4,876 research outputs found
Figure of Merit for Dark Energy Constraints from Current Observational Data
Choosing the appropriate figure of merit (FoM) for dark energy (DE)
constraints is key in comparing different DE experiments. Here we show that for
a set of DE parameters {f_i}, it is most intuitive to define FoM =
1/\sqrt{Cov(f1,f2,f3,...)}, where Cov(f1,f2,f3,...) is the covariance matrix of
{f_i}. The {f_i} should be minimally correlated. We demonstrate two useful
choices of {f_i} using 182 SNe Ia (compiled by Riess et al. 2007), [R(z_*),
l_a(z_*), \Omega_b h^2] from the five year Wilkinson Microwave Anisotropy Probe
(WMAP) observations, and SDSS measurement of the baryon acoustic oscillation
(BAO) scale, assuming the HST prior of H_0=72+/-8 km/s Mpc^{-1} and without
assuming spatial flatness. We find that the correlation of (w_0,w_{0.5})
[w_0=w_X(z=0), w_{0.5}=w_X(z=0.5), w_X(a) = 3w_{0.5}-2w_0+3(w_0-w_{0.5})a] is
significantly smaller than that of (w_0,w_a) [w_X(a)=w_0+(1-a)w_a]. In order to
obtain model-independent constraints on DE, we parametrize the DE density
function X(z)=\rho_X(z)/\rho_X(0) as a free function with X_{0.5}, X_{1.0}, and
X_{1.5} [values of X(z) at z=0.5, 1.0, and 1.5] as free parameters estimated
from data. If one assumes a linear DE equation of state, current data are
consistent with a cosmological constant at 68% C.L. If one assumes X(z) to be a
free function parametrized by (X_{0.5}, X_{1.0}, X_{1.5}), current data deviate
from a cosmological constant at z=1 at 68% C.L., but are consistent with a
cosmological constant at 95% C.L.. Future DE experiments will allow us to
dramatically increase the FoM of constraints on (w_0,w_{0.5}) and of (X_{0.5},
X_{1.0}, X_{1.5}). This will significantly shrink the DE parameter space to
enable the discovery of DE evolution, or the conclusive evidence for a
cosmological constant.Comment: 7 pages, 3 color figures. Submitte
Vacuum Decay on a Brane World
The bubble nucleation rate for a first order phase transition occurring on a
brane world is calculated. Both the Coleman-de Luccia thin wall instanton and
the Hawking-Moss instanton are considered. The results are compared with the
corresponding nucleation rates for standard four-dimensional gravity.Comment: 5 page
Stationarity of Inflation and Predictions of Quantum Cosmology
We describe several different regimes which are possible in inflationary
cosmology. The simplest one is inflation without self-reproduction of the
universe. In this scenario the universe is not stationary. The second regime,
which exists in a broad class of inflationary models, is eternal inflation with
the self-reproduction of inflationary domains. In this regime local properties
of domains with a given density and given values of fields do not depend on the
time when these domains were produced. The probability distribution to find a
domain with given properties in a self-reproducing universe may or may not be
stationary, depending on the choice of an inflationary model. We give examples
of models where each of these possibilities can be realized, and discuss some
implications of our results for quantum cosmology. In particular, we propose a
new mechanism which may help solving the cosmological constant problem.Comment: 30 pages, Stanford preprint SU-ITP-94-24, LaTe
Cosmological Dynamics of a Dirac-Born-Infeld field
We analyze the dynamics of a Dirac-Born-Infeld (DBI) field in a cosmological
set-up which includes a perfect fluid. Introducing convenient dynamical
variables, we show the evolution equations form an autonomous system when the
potential and the brane tension of the DBI field are arbitrary power-law or
exponential functions of the DBI field. In particular we find scaling solutions
can exist when powers of the field in the potential and warp-factor satisfy
specific relations. A new class of fixed-point solutions are obtained
corresponding to points which initially appear singular in the evolution
equations, but on closer inspection are actually well defined. In all cases, we
perform a phase-space analysis and obtain the late-time attractor structure of
the system. Of particular note when considering cosmological perturbations in
DBI inflation is a fixed-point solution where the Lorentz factor is a finite
large constant and the equation of state parameter of the DBI field is .
Since in this case the speed of sound becomes constant, the solution can
be thought to serve as a good background to perturb about.Comment: 24 pages, 7 figures, minor corrections, references adde
A Comparative Study of Dark Energy Constraints from Current Observational Data
We examine how dark energy constraints from current observational data depend
on the analysis methods used: the analysis of Type Ia supernovae (SNe Ia), and
that of galaxy clustering data. We generalize the flux-averaging analysis
method of SNe Ia to allow correlated errors of SNe Ia, in order to reduce the
systematic bias due to weak lensing of SNe Ia. We find that flux-averaging
leads to larger errors on dark energy and cosmological parameters if only SN Ia
data are used. When SN Ia data (the latest compilation by the SNLS team) are
combined with WMAP 7 year results (in terms of our Gaussian fits to the
probability distributions of the CMB shift parameters), the latest Hubble
constant (H_0) measurement using the Hubble Space Telescope (HST), and gamma
ray burst (GRB) data, flux-averaging of SNe Ia increases the concordance with
other data, and leads to significantly tighter constraints on the dark energy
density at z=1, and the cosmic curvature \Omega_k. The galaxy clustering
measurements of H(z=0.35)r_s(z_d) and r_s(z_d)/D_A(z=0.35) (where H(z) is the
Hubble parameter, D_A(z) is the angular diameter distance, and r_s(z_d) is the
sound horizon at the drag epoch) by Chuang & Wang (2011) are consistent with SN
Ia data, given the same pirors (CMB+H_0+GRB), and lead to significantly
improved dark energy constraints when combined. Current data are fully
consistent with a cosmological constant and a flat universe.Comment: 11 pages, 9 figures. Slightly revised version, to appear in PRD.
