4,922 research outputs found
Reconstructing the Distortion Function for Nonlocal Cosmology
We consider the cosmology of modified gravity models in which Newton's
constant is distorted by a function of the inverse d'Alembertian acting on the
Ricci scalar. We derive a technique for choosing the distortion function so as
to fit an arbitrary expansion history. This technique is applied numerically to
the case of LambdaCDM cosmology, and the result agrees well with a simple
hyperbolic tangent.Comment: 17 pages, 1 figure, dedicated to Stanley Deser on the occasion of his
78th birthday, revised version for publication in JCA
Matter Contributions to the Expansion Rate of the Universe
We consider the effect of various particles on the cosmic expansion rate
relative to that of the graviton. Effectively massless fermions, gauge bosons
and conformally coupled scalars make only minuscule contributions due to local
conformal invariance. Minimally coupled scalars can give much stronger
contributions, but they are still sub-dominant to those of gravitons on account
of global conformal invariance. Unless effectively massless scalar particles
with very particular couplings exist, the leading effect on the expansion rate
is furnished solely by the graviton. An upper bound on the mass of such scalar
particles is obtained.Comment: 14 pages, plain TeX, 7 Postscript files, uses psfig.st
Quantum Gravity Slows Inflation
We consider the quantum gravitational back-reaction on an initially
inflating, homogeneous and isotropic universe whose topology is . Although there is no secular effect at one loop, an explicit calculation
shows that two-loop processes act to slow the rate of expansion by an amount
which becomes non-perturbatively large at late times. By exploiting Feynman's
tree theorem we show that all higher loops act in the same sense.Comment: 19 pages, plain TeX, 1 Postscript file, uses psfig.sty, revised June
1996 for publication in Nuclear Physics
Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions
We give conditions under which a Markov chain constructed via parallel or
simulated tempering is guaranteed to be rapidly mixing, which are applicable to
a wide range of multimodal distributions arising in Bayesian statistical
inference and statistical mechanics. We provide lower bounds on the spectral
gaps of parallel and simulated tempering. These bounds imply a single set of
sufficient conditions for rapid mixing of both techniques. A direct consequence
of our results is rapid mixing of parallel and simulated tempering for several
normal mixture models, and for the mean-field Ising model.Comment: Published in at http://dx.doi.org/10.1214/08-AAP555 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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