442 research outputs found
Dominance of gauge artifact in the consistency relation for the primordial bispectrum
The conventional cosmological perturbation theory has been performed under
the assumption that we know the whole spatial region of the universe with
infinite volume. This is, however, not the case in the actual observations
because observable portion of the universe is limited. To give a theoretical
prediction to the observable fluctuations, gauge-invariant observables should
be composed of the information in our local observable universe with finite
volume. From this point of view, we reexamine the primordial non-Gaussianity in
single field models, focusing on the bispectrum in the squeezed limit. A
conventional prediction states that the bispectrum in this limit is related to
the power spectrum through the so-called consistency relation. However, it
turns out that, if we adopt a genuine gauge invariant variable which is
naturally composed purely of the information in our local universe, the leading
term for the bispectrum in the squeezed limit predicted by the consistency
relation vanishes.Comment: 12 pages; v2: accepted version in JCA
Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Bispectrum
The methods of effective field theory are used to study generic theories of
inflation with a single inflaton field and to perform a general analysis of the
associated non-Gaussianities. We investigate the amplitudes and shapes of the
various generic three-point correlators, the bispectra, which may be generated
by different classes of single-field inflationary models. Besides the
well-known results for the DBI-like models and the ghost inflationary theories,
we point out that curvature-related interactions may give rise to large
non-Gaussianities in the form of bispectra characterized by a flat shape which,
quite interestingly, is independently produced by several interaction terms. In
a subsequent work, we will perform a similar general analysis for the
non-Gaussianities generated by the generic four-point correlator, the
trispectrum.Comment: Version matching the one published in JCAP, 2 typos fixed, references
added. 30 pages, 20 figure
Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Trispectrum
We perform the analysis of the trispectrum of curvature perturbations
generated by the interactions characterizing a general theory of single-field
inflation obtained by effective field theory methods. We find that
curvature-generated interaction terms, which can in general give an important
contribution to the amplitude of the four-point function, show some new
distinctive features in the form of their trispectrum shape-function. These
interesting interactions are invariant under some recently proposed symmetries
of the general theory and, as shown explicitly, do allow for a large value of
the trispectrum.Comment: 29 pages, 13 figure
The δN formula is the dynamical renormalization group
We derive the 'separate universe' method for the inflationary bispectrum,
beginning directly from a field-theory calculation. We work to tree-level in
quantum effects but to all orders in the slow-roll expansion, with masses
accommodated perturbatively. Our method provides a systematic basis to account
for novel sources of time-dependence in inflationary correlation functions, and
has immediate applications. First, we use our result to obtain the correct
matching prescription between the 'quantum' and 'classical' parts of the
separate universe computation. Second, we elaborate on the application of this
method in situations where its validity is not clear. As a by-product of our
calculation we give the leading slow-roll corrections to the three-point
function of field fluctuations on spatially flat hypersurfaces in a canonical,
multiple-field model.Comment: v1: 33 pages, plus appendix and references; 5 figures. v2:
typographical typos fixed, minor changes to the main text and abstract,
reference added; matches version published in JCA
de Sitter limit of inflation and nonlinear perturbation theory
We study the fourth order action of the comoving curvature perturbation in an
inflationary universe in order to understand more systematically the de Sitter
limit in nonlinear cosmological perturbation theory. We derive the action of
the curvature perturbation to fourth order in the comoving gauge, and show that
it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter
limit, we then extrapolate to the n'th order action of the comoving curvature
perturbation and discuss the slow-roll order of the n-point correlation
function.Comment: 14 pages, 1 figure; typos corrected and discussion of tensor modes
adde
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
Evolution of fNL to the adiabatic limit
We study inflationary perturbations in multiple-field models, for which zeta
typically evolves until all isocurvature modes decay--the "adiabatic limit". We
use numerical methods to explore the sensitivity of the nonlinear parameter fNL
to the process by which this limit is achieved, finding an appreciable
dependence on model-specific data such as the time at which slow-roll breaks
down or the timescale of reheating. In models with a sum-separable potential
where the isocurvature modes decay before the end of the slow-roll phase we
give an analytic criterion for the asymptotic value of fNL to be large. Other
examples can be constructed using a waterfall field to terminate inflation
while fNL is transiently large, caused by descent from a ridge or convergence
into a valley. We show that these two types of evolution are distinguished by
the sign of the bispectrum, and give approximate expressions for the peak fNL.Comment: v1: 25 pages, plus Appendix and bibliography, 6 figures. v2: minor
edits to match published version in JCA
A parton picture of de Sitter space during slow-roll inflation
It is well-known that expectation values in de Sitter space are afflicted by
infra-red divergences. Long ago, Starobinsky proposed that infra-red effects in
de Sitter space could be accommodated by evolving the long-wavelength part of
the field according to the classical field equations plus a stochastic source
term. I argue that--when quantum-mechanical loop corrections are taken into
account--the separate-universe picture of superhorizon evolution in de Sitter
space is equivalent, in a certain leading-logarithm approximation, to
Starobinsky's stochastic approach. In particular, the time evolution of a box
of de Sitter space can be understood in exact analogy with the DGLAP evolution
of partons within a hadron, which describes a slow logarithmic evolution in the
distribution of the hadron's constituent partons with the energy scale at which
they are probed.Comment: 36 pages; uses iopart.cls and feynmp.sty. v2: Minor typos corrected.
Matches version published in JCA
Semiclassical relations and IR effects in de Sitter and slow-roll space-times
We calculate IR divergent graviton one-loop corrections to scalar correlators
in de Sitter space, and show that the leading IR contribution may be reproduced
via simple semiclassical consistency relations. One can likewise use such
semiclassical relations to calculate leading IR corrections to correlators in
slow-roll inflation. The regulated corrections shift the tensor/scalar ratio
and consistency relation of single field inflation, and non-gaussianity
parameters averaged over very large distances. For inflation of sufficient
duration, for example arising from a chaotic inflationary scenario, these
corrections become of order unity. First-order corrections of this size
indicate a breakdown of the perturbative expansion, and suggest the need for a
non-perturbative description of the corresponding regime. This is analogous to
a situation argued to arise in black hole evolution, and to interfere with a
sharp perturbative calculation of "missing information" in Hawking radiation.Comment: 32 pages, 2 figures; v2: running of spectral index included and other
minor changes; v3: minor changes to agree with published versio
Large slow-roll corrections to the bispectrum of noncanonical inflation
Nongaussian statistics are a powerful discriminant between inflationary
models, particularly those with noncanonical kinetic terms. Focusing on
theories where the Lagrangian is an arbitrary Lorentz-invariant function of a
scalar field and its first derivatives, we review and extend the calculation of
the observable three-point function. We compute the "next-order" slow-roll
corrections to the bispectrum in closed form, and obtain quantitative estimates
of their magnitude in DBI and power-law k-inflation. In the DBI case our
results enable us to estimate corrections from the shape of the potential and
the warp factor: these can be of order several tens of percent. We track the
possible sources of large logarithms which can spoil ordinary perturbation
theory, and use them to obtain a general formula for the scale dependence of
the bispectrum. Our result satisfies the next-order version of Maldacena's
consistency condition and an equivalent consistency condition for the scale
dependence. We identify a new bispectrum shape available at next-order, which
is similar to a shape encountered in Galileon models. If fNL is sufficiently
large this shape may be independently detectable.Comment: v1: 37 pages, plus tables, figures and appendices. v2: supersedes
version published in JCAP; some clarifications and more detailed comparison
with earlier literature. All results unchanged. v3:improvements to some
plots; text unchange
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