339 research outputs found
Transport equations for the inflationary trispectrum
We use transport techniques to calculate the trispectrum produced in
multiple-field inflationary models with canonical kinetic terms. Our method
allows the time evolution of the local trispectrum parameters, tauNL and gNL,
to be tracked throughout the inflationary phase. We illustrate our approach
using examples. We give a simplified method to calculate the superhorizon part
of the relation between field fluctuations on spatially flat hypersurfaces and
the curvature perturbation on uniform density slices, and obtain its
third-order part for the first time. We clarify how the 'backwards' formalism
of Yokoyama et al. relates to our analysis and other recent work. We supply
explicit formulae which enable each inflationary observable to be computed in
any canonical model of interest, using a suitable first-order ODE solver.Comment: 24 pages, plus references and appendix. v2: matches version published
in JCAP; typo fixed in Eq. (54
Infrared effects in inflationary correlation functions
In this article, I briefly review the status of infrared effects which occur
when using inflationary models to calculate initial conditions for a subsequent
hot, dense plasma phase. Three types of divergence have been identified in the
literature: secular, "time-dependent" logarithms, which grow with time spent
outside the horizon; "box-cutoff" logarithms, which encode a dependence on the
infrared cutoff when calculating in a finite-sized box; and "quantum"
logarithms, which depend on the ratio of a scale characterizing new physics to
the scale of whatever process is under consideration, and whose interpretation
is the same as conventional field theory. I review the calculations in which
these divergences appear, and discuss the methods which have been developed to
deal with them.Comment: Invited review for focus section of Classical & Quantum Gravity on
nonlinear and nongaussian perturbation theory. Some improvements compared to
version which will appear in CQG, especially in Sec. 2.3. 30 pages +
references
Gravity and non-gravity mediated couplings in multiple-field inflation
Mechanisms for the generation of primordial non-Gaussian metric fluctuations
in the context of multiple-field inflation are reviewed. As long as kinetic
terms remain canonical, it appears that nonlinear couplings inducing
non-gaussianities can be split into two types. The extension of the one-field
results to multiple degrees of freedom leads to gravity mediated couplings that
are ubiquitous but generally modest. Multiple-field inflation offers however
the possibility of generating non-gravity mediated coupling in isocurvature
directions that can eventually induce large non-Gaussianities in the metric
fluctuations. The robustness of the predictions of such models is eventually
examined in view of a case study derived from a high-energy physics
construction.Comment: 14 pages, 3 figures, invited review for CQG issue on non-linear
cosmolog
Inflationary perturbation theory is geometrical optics in phase space
A pressing problem in comparing inflationary models with observation is the
accurate calculation of correlation functions. One approach is to evolve them
using ordinary differential equations ("transport equations"), analogous to the
Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this
approach to the complete set of momentum space correlation functions. A formal
solution can be obtained using raytracing techniques adapted from geometrical
optics. We reformulate inflationary perturbation theory in this language, and
show that raytracing reproduces the familiar "delta N" Taylor expansion. Our
method produces ordinary differential equations which allow the Taylor
coefficients to be computed efficiently. We use raytracing methods to express
the gauge transformation between field fluctuations and the curvature
perturbation, zeta, in geometrical terms. Using these results we give a compact
expression for the nonlinear gauge-transform part of fNL in terms of the
principal curvatures of uniform energy-density hypersurfaces in field space.Comment: 22 pages, plus bibliography and appendix. v2: minor changes, matches
version published in JCA
Issues Concerning Loop Corrections to the Primordial Power Spectra
We expound ten principles in an attempt to clarify the debate over infrared
loop corrections to the primordial scalar and tensor power spectra from
inflation. Among other things we note that existing proposals for nonlinear
extensions of the scalar fluctuation field introduce new ultraviolet
divergences which no one understands how to renormalize. Loop corrections and
higher correlators of these putative observables would also be enhanced by
inverse powers of the slow roll parameter . We propose an extension
which should be better behaved.Comment: 36 pages, uses LaTeX2e, version 3 revised for publication with a much
expanded section 4, proving that our proposed extension of the zeta-zeta
correlator absorbs the one loop infrared divergences from graviton
