585 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
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
Gravitational waves from brane-world inflation with induced gravity
We calculate the amplitude of gravitational waves produced by inflation on a
de Sitter brane embedded in five-dimensional anti-de Sitter bulk spacetime,
extending previous calculations in Randall-Sundrum type cosmology to include
the effect of induced gravity corrections on the brane. These corrections arise
via a term in the brane action that is proportional to the brane Ricci scalar.
We find that, as in the Randall-Sundrum case, there is a mass gap between the
discrete zero-mode and a continuum of massive bulk modes, which are too heavy
to be excited during inflation. We give the normalization of the zero-mode as a
function of the Hubble rate on the brane and are thus able to calculate the
high energy correction to the spectrum of gravitational wave (tensor) modes
excited on large scales during inflation from initial vacuum fluctuations on
small scales. We also calculate the amplitude of density (scalar) perturbations
expected due to inflaton fluctuations on the brane, and show that the usual
four-dimensional consistency relation for the tensor/scalar ratio remains valid
for brane inflation with induced gravity corrections.Comment: 8 pages, 2 figure
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
Flow equations in generalized braneworld scenarios
We discuss the flow equations in the context of general braneworld
cosmologies with a modified Friedmann equation, for either an ordinary scalar
field or a Dirac-Born-Infeld tachyon as inflaton candidates. The 4D,
Randall-Sundrum, and Gauss-Bonnet cases are compared, using the patch formalism
which provides a unified description of these models. The inflationary dynamics
is described by a tower of flow parameters that can be evolved in time to
select a particular subset of points in the space of cosmological observables.
We analyze the stability of the fixed points in all the cosmologies (our
results in the 4D case already extending those in the literature). Numerical
integration of the flow equations shows that the predictions of the
Gauss-Bonnet braneworld differ significantly as compared to the Randall-Sundrum
and 4D scenarios, whereas tachyon inflation gives tensor perturbations smaller
than those in the presence of a normal scalar field. These results are extended
to the realization of a noncommutative space-time preserving maximal symmetry.
In this case the tensor-to-scalar signal is unchanged, while blue-tilted
spectra are favoured.Comment: 10 pages RevTeX4 with 3 figures included. Matches published version.
Note change of title from original submissio
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