19 research outputs found
Do the Age of the Universe and the Hubble Constant Depend on What Scale One Observes Them?
The apparent cosmological conflict between the age of the Universe, predicted
in the standard Friedman cosmology by using the recent measurement of the
larger Hubble constant from a direct calibration of the distance to the Virgo
galaxy cluster, and the ages of the oldest stars and globular clusters is
resolved by invoking the scale dependence of cosmological quantities, including
the age of the Universe. The distance dependence or the running of cosmological
quantities is motivated by the asymptotically-free higher- derivative quantum
gravity. The running can also be derived by ``properly" modifying the Friedman
equations. This property can also provide partial explanation of the apparent
disagreement between the two recent measurements of the Hubble constant using
NGC 4571 at 15 Mpc and NGC 5253 at 4 Mpc.Comment: Revtex file, 9 pages (no figures
The Dark Matter Problem in Light of Quantum Gravity
We show how, by considering the cumulative effect of tiny quantum
gravitational fluctuations over very large distances, it may be possible to:
() reconcile nucleosynthesis bounds on the density parameter of the Universe
with the predictions of inflationary cosmology, and () reproduce the
inferred variation of the density parameter with distance. Our calculation can
be interpreted as a computation of the contribution of quantum gravitational
degrees of freedom to the (local) energy density of the Universe.Comment: 13 pages, LaTeX, (3 figues, not included
Covariant perturbation theory and the Randall-Sundrum picture
The effective action for quantum fields on a -dimensional spacetime can be
computed using a non local expansion in powers of the curvature. We show
explicitly that, for conformal fields and up to quadratic order in the
curvature, the non local effective action is equivalent to the action for
classical gravity in restricted to a -brane. This generalizes
previous results about quantum corrections to the Newtonian potential and
provides an alternative method for making local a non-local effective action.
The equivalence can be easily understood by comparing the Kallen-Lehmann
decomposition of the classical propagator with the spectral representation of
the non local form factors in the quantum effective action.Comment: 8 pages, Latex. Minor corrections. To appear in Phys. Lett.
Geodesics, gravitons and the gauge fixing problem
When graviton loops are taken into account, the background metric obtained as
a solution to the one-loop corrected Einstein equations turns out to be gauge
fixing dependent. Therefore it is of no physical relevance. Instead we consider
a physical observable, namely the trajectory of a test particle in the presence
of gravitons. We derive a quantum corrected geodesic equation that includes
backreaction effects and is explicitly independent of any gauge fixing
parameter.Comment: 21 pages, no figures, RevTe
Wheeler-DeWitt equation and Feynman diagrams
We present a systematic expansion of all constraint equations in canonical
quantum gravity up to the order of the inverse Planck mass squared. It is
demonstrated that this method generates the conventional Feynman diagrammatic
technique involving graviton loops and vertices. It also reveals explicitly the
back reaction effects of quantized matter and graviton vacuum polarization.
This provides an explicit correspondence between the frameworks of canonical
and covariant quantum gravity in the semiclassical limit.Comment: 35 pages, LATEX, 1 figur
Gauge and parametrization dependence in higher derivative quantum gravity
The structure of counterterms in higher derivative quantum gravity is
reexamined. Nontrivial dependence of charges on the gauge and parametrization
is established. Explicit calculations of two-loop contributions are carried out
with the help of the generalized renormgroup method demonstrating consistency
of the results obtained.Comment: 22 pages, Latex, no figure
Simplicial Gravity Coupled to Scalar Matter
A model for quantized gravity coupled to matter in the form of a single
scalar field is investigated in four dimensions. For the metric degrees of
freedom we employ Regge's simplicial discretization, with the scalar fields
defined at the vertices of the four-simplices. We examine how the continuous
phase transition found earlier, separating the smooth from the rough phase of
quantized gravity, is influenced by the presence of scalar matter. A
determination of the critical exponents seems to indicate that the effects of
matter are rather small, unless the number of scalar flavors is large. Close to
the critical point where the average curvature approaches zero, the coupling of
matter to gravity is found to be weak. The nature of the phase diagram and the
values for the critical exponents suggest that gravitational interactions
increase with distance. \vspace{24pt} \vfillComment: (34 pages + 8 figures
A Renormalization Group Approach to Relativistic Cosmology
We discuss the averaging hypothesis tacitly assumed in standard cosmology.
Our approach is implemented in a "3+1" formalism and invokes the coarse
graining arguments, provided and supported by the real-space Renormalization
Group (RG) methods. Block variables are introduced and the recursion relations
written down explicitly enabling us to characterize the corresponding RG flow.
To leading order, the RG flow is provided by the Ricci-Hamilton equations
studied in connection with the geometry of three-manifolds. The properties of
the Ricci-Hamilton flow make it possible to study a critical behaviour of
cosmological models. This criticality is discussed and it is argued that it may
be related to the formation of sheet-like structures in the universe. We
provide an explicit expression for the renormalized Hubble constant and for the
scale dependence of the matter distribution. It is shown that the Hubble
constant is affected by non-trivial scale dependent shear terms, while the
spatial anisotropy of the metric influences significantly the scale-dependence
of the matter distribution.Comment: 57 pages, LaTeX, 15 pictures available on request from the Author
Invariant Correlations in Simplicial Gravity
Some first results are presented regarding the behavior of invariant
correlations in simplicial gravity, with an action containing both a bare
cosmological term and a lattice higher derivative term. The determination of
invariant correlations as a function of geodesic distance by numerical methods
is a difficult task, since the geodesic distance between any two points is a
function of the fluctuating background geometry, and correlation effects become
rather small for large distances. Still, a strikingly different behavior is
found for the volume and curvature correlation functions. While the first one
is found to be negative definite at large geodesic distances, the second one is
always positive for large distances. For both correlations the results are
consistent in the smooth phase with an exponential decay, turning into a power
law close to the critical point at . Such a behavior is not completely
unexpected, if the model is to reproduce the classical Einstein theory at
distances much larger than the ultraviolet cutoff scale.Comment: 27 pages, conforms to published versio
Tomographic Representation of Minisuperspace Quantum Cosmology and Noether Symmetries
The probability representation, in which cosmological quantum states are
described by a standard positive probability distribution, is constructed for
minisuperspace models selected by Noether symmetries. In such a case, the
tomographic probability distribution provides the classical evolution for the
models and can be considered an approach to select "observable" universes. Some
specific examples, derived from Extended Theories of Gravity, are worked out.
We discuss also how to connect tomograms, symmetries and cosmological
parameters.Comment: 15 page