368 research outputs found
Non-linear inflationary perturbations
We present a method by which cosmological perturbations can be quantitatively
studied in single and multi-field inflationary models beyond linear
perturbation theory. A non-linear generalization of the gauge-invariant
Sasaki-Mukhanov variables is used in a long-wavelength approximation. These
generalized variables remain invariant under time slicing changes on long
wavelengths. The equations they obey are relatively simple and can be
formulated for a number of time slicing choices. Initial conditions are set
after horizon crossing and the subsequent evolution is fully non-linear. We
briefly discuss how these methods can be implemented numerically in the study
of non-Gaussian signatures from specific inflationary models.Comment: 10 pages, replaced to match JCAP versio
Quantum inflaton, primordial metric perturbations and CMB fluctuations
We compute the primordial scalar, vector and tensor metric perturbations
arising from quantum field inflation. Quantum field inflation takes into
account the nonperturbative quantum dynamics of the inflaton consistently
coupled to the dynamics of the (classical) cosmological metric. For chaotic
inflation, the quantum treatment avoids the unnatural requirements of an
initial state with all the energy in the zero mode. For new inflation it allows
a consistent treatment of the explosive particle production due to spinodal
instabilities. Quantum field inflation (under conditions that are the quantum
analog of slow roll) leads, upon evolution, to the formation of a condensate
starting a regime of effective classical inflation. We compute the primordial
perturbations taking the dominant quantum effects into account. The results for
the scalar, vector and tensor primordial perturbations are expressed in terms
of the classical inflation results. For a N-component field in a O(N) symmetric
model, adiabatic fluctuations dominate while isocurvature or entropy
fluctuations are negligible. The results agree with the current WMAP
observations and predict corrections to the power spectrum in classical
inflation. Such corrections are estimated to be of the order of m^2/H^2 where m
is the inflaton mass and H the Hubble constant at horizon crossing. This turns
to be about 4% for the cosmologically relevant scales. This quantum field
treatment of inflation provides the foundations to the classical inflation and
permits to compute quantum corrections to it.Comment: LaTeX, 8 pages, no figures. To appear in the Proceedings of the ERE
2006 Meeting, Journal of Physics: Conference Serie
Non-Gaussian perturbations from multi-field inflation
We show how the primordial bispectrum of density perturbations from inflation
may be characterised in terms of manifestly gauge-invariant cosmological
perturbations at second order. The primordial metric perturbation, zeta,
describing the perturbed expansion of uniform-density hypersurfaces on large
scales is related to scalar field perturbations on unperturbed (spatially-flat)
hypersurfaces at first- and second-order. The bispectrum of the metric
perturbation is thus composed of (i) a local contribution due to the
second-order gauge-transformation, and (ii) the instrinsic bispectrum of the
field perturbations on spatially flat hypersurfaces. We generalise previous
results to allow for scale-dependence of the scalar field power spectra and
correlations that can develop between fields on super-Hubble scales.Comment: 11 pages, RevTex; minor changes to text; conclusions unchanged;
version to appear in JCA
Gauge-invariant perturbations at second order in two-field inflation
We study the second-order gauge-invariant adiabatic and isocurvature
perturbations in terms of the scalar fields present during inflation, along
with the related fully non-linear space gradient of these quantities. We
discuss the relation with other perturbation quantities defined in the
literature. We also construct the exact cubic action of the second-order
perturbations (beyond any slow-roll or super-horizon approximations and
including tensor perturbations), both in the uniform energy density gauge and
the flat gauge in order to settle various gauge-related issues. We thus provide
the tool to calculate the exact non-Gaussianity beyond slow-roll and at any
scale.Comment: 28 pages, no figures. v2: Added a summary subsection 4.3 with further
discussion of the results. Generalized all super-horizon results of section 4
and appendix A to exact ones. Other minor textual changes and references
added. Conclusions unchanged. Matches published versio
Multiple-field inflation and the CMB
In this paper, we investigate some consequences of multiple-field inflation
for the cosmic microwave background radiation (CMB). We derive expressions for
the amplitudes, the spectral indices and the derivatives of the indices of the
CMB power spectrum in the context of a very general multiple-field theory of
slow-roll inflation, where the field metric can be non-trivial. Both scalar
(adiabatic, isocurvature and mixing) and tensor perturbations are treated and
the differences with single-field inflation are discussed. From these
expressions, several relations are derived that can be used to determine the
importance of multiple-field effects observationally from the CMB. We also
study the evolution of the total entropy perturbation during radiation and
