735 research outputs found
Inflationary spectra and observations in loop quantum cosmology
We review some recent progress in the extraction of inflationary observables in loop quantum cosmology. Inverse-volume quantum corrections induce a growth of power in the large-scale cosmological spectra and are constrained by observations
Gravity on a multifractal
Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of these models of Nature. Thus motivated, we entertain the idea that spacetime is a multifractal with integer dimension 4 at large scales, while it is two-dimensional in the ultraviolet. Consequences for particle physics, gravity and cosmology are discussed
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
New Models of f(R) Theories of Gravity
We introduce new models of f(R) theories of gravity that are generalization
of Horava-Lifshitz gravity.Comment: 16 pages, typos corrected, v2:minor changes, references adde
Nonlocal gravity and the diffusion equation
We propose a nonlocal scalar-tensor model of gravity with pseudodifferential
operators inspired by the effective action of p-adic string and string field
theory on flat spacetime. An infinite number of derivatives act both on the
metric and scalar field sector. The system is localized via the diffusion
equation approach and its cosmology is studied. We find several exact dynamical
solutions, also in the presence of a barotropic fluid, which are stationary in
the diffusion flow. In particular, and contrary to standard general relativity,
there exist solutions with exponential and power-law scale factor also in an
open universe, as well as solutions with sudden future singularities or a
bounce. Also, from the point of view of quantum field theory, spontaneous
symmetry breaking can be naturally realized in the class of actions we
consider.Comment: 18 pages, 5 figures. v2: typos corrected, references added. Major
changes are an expansion of the discussion of homogeneous perturbations and
the inclusion of cosmological fluids in the dynamic
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
Observational test of inflation in loop quantum cosmology
We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous settings, we show that they can generate large running spectral indices, which generally lead to an enhancement of power at large scales. We provide explicit formulas for the scalar/tensor power spectra under the slow-roll approximation, by taking into account corrections of order higher than the runnings. We place observational bounds on the inverse-volume quantum correction \delta ~ a^{- \sigma} (\sigma >0, is the scale factor) and the slow-roll parameter \epsilon_V for power-law potentials as well as exponential potentials by using the data of WMAP 7yr combined with other observations. We derive the constraints on \delta for two pivot wavenumbers k_0 for several values of \delta. The quadratic potential can be compatible with the data even in the presence of the LQC corrections, but the quartic potential is in tension with observations. We also find that the upper bounds on \delta (k_0) for given \sigma and k_0 are insensitive to the choice of the inflaton potentials
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
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