81 research outputs found
The four fixed points of scale invariant single field cosmological models
We introduce a new set of flow parameters to describe the time dependence of
the equation of state and the speed of sound in single field cosmological
models. A scale invariant power spectrum is produced if these flow parameters
satisfy specific dynamical equations. We analyze the flow of these parameters
and find four types of fixed points that encompass all known single field
models. Moreover, near each fixed point we uncover new models where the scale
invariance of the power spectrum relies on having simultaneously time varying
speed of sound and equation of state. We describe several distinctive new
models and discuss constraints from strong coupling and superluminality.Comment: 24 pages, 6 figure
Perturbations in a regular bouncing Universe
We consider a simple toy model of a regular bouncing universe. The bounce is
caused by an extra time-like dimension, which leads to a sign flip of the
term in the effective four dimensional Randall Sundrum-like
description. We find a wide class of possible bounces: big bang avoiding ones
for regular matter content, and big rip avoiding ones for phantom matter.
Focusing on radiation as the matter content, we discuss the evolution of
scalar, vector and tensor perturbations. We compute a spectral index of
for scalar perturbations and a deep blue index for tensor
perturbations after invoking vacuum initial conditions, ruling out such a model
as a realistic one. We also find that the spectrum (evaluated at Hubble
crossing) is sensitive to the bounce. We conclude that it is challenging, but
not impossible, for cyclic/ekpyrotic models to succeed, if one can find a
regularized version.Comment: v3: 10 pages, 1 figure, section III revised, conclusions changed,
references added, typos corrected; v4: numerics added, identical with version
accepted in PR
Gauge invariant averages for the cosmological backreaction
We show how to provide suitable gauge invariant prescriptions for the
classical spatial averages (resp. quantum expectation values) that are needed
in the evaluation of classical (resp. quantum) backreaction effects. We also
present examples illustrating how the use of gauge invariant prescriptions can
avoid interpretation problems and prevent misleading conclusions.Comment: 21 pages, no figures. Comments and references added, typos corrected.
Small corrections and reference added, matches version published in JCA
Horizon-preserving dualities and perturbations in non-canonical scalar field cosmologies
We generalize the cosmological duality between inflation and cyclic
contraction under the interchange to the case of
non-canonical scalar field theories with varying speed of sound. The single
duality in the canonical case generalizes to a family of three dualities
constructed to leave the cosmological acoustic horizon invariant. We find three
classes of models: (I) DBI inflation, (II) the non-canonical generalization of
cyclic contraction, and (III) a new cosmological solution with rapidly
decreasing speed of sound and relatively slowly growing scale factor, which we
dub {\it stalled} cosmology. We construct dual analogs to the inflationary slow
roll approximation, and solve for the curvature perturbation in all three
cases. Both cyclic contraction and stalled cosmology predict a strongly blue
spectrum for the curvature perturbations inconsistent with observations.Comment: 36 pages, LaTeX (v2: references added, version submitted to JCAP
General plane wave mode functions for scalar-driven cosmology
We give a solution for plane wave scalar, vector and tensor mode functions in
the presence of any homogeneous, isotropic and spatially flat cosmology which
is driven by a single, minimally coupled scalar. The solution is obtained by
rescaling the various mode functions so that they reduce, with a suitable scale
factor and a suitable time variable, to those of a massless, minimally coupled
scalar. We then express the general solution in terms of co-moving time and the
original scale factor.Comment: 6 pages, revtex4, no figures, revised version corrects an
embarrassing mistake (in the published version) for the parameter q_C.
Affected eqns are 45 and 6
Averaging Robertson-Walker Cosmologies
The cosmological backreaction arises when one directly averages the Einstein
equations to recover an effective Robertson-Walker cosmology, rather than
assuming a background a priori. While usually discussed in the context of dark
energy, strictly speaking any cosmological model should be recovered from such
a procedure. We apply the Buchert averaging formalism to linear
Robertson-Walker universes containing matter, radiation and dark energy and
evaluate numerically the discrepancies between the assumed and the averaged
behaviour, finding the largest deviations for an Einstein-de Sitter universe,
increasing rapidly with Hubble rate to a 0.01% effect for h=0.701. For the LCDM
concordance model, the backreaction is of the order of Omega_eff~4x10^-6, with
those for dark energy models being within a factor of two or three. The impacts
at recombination are of the order of 10^-8 and those in deep radiation
domination asymptote to a constant value. While the effective equations of
state of the backreactions in Einstein-de Sitter, concordance and quintessence
models are generally dust-like, a backreaction with an equation of state
w_eff<-1/3 can be found for strongly phantom models.Comment: 18 pages, 11 figures, ReVTeX. Updated to version accepted by JCA
The IR-Completion of Gravity: What happens at Hubble Scales?
