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

Degeneracy of consistency equations in braneworld inflation

In a Randall-Sundrum type II inflationary scenario we compute perturbation amplitudes and spectral indices up to next-to-lowest order in the slow-roll parameters, starting from the well-known lowest-order result for a de Sitter brane. Using two different prescriptions for the tensor amplitude, we show that the braneworld consistency equations are not degenerate with respect to the standard relations and we explore their observational consequences. It is then shown that, while the degeneracy between high- and low-energy regimes can come from suitable values of the cosmological observables, exact functional matching between consistency expressions is plausibly discarded. This result is then extended to the Gauss-Bonnet case.Comment: 16 pages, 3 figures. v3: major revision. Changed title, updated references, rearranged material, new prescription for the tensor spectrum, new figures, extended and more robust conclusion

Fractal universe and quantum gravity

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.Comment: 4 pages. v2: typos corrected; v3: discussion improved, intuitive introduction added, matches the published versio

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