Supernova flux-averaging code available at
http://www.nhn.ou.edu/~wang/SNcode
Quintessential inflation from 5D warped product spaces on a dynamical foliation
Assuming the existence of a 5D purely kinetic scalar field on the class of
warped product spaces we investigate the possibility of mimic both an
inflationary and a quintessential scenarios on 4D hypersurfaces, by
implementing a dynamical foliation on the fifth coordinate instead of a
constant one. We obtain that an induced chaotic inflationary scenario with a
geometrically induced scalar potential and an induced quasi-vacuum equation of
state on 4D dynamical hypersurfaces is possible. While on a constant foliation
the universe can be considered as matter dominated today, in a family of 4D
dynamical hypersurfaces the universe can be passing for a period of accelerated
expansion with a deceleration parameter nearly -1. This effect of the dynamical
foliation results negligible at the inflationary epoch allowing for a chaotic
scenario and becomes considerable at the present epoch allowing a
quintessential scenario.Comment: 7 pages, 1 figure Accepted for publication in Modern Physics Letters
Creation of a Compact Topologically Nontrivial Inflationary Universe
If inflation can occur only at the energy density V much smaller than the
Planck density, which is the case for many inflationary models based on string
theory, then the probability of quantum creation of a closed or an infinitely
large open inflationary universe is exponentially suppressed for all known
choices of the wave function of the universe. Meanwhile under certain
conditions there is no exponential suppression for creation of topologically
nontrivial compact flat or open inflationary universes. This suggests, contrary
to the standard textbook lore, that compact flat or open universes with
nontrivial topology should be considered a rule rather than an exception.Comment: 9 pages 2 figures, new materials and references adde
From the Big Bang Theory to the Theory of a Stationary Universe
We consider chaotic inflation in the theories with the effective potentials
phi^n and e^{\alpha\phi}. In such theories inflationary domains containing
sufficiently large and homogeneous scalar field \phi permanently produce new
inflationary domains of a similar type. We show that under certain conditions
this process of the self-reproduction of the Universe can be described by a
stationary distribution of probability, which means that the fraction of the
physical volume of the Universe in a state with given properties (with given
values of fields, with a given density of matter, etc.) does not depend on
time, both at the stage of inflation and after it. This represents a strong
deviation of inflationary cosmology from the standard Big Bang paradigm. We
compare our approach with other approaches to quantum cosmology, and illustrate
some of the general conclusions mentioned above with the results of a computer
simulation of stochastic processes in the inflationary Universe.Comment: No changes to the file, but original figures are included. They
substantially help to understand this paper, as well as eternal inflation in
general, and what is now called the "multiverse" and the "string theory
landscape." High quality figures can be found at
http://www.stanford.edu/~alinde/LLMbigfigs
Dynamics of a scalar field in Robertson-Walker spacetimes
We analyze the dynamics of a single scalar field in
Friedmann-Robertson-Walker universes with spatial curvature. We obtain the
fixed point solutions which are shown to be late time attractors. In
particular, we determine the corresponding scalar field potentials which
correspond to these stable solutions. The analysis is quite general and
incorporates expanding and contracting universes with both positive and
negative scalar potentials. We demonstrate that the known power law,
exponential, and de-Sitter solutions are certain limits of our general set of
solutions.Comment: 10 pages, v2:references added. Accepted for publication in PR
Bayesian Analysis of Inflation II: Model Selection and Constraints on Reheating
We discuss the model selection problem for inflationary cosmology. We couple
ModeCode, a publicly-available numerical solver for the primordial perturbation
spectra, to the nested sampler MultiNest, in order to efficiently compute
Bayesian evidence. Particular attention is paid to the specification of
physically realistic priors, including the parametrization of the
post-inflationary expansion and associated thermalization scale. It is
confirmed that while present-day data tightly constrains the properties of the
power spectrum, it cannot usefully distinguish between the members of a large
class of simple inflationary models. We also compute evidence using a simulated
Planck likelihood, showing that while Planck will have more power than WMAP to
discriminate between inflationary models, it will not definitively address the
inflationary model selection problem on its own. However, Planck will place
very tight constraints on any model with more than one observationally-distinct
inflationary regime -- e.g. the large- and small-field limits of the hilltop
inflation model -- and put useful limits on different reheating scenarios for a
given model.Comment: ModeCode package available from
http://zuserver2.star.ucl.ac.uk/~hiranya/ModeCode/ModeCode (requires CosmoMC
and MultiNest); to be published in PRD. Typos fixe
- …