We have recently proposed an "Ultra-Strong" version of the Equivalence
Principle (EP) that is not satisfied by standard semiclassical gravity. In the
theory that we are conjecturing, the vacuum expectation value of the (bare)
energy momentum tensor is exactly the same as in flat space: quartically
divergent with the cut-off and with no spacetime dependent (subleading) ter ms.
The presence of such terms seems in fact related to some known difficulties,
such as the black hole information loss and the cosmological constant problem.
Since the terms that we want to get rid of are subleading in the high-momentum
expansion, we attempt to explore the conjectured theory by "IR-completing" GR.
We consider a scalar field in a flat FRW Universe and isolate the first
IR-correction to its Fourier modes operators that kills the quadratic (next to
leading) time dependent divergence of the stress energy tensor VEV. Analogously
to other modifications of field operators that have been proposed in the
literature (typically in the UV), the present approach seems to suggest a
breakdown (here, in the IR, at large distances) of the metric manifold
description. We show that corrections to GR are in fact very tiny, become
effective at distances comparable to the inverse curvature and do not contain
any adjustable parameter. Finally, we derive some cosmological implications. By
studying the consistency of the canonical commutation relations, we infer a
correction to the distance between two comoving observers, which grows as the
scale factor only when small compared to the Hubble length, but gets relevant
corrections otherwise. The corrections to cosmological distance measures are
also calculable and, for a spatially flat matter dominated Universe, go in the
direction of an effective positive acceleration.Comment: 27 pages, 2 figures. Final version, references adde
The effect of extra dimensions on gravity wave bursts from cosmic string cusps
We explore the kinematical effect of having extra dimensions on the gravity
wave emission from cosmic strings. Additional dimensions both round off cusps,
and reduce the probability of their formation. We recompute the gravity wave
burst, taking into account these two factors, and find a potentially
significant damping on the gravity waves of the strings.Comment: 33 pages, 8 figures, published versio
Stress tensor fluctuations in de Sitter spacetime
The two-point function of the stress tensor operator of a quantum field in de
Sitter spacetime is calculated for an arbitrary number of dimensions. We assume
the field to be in the Bunch-Davies vacuum, and formulate our calculation in
terms of de Sitter-invariant bitensors. Explicit results for free minimally
coupled scalar fields with arbitrary mass are provided. We find long-range
stress tensor correlations for sufficiently light fields (with mass m much
smaller than the Hubble scale H), namely, the two-point function decays at
large separations like an inverse power of the physical distance with an
exponent proportional to m^2/H^2. In contrast, we show that for the massless
case it decays at large separations like the fourth power of the physical
distance. There is thus a discontinuity in the massless limit. As a byproduct
of our work, we present a novel and simple geometric interpretation of de
Sitter-invariant bitensors for pairs of points which cannot be connected by
geodesics.Comment: 35 pages, 4 figure
Stochastic Inflation Revisited: Non-Slow Roll Statistics and DBI Inflation
Stochastic inflation describes the global structure of the inflationary
universe by modeling the super-Hubble dynamics as a system of matter fields
coupled to gravity where the sub-Hubble field fluctuations induce a stochastic
force into the equations of motion. The super-Hubble dynamics are ultralocal,
allowing us to neglect spatial derivatives and treat each Hubble patch as a
separate universe. This provides a natural framework in which to discuss
probabilities on the space of solutions and initial conditions. In this article
we derive an evolution equation for this probability for an arbitrary class of
matter systems, including DBI and k-inflationary models, and discover
equilibrium solutions that satisfy detailed balance. Our results are more
general than those derived assuming slow roll or a quasi-de Sitter geometry,
and so are directly applicable to models that do not satisfy the usual slow
roll conditions. We discuss in general terms the conditions for eternal
inflation to set in, and we give explicit numerical solutions of highly
stochastic, quasi-stationary trajectories in the relativistic DBI regime.
Finally, we show that the probability for stochastic/thermal tunneling can be
significantly enhanced relative to the Hawking-Moss instanton result due to
relativistic DBI effects.Comment: 38 pages, 2 figures. v3: minor revisions; version accepted into JCA
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