matter domination and the influence of this on the isocurvature spectral
quantities.Comment: 24 pages. References added, some very minor textual changes, matches
version to be published in CQ
Non-Gaussianity in braneworld and tachyon inflation
We calculate the bispectrum of single-field braneworld inflation, triggered
by either an ordinary scalar field or a cosmological tachyon, by means of a
gradient expansion of large-scale non-linear perturbations coupled to
stochastic dynamics. The resulting effect is identical to that for single-field
4D standard inflation, the non-linearity parameter being proportional to the
scalar spectral index in the limit of collapsing momentum. If the slow-roll
approximation is assumed, braneworld and tachyon non-Gaussianities are
subdominant with respect to the post-inflationary contribution. However, bulk
physics may considerably strengthen the non-linear signatures. These features
do not change significantly when considered in a non-commutative framework.Comment: 17 pages; v2: added references and previously skipped details in the
derivation of the result; v3: improved discussio
Tachyonic preheating using 2PI-1/N dynamics and the classical approximation
We study the process of tachyonic preheating using approximative quantum
equations of motion derived from the 2PI effective action. The O(N) scalar
(Higgs) field is assumed to experience a fast quench which is represented by an
instantaneous flip of the sign of the mass parameter. The equations of motion
are solved numerically on the lattice, and the Hartree and 1/N-NLO
approximations are compared to the classical approximation. Classical dynamics
is expected to be valid, since the occupation numbers can rise to large values
during tachyonic preheating. We find that the classical approximation performs
excellently at short and intermediate times, even for couplings in the larger
region currently allowed for the SM Higgs. This is reassuring, since all
previous numerical studies of tachyonic preheating and baryogenesis during
tachyonic preheating have used classical dynamics. We also compare different
initializations for the classical simulations.Comment: 32 pages, 21 figures. Published version: Some details added, section
added, references added, conclusions unchange
Diagrammatic approach to non-Gaussianity from inflation
We present Feynman type diagrams for calculating the n-point function of the
primordial curvature perturbation in terms of scalar field perturbations during
inflation. The diagrams can be used to evaluate the corresponding terms in the
n-point function at tree level or any required loop level. Rules are presented
for drawing the diagrams and writing down the corresponding terms in real space
and Fourier space. We show that vertices can be renormalised to automatically
account for diagrams with dressed vertices. We apply these rules to calculate
the primordial power spectrum up to two loops, the bispectrum including loop
corrections, and the trispectrum.Comment: 17 pages, 13 figures. v2: Comments and references added, v3:
Introduction expanded, subsection on evaluating loop diagrams added, minor
errors corrected, references adde
On the Transverse-Traceless Projection in Lattice Simulations of Gravitational Wave Production
It has recently been pointed out that the usual procedure employed in order
to obtain the transverse-traceless (TT) part of metric perturbations in lattice
simulations was inconsistent with the fact that those fields live in the
lattice and not in the continuum. It was claimed that this could lead to a
larger amplitude and a wrong shape for the gravitational wave (GW) spectra
obtained in numerical simulations of (p)reheating. In order to address this
issue, we have defined a consistent prescription in the lattice for extracting
the TT part of the metric perturbations. We demonstrate explicitly that the GW
spectra obtained with the old continuum-based TT projection only differ
marginally in amplitude and shape with respect to the new lattice-based ones.
We conclude that one can therefore trust the predictions appearing in the
literature on the spectra of GW produced during (p)reheating and similar
scenarios simulated on a lattice.Comment: 22 pages, 8 figures, Submitted to JCA
Kahler Moduli Inflation
We show that under general conditions there is at least one natural
inflationary direction for the Kahler moduli of type IIB flux
compactifications. This requires a Calabi-Yau which has h^{2,1}>h^{1,1}>2 and
for which the structure of the scalar potential is as in the recently found
exponentially large volume compactifications. We also need - although these
conditions may be relaxed - at least one Kahler modulus whose only
non-vanishing triple-intersection is with itself and which appears by itself in
the non-perturbative superpotential. Slow-roll inflation then occurs without a
fine tuning of parameters, evading the eta problem of F-term inflation. In
order to obtain COBE-normalised density perturbations, the stabilised volume of
the Calabi-Yau must be O(10^5-10^7) in string units, and the inflationary scale
M_{infl} ~ 10^{13} GeV. We find a robust model independent prediction for the
spectral index of 1 - 2/N_e = 0.960 - 0.967, depending on the number of
efoldings.Comment: 17 pages, 1 figure; v2. references adde
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