One-loop corrections to the curvature perturbation from inflation
An estimate of the one-loop correction to the power spectrum of the
primordial curvature perturbation is given, assuming it is generated during a
phase of single-field, slow-roll inflation. The loop correction splits into two
parts, which can be calculated separately: a purely quantum-mechanical
contribution which is generated from the interference among quantized field
modes around the time when they cross the horizon, and a classical contribution
which comes from integrating the effect of field modes which have already
passed far beyond the horizon. The loop correction contains logarithms which
may invalidate the use of naive perturbation theory for cosmic microwave
background (CMB) predictions when the scale associated with the CMB is
exponentially different from the scale at which the fundamental theory which
governs inflation is formulated.Comment: 28 pages, uses feynmp.sty and ioplatex journal style. v2: supersedes
version published in JCAP. Some corrections and refinements to the discussion
and conclusions. v3: Corrects misidentification of quantum correction with an
IR effect. Improvements to the discussio
Non-gaussianity of inflationary field perturbations from the field equation
We calculate the tree-level bispectrum of the inflaton field perturbation
directly from the field equations, and construct the corresponding f_NL
parameter. Our results agree with previous ones derived from the Lagrangian. We
argue that quantum theory should only be used to calculate the correlators when
they first become classical a few Hubble times after horizon exit, the
classical evolution taking over thereafter.Comment: 16 pages, uses iopart.sty. v2: replaced with version accepted by
JCAP; minor changes of wording only. v3: supersedes version published by
journal; typo fixed in Eq. (20) and updated references. v4: sign errors in
Eqs. (32) and (38) correcte
On the Physical Significance of Infra-red Corrections to Inflationary Observables
Inflationary observables, like the power spectrum, computed at one- and
higher-order loop level seem to be plagued by large infra-red corrections. In
this short note, we point out that these large infra-red corrections appear
only in quantities which are not directly observable. This is in agreement with
general expectations concerning infra-red effects.Comment: 11 pages; LateX file; 5 figures. Some coefficients in Eq.(A6)
corrected; References adde
Cosmic No Hair for Braneworlds with a Bulk Dilaton Field
Braneworld cosmology supported by a bulk scalar field with an exponential
potential is developed. A general class of separable backgrounds for both
single and two-brane systems is derived, where the bulk metric components are
given by products of world-volume and bulk coordinates and the world-volumes
represent any anisotropic and inhomogeneous solution to an effective
four-dimensional Brans-Dicke theory of gravity. We deduce a cosmic no hair
theorem for all ever expanding, spatially homogeneous Bianchi world-volumes and
find that the spatially flat and isotropic inflationary scaling solution
represents a late-time attractor when the bulk potential is sufficiently flat.
The dependence of this result on the separable nature of the bulk metric is
investigated by applying the techniques of Hamilton-Jacobi theory to
five-dimensional Einstein gravity. We employ the spatial gradient expansion
method to determine the asymptotic form of the bulk metric up to third-order in
spatial gradients. It is found that the condition for the separable form of the
metric to represent the attractor of the system is precisely the same as that
for the four-dimensional world-volume to isotropize. We also derive the
fourth-order contribution to the Hamilton-Jacobi generating functional.
Finally, we conclude by placing our results within the context of the
holographic approach to braneworld cosmology.Comment: 13 pages, uses RevTeX
Phenomenology of a Pseudo-Scalar Inflaton: Naturally Large Nongaussianity
Many controlled realizations of chaotic inflation employ pseudo-scalar
axions. Pseudo-scalars \phi are naturally coupled to gauge fields through c
\phi F \tilde{F}. In the presence of this coupling, gauge field quanta are
copiously produced by the rolling inflaton. The produced gauge quanta, in turn,
source inflaton fluctuations via inverse decay. These new cosmological
perturbations add incoherently with the "vacuum" perturbations, and are highly
nongaussian. This provides a natural mechanism to generate large nongaussianity
in single or multi field slow-roll inflation. The resulting phenomenological
signatures are highly distinctive: large nongaussianity of (nearly) equilateral
shape, in addition to detectably large values of both the scalar spectral tilt
and tensor-to-scalar ratio (both being typical of large field inflation). The
WMAP bound on nongaussianity implies that the coupling, c, of the pseudo-scalar
inflaton to any gauge field must be smaller than about 10^{2} M_p^{-1}.Comment: 45 pages, 7 figure
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