136 research outputs found
Trans-Planckian Physics and the Spectrum of Fluctuations in a Bouncing Universe
In this paper, we calculate the spectrum of scalar field fluctuations in a
bouncing, asymptotically flat Universe, and investigate the dependence of the
result on changes in the physics on length scales shorter than the Planck
length which are introduced via modifications of the dispersion relation. In
this model, there are no ambiguities concerning the choice of the initial
vacuum state. We study an example in which the final spectrum of fluctuations
depends sensitively on the modifications of the dispersion relation without
needing to invoke complex frequencies. Changes in the amplitude and in the
spectral index are possible, in addition to modulations of the spectrum. This
strengthens the conclusions of previous work in which the spectrum of
cosmological perturbations in expanding inflationary cosmologies was studied,
and it was found that, for dispersion relations for which the evolution is not
adiabatic, the spectrum changes from the standard prediction of
scale-invariance.Comment: 10 pages, 6 figures, RevTeX4. Analytical determination of the
spectrum, corrected some typos, conclusions unchange
Evolution of Fields in a Second Order Phase Transition
We analyse the evolution of scalar and gauge fields during a second order
phase transition using a Langevin equation approach. We show that topological
defects formed during the phase transition are stable to thermal fluctuations.
Our method allows the field evolution to be followed throughout the phase
transition, for both expanding and non-expanding Universes. The results verify
the Kibble mechanism for defect formation during phase transitions.Comment: 12 pages of text plus 17 diagrams available on request, DAMTP 94-8
A general condition of inflationary cosmology on trans-Planckian physics
We consider a more general initial condition satisfying the minimal
uncertainty relationship. We calculate the power spectrum of a simple model in
inflationary cosmology. The results depend on perturbations generated below a
fundamental scale, e.g. the Planck scale.Comment: 7 pages, References adde
On Signatures of Short Distance Physics in the Cosmic Microwave Background
Following a self-contained review of the basics of the theory of cosmological
perturbations, we discuss why the conclusions reached in the recent paper by
Kaloper et al are too pessimistic estimates of the amplitude of possible
imprints of trans-Planckian (string) physics on the spectrum of cosmic
microwave anisotropies in an inflationary Universe. It is shown that the likely
origin of large trans-Planckian effects on late time cosmological fluctuations
comes from nonadiabatic evolution of the state of fluctuations while the
wavelength is smaller than the Planck (string) scale, resulting in an excited
state at the time that the wavelength crosses the Hubble radius during
inflation.Comment: 11 pages, 4 figure
Trans-Planckian Dark Energy?
It has recently been proposed by Mersini et al. 01, Bastero-Gil and Mersini
02 that the dark energy could be attributed to the cosmological properties of a
scalar field with a non-standard dispersion relation that decreases
exponentially at wave-numbers larger than Planck scale (k_phys > M_Planck). In
this scenario, the energy density stored in the modes of trans-Planckian
wave-numbers but sub-Hubble frequencies produced by amplification of the vacuum
quantum fluctuations would account naturally for the dark energy. The present
article examines this model in detail and shows step by step that it does not
work. In particular, we show that this model cannot make definite predictions
since there is no well-defined vacuum state in the region of wave-numbers
considered, hence the initial data cannot be specified unambiguously. We also
show that for most choices of initial data this scenario implies the production
of a large amount of energy density (of order M_Planck^4) for modes with
momenta of order M_Planck, far in excess of the background energy density. We
evaluate the amount of fine-tuning in the initial data necessary to avoid this
back-reaction problem and find it is of order H/M_Planck. We also argue that
the equation of state of the trans-Planckian modes is not vacuum-like.
Therefore this model does not provide a suitable explanation for the dark
energy.Comment: RevTeX - 15 pages, 7 figures: final version to appear in PRD, minor
changes, 1 figure adde
The Corley-Jacobson dispersion relation and trans-Planckian inflation
In this Letter we study the dependence of the spectrum of fluctuations in
inflationary cosmology on possible effects of trans-Planckian physics, using
the Corley/Jacobson dispersion relations as an example. We compare the methods
used in previous work [1] with the WKB approximation, give a new exact
analytical result, and study the dependence of the spectrum obtained using the
approximate method of Ref. [1] on the choice of the matching time between
different time intervals. We also comment on recent work subsequent to Ref. [1]
on the trans-Planckian problem for inflationary cosmology.Comment: 6 pages, Revtex
The Trans-Planckian Problem of Inflationary Cosmology
In most current models of inflation based on a weakly self-coupled scalar
matter field minimally coupled to gravity, the period of inflation lasts so
long that, at the beginning of the inflationary period, the physical
wavelengths of comoving scales which correspond to the present large-scale
structure of the Universe were smaller than the Planck length. Thus, the usual
computations of the spectrum of fluctuations in these models involve
extrapolating low energy physics (both in the matter and gravitational sector)
into regions where this physics is not applicable. In this paper we demonstrate
that the usual predictions of inflation for the spectrum of cosmological
fluctuations do indeed depend on the hidden assumptions about super-Planck
scale physics. We introduce a class of modified dispersion relations to mimic
possible effects of super-Planck scale physics, and show that in some cases
important deviations from the usual predictions of inflation are obtained. Some
implications of this result for the unification of fundamental physics and
early Universe cosmology are discussed.Comment: 16 pages, 2 figures. One important correction in the Corley/Jacobson
case with b_m>0 and some misprints corrected. Version published in PR
Unconventional Cosmology
I review two cosmological paradigms which are alternative to the current
inflationary scenario. The first alternative is the "matter bounce", a
non-singular bouncing cosmology with a matter-dominated phase of contraction.
The second is an "emergent" scenario, which can be implemented in the context
of "string gas cosmology". I will compare these scenarios with the inflationary
one and demonstrate that all three lead to an approximately scale-invariant
spectrum of cosmological perturbations.Comment: 45 pages, 10 figures; invited lectures at the 6th Aegean Summer
School "Quantum Gravity and Quantum Cosmology", Chora, Naxos, Greece, Sept.
12 - 17 2012, to be publ. in the proceedings; these lecture notes form an
updated version of arXiv:1003.1745 and arXiv:1103.227
Holographic bounds on the UV cutoff scale in inflationary cosmology
We discuss how holographic bounds can be applied to the quantum fluctuations
of the inflaton. In general the holographic principle will lead to a bound on
the UV cutoff scale of the effective theory of inflation, but it will depend on
the coarse-graining prescription involved in calculating the entropy. We
propose that the entanglement entropy is a natural measure of the entropy of
the quantum perturbations, and show which kind of bound on the cutoff it leads
to. Such bounds are related to whether the effects of new physics will show up
in the CMB.Comment: 19 pages, 2 figures;(V3):Comments and references adde
Inflation as a probe of new physics
In this paper we consider inflation as a probe of new physics near the string
or Planck scale. We discuss how new physics can be captured by the choice of
vacuum, and how this leads to modifications of the primordial spectrum as well
as the way in which the universe expands during inflation. Provided there is a
large number of fields contributing to the vacuum energy -- as typically is
expected in string theory -- we will argue that both types of effects can be
present simultaneously and be of observational relevance. Our conclusion is
that the ambiguity in choice of vacuum is an interesting new parameter in
serious model building.Comment: 14 page
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