these sectors and the inner product are reinterpreted.Comment: 4 pages, based on a talk given at Loops '11, Madrid, to appear in Journal of Physics: Conference Series (JPCS

On topological charged braneworld black holes

We study a class of topological black hole solutions in RSII braneworld scenario in the presence of a localized Maxwell field on the brane. Such a black hole can carry two types of charge, one arising from the extra dimension, the tidal charge, and the other one from a localized gauge field confined to the brane. We find that the localized charge on the brane modifies the bulk geometry and in particular the bulk Weyl tensor. The bulk geometry does not depend on different topologies of the horizons. We present the temperature and entropy expressions associated with the event horizon of the braneworld black hole and by using the first law of black hole thermodynamics we calculate the mass of the black hole.Comment: 9 pages, references added, to appear in MPL

Primordial perturbations from slow-roll inflation on a brane

In this paper we quantise scalar perturbations in a Randall-Sundrum-type model of inflation where the inflaton field is confined to a single brane embedded in five-dimensional anti-de Sitter space-time. In the high energy regime, small-scale inflaton fluctuations are strongly coupled to metric perturbations in the bulk and gravitational back-reaction has a dramatic effect on the behaviour of inflaton perturbations on sub-horizon scales. This is in contrast to the standard four-dimensional result where gravitational back-reaction can be neglected on small scales. Nevertheless, this does not give rise to significant particle production, and the correction to the power spectrum of the curvature perturbations on super-horizon scales is shown to be suppressed by a slow-roll parameter. We calculate the complete first order slow-roll corrections to the spectrum of primordial curvature perturbations.Comment: 23 pages, 10 figure

Slow-roll corrections to inflaton fluctuations on a brane

Quantum fluctuations of an inflaton field, slow-rolling during inflation are coupled to metric fluctuations. In conventional four dimensional cosmology one can calculate the effect of scalar metric perturbations as slow-roll corrections to the evolution of a massless free field in de Sitter spacetime. This gives the well-known first-order corrections to the field perturbations after horizon-exit. If inflaton fluctuations on a four dimensional brane embedded in a five dimensional bulk spacetime are studied to first-order in slow-roll then we recover the usual conserved curvature perturbation on super-horizon scales. But on small scales, at high energies, we find that the coupling to the bulk metric perturbations cannot be neglected, leading to a modified amplitude of vacuum oscillations on small scales. This is a large effect which casts doubt on the reliability of the usual calculation of inflaton fluctuations on the brane neglecting their gravitational coupling.Comment: 18 pages, 4 figure