21 research outputs found
Non-Perturbative Models For The Quantum Gravitational Back-Reaction On Inflation
We consider a universe in which inflation commences because of a positive
cosmological constant, the effect of which is progressively screened by the
interaction between virtual gravitons that become trapped in the expansion of
spacetime. Perturbative calculations have shown that screening becomes
non-perturbatively large at late times. In this paper we consider effective
field equations which can be evolved numerically to provide a non-perturbative
description of the process. The induced stress tensor is that of an effective
scalar field which is a non-local functional of the metric. We use the known
perturbative result, constrained by general principles and guided by a physical
description of the screening mechanism, to formulate a class of ansatze for
this functional. A scheme is given for numerically evolving the field equations
which result from a simple ansatz, from the beginning of inflation past the
time when it ends. We find that inflation comes to a sudden end, producing a
system whose equation of state rapidly approaches that of radiation. Explicit
numerical results are presented.Comment: 50 pages, LaTeX 2 epsilon, 11 Postscript files, uses psfig.st
Dimensionally Regulated Graviton 1-Point Function in de Sitter
We use dimensional regularization to compute the 1PI 1-point function of
quantum gravity at one loop order in a locally de Sitter background. As with
other computations, the result is a finite constant at this order. It
corresponds to a small positive renormalization of the cosmological constant.Comment: 25 pages, LaTeX 2epsilon, uses Axodraw for one figure, revised to add
some reference
One Loop Vaccum Polarization in a Locally de Sitter Background
We compute the one loop vacuum polarization from massless, minimally coupled
scalar QED in a locally de Sitter background. Gauge invariance is maintained
through the use of dimensional regularization, whereas conformal invariance is
explicitly broken by the scalar kinetic term as well as through the conformal
anomaly. A fully renormalized result is obtained. The one loop corrections to
the linearized, effective field equations do not vanish when evaluated
on-shell. In fact the on-shell one loop correction depends quadratically on the
inflationary scale factor, similar to a photon mass. The contribution from the
conformal anomaly is insignificant by comparison.Comment: 31 pages, LaTeX 2 epsilon, 4 figure
Computing the Primordial Power Spectra Directly
The tree order power spectra of primordial inflation depend upon the
norm-squared of mode functions which oscillate for early times and then freeze
in to constant values. We derive simple differential equations for the power
spectra, that avoid the need to numerically simulate the physically irrelevant
phases of the mode functions. We also derive asymptotic expansions which should
be valid until a few e-foldings before first horizon crossing, thereby avoiding
the need to evolve mode functions from the ultraviolet over long periods of
inflation.Comment: 11 pages, uses LaTex2
A generic problem with purely metric formulations of MOND
We give a simple argument to show that no purely metric-based, relativistic
formulation of Milgrom's Modified Newtonian Dynamics (MOND) whose energy
functional is stable (in the sense of being quadratic in perturbations) can be
consistent with the observed amount of gravitational lensing from galaxies. An
important part of the argument is the fact that reproducing the MOND force law
requires any completely stable, metric-based theory of gravity to become
conformally invariant in the weak field limit. We discuss the prospects for a
formulation with a very weak instability.Comment: 4 pages, revtex4, no figure
Issues Concerning Loop Corrections to the Primordial Power Spectra
We expound ten principles in an attempt to clarify the debate over infrared
loop corrections to the primordial scalar and tensor power spectra from
inflation. Among other things we note that existing proposals for nonlinear
extensions of the scalar fluctuation field introduce new ultraviolet
divergences which no one understands how to renormalize. Loop corrections and
higher correlators of these putative observables would also be enhanced by
inverse powers of the slow roll parameter . We propose an extension
which should be better behaved.Comment: 36 pages, uses LaTeX2e, version 3 revised for publication with a much
expanded section 4, proving that our proposed extension of the zeta-zeta
correlator absorbs the one loop infrared divergences from graviton
Looking Beyond Inflationary Cosmology
In spite of the phenomenological successes of the inflationary universe
scenario, the current realizations of inflation making use of scalar fields
lead to serious conceptual problems which are reviewed in this lecture. String
theory may provide an avenue towards addressing these problems. One particular
approach to combining string theory and cosmology is String Gas Cosmology. The
basic principles of this approach are summarized.Comment: invited talk at "Theory Canada 1" (Univ. of British Columbia,
Vancouver, Canada, June 2 - 4, 2005) (references updated
The Hubble Effective Potential
We generalize the effective potential to scalar field configurations which
are proportional to the Hubble parameter of a homogeneous and isotropic
background geometry. This may be useful in situations for which curvature
effects are significant. We evaluate the one loop contribution to the Hubble
Effective Potential for a massless scalar with arbitrary conformal and quartic
couplings, on a background for which the deceleration parameter is constant.
Among other things, we find that inflationary particle production leads to
symmetry restoration at late times.Comment: 32 pages, 6 figures, version 2 published in JCAP with some typoes
corrected and two additional reference
A parton picture of de Sitter space during slow-roll inflation
It is well-known that expectation values in de Sitter space are afflicted by
infra-red divergences. Long ago, Starobinsky proposed that infra-red effects in
de Sitter space could be accommodated by evolving the long-wavelength part of
the field according to the classical field equations plus a stochastic source
term. I argue that--when quantum-mechanical loop corrections are taken into
account--the separate-universe picture of superhorizon evolution in de Sitter
space is equivalent, in a certain leading-logarithm approximation, to
Starobinsky's stochastic approach. In particular, the time evolution of a box
of de Sitter space can be understood in exact analogy with the DGLAP evolution
of partons within a hadron, which describes a slow logarithmic evolution in the
distribution of the hadron's constituent partons with the energy scale at which
they are probed.Comment: 36 pages; uses iopart.cls and feynmp.sty. v2: Minor typos corrected.
Matches version published in JCA
Light propagation in statistically homogeneous and isotropic universes with general matter content
We derive the relationship of the redshift and the angular diameter distance
to the average expansion rate for universes which are statistically homogeneous
and isotropic and where the distribution evolves slowly, but which have
otherwise arbitrary geometry and matter content. The relevant average expansion
rate is selected by the observable redshift and the assumed symmetry properties
of the spacetime. We show why light deflection and shear remain small. We write
down the evolution equations for the average expansion rate and discuss the
validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular
diameter distance and two typos. No change in result