2,733 research outputs found
Inflation over the hill
We calculate the power spectrum of curvature perturbations when the inflaton
field is rolling over the top of a local maximum of a potential. We show that
the evolution of the field can be decomposed into a late-time attractor, which
is identified as the slow roll solution, plus a rapidly decaying non-slow roll
solution, corresponding to the field rolling ``up the hill'' to the maximum of
the potential. The exponentially decaying transient solution can map to an
observationally relevant range of scales because the universe is also expanding
exponentially. We consider the two branches separately and we find that they
are related through a simple transformation of the slow roll parameter
and they predict identical power spectra. We generalize this approach to the
case where the inflaton field is described by both branches simultaneously and
find that the mode equation can be solved exactly at all times. Even though the
slow roll parameter is evolving rapidly during the transition from the
transient solution to the late-time attractor solution, the resultant power
spectrum is an exact power-law spectrum. Such solutions may be useful for
model-building on the string landscape.Comment: 11 pages, 1 figure (V3: Version accepted by PRD, title changed by
journal
Perturbations in k-inflation
We extend the theory of cosmological perturbations to the case when the
``matter'' Lagrangian is an arbitrary function of the scalar field and its
first derivatives. In particular, this extension provides a unified description
of known cases such as the usual scalar field and the hydrodynamical perfect
fluid. In addition, it applies to the recently proposed k-inflation, which is
driven by non-minimal kinetic terms in the Lagrangian. The spectrum of quantum
fluctuations for slow-roll and power law k-inflation is calculated. We find,
for instance, that the usual ``consistency relation'' between the tensor
spectral index and the relative amplitude of scalar and tensor perturbations is
modified. Thus, at least in principle, k-inflation is phenomenologically
distinguishable from standard inflation.Comment: 12 pages, LaTe
Spectroscopy of the quantum black hole
We develop the idea that, in quantum gravity where the horizon fluctuates, a
black hole should have a discrete mass spectrum with concomitant line emission.
Simple arguments fix the spacing of the lines, which should be broad but
unblended. Assuming uniformity of the matrix elements for quantum transitions
between near levels, we work out the probabilities for the emission of a
specified series of quanta and the intensities of the spectral lines. The
thermal character of the radiation is entirely due to the degeneracy of the
levels, the same degeneracy that becomes manifest as black hole entropy. One
prediction is that there should be no lines with wavelength of order the black
hole size or larger. This makes it possible to test quantum gravity with black
holes well above Planck scale.Comment: RevTeX, 9 page
On Adiabatic Renormalization of Inflationary Perturbations
We discuss the impact of adiabatic renormalization on the power spectrum of
scalar and tensor perturbations from inflation. We show that adiabatic
regularization is ambiguous as it leads to very different results, for
different adiabatic subtraction schemes, both in the range v\equiv k/(aH)
\gsim 0.1 and in the infrared regime. All these schemes agree in the far
ultraviolet, . Therefore, we argue that in the far infrared regime,
, the adiabatic expansion is no longer valid, and the unrenormalized
spectra are the physical, measurable quantities. These findings cast some doubt
on the validity of the adiabatic subtraction at horizon exit, , to
determine the perturbation spectra from inflation which has recently advocated
in the literature.Comment: 7 pages, 3 figures, revtex. New version with more results and
modified plot
Path Integral Quantization of Cosmological Perturbations
We derive the first order canonical formulation of cosmological perturbation
theory in a Universe filled by a few scalar fields. This theory is quantized
via well-defined Hamiltonian path integral. The propagator which describes the
evolution of the initial (for instance, vacuum) state, is calculated.Comment: 16 pages, ETH-TH/94-0
Nucleosynthesis Without a Computer
I derive completely analytically the time evolution and final abundances of
the light elements (up to Be-7) formed in the big-bang nucleosynthesis.This
highlights an interesting physics taking place during the formation of light
elements in the early universe.Comment: 3 figures; uses tcilate
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