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Observational Signatures and Non-Gaussianities of General Single Field Inflation
We perform a general study of primordial scalar non-Gaussianities in single field inflationary models. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ``shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results
Comparing Brane Inflation to WMAP
We compare the simplest realistic brane inflationary model to recent
cosmological data, including WMAP 3-year cosmic microwave background (CMB)
results, Sloan Digital Sky Survey luminous red galaxies (SDSS LRG) power
spectrum data and Supernovae Legacy Survey (SNLS) Type 1a supernovae distance
measures. Here, the inflaton is simply the position of a -brane which is
moving towards a -brane sitting at the bottom of a throat (a warped,
deformed conifold) in the flux compactified bulk in Type IIB string theory. The
analysis includes both the usual slow-roll scenario and the Dirac-Born-Infeld
scenario of slow but relativistic rolling. Requiring that the throat is inside
the bulk greatly restricts the allowed parameter space. We discuss possible
scenarios in which large tensor mode and/or non-Gaussianity may emerge. Here,
the properties of a large tensor mode deviate from that in the usual slow-roll
scenario, providing a possible stringy signature. Overall, within the brane
inflationary scenario, the cosmological data is providing information about the
properties of the compactification of the extra dimensions.Comment: 45 pages 11 figure
Duality Cascade in Brane Inflation
We show that brane inflation is very sensitive to tiny sharp features in
extra dimensions, including those in the potential and in the warp factor. This
can show up as observational signatures in the power spectrum and/or
non-Gaussianities of the cosmic microwave background radiation (CMBR). One
general example of such sharp features is a succession of small steps in a
warped throat, caused by Seiberg duality cascade using gauge/gravity duality.
We study the cosmological observational consequences of these steps in brane
inflation. Since the steps come in a series, the prediction of other steps and
their properties can be tested by future data and analysis. It is also possible
that the steps are too close to be resolved in the power spectrum, in which
case they may show up only in the non-Gaussianity of the CMB temperature
fluctuations and/or EE polarization. We study two cases. In the slow-roll
scenario where steps appear in the inflaton potential, the sensitivity of brane
inflation to the height and width of the steps is increased by several orders
of magnitude comparing to that in previously studied large field models. In the
IR DBI scenario where steps appear in the warp factor, we find that the
glitches in the power spectrum caused by these sharp features are generally
small or even unobservable, but associated distinctive non-Gaussianity can be
large. Together with its large negative running of the power spectrum index,
this scenario clearly illustrates how rich and different a brane inflationary
scenario can be when compared to generic slow-roll inflation. Such distinctive
stringy features may provide a powerful probe of superstring theory.Comment: Corrections in Eq.(5.47), Eq (5.48), Eq(5.49) and Fig
Observing Brane Inflation
Linking the slow-roll scenario and the Dirac-Born-Infeld scenario of
ultra-relativistic roll (where, thanks to the warp factor, the inflaton moves
slowly even with an ultra-relativistic Lorentz factor), we find that the KKLMMT
D3/anti-D3 brane inflation is robust, that is, enough e-folds of inflation is
quite generic in the parameter space of the model. We show that the
intermediate regime of relativistic roll can be quite interesting
observationally. Introducing appropriate inflationary parameters, we explore
the parameter space and give the constraints and predictions for the
cosmological observables in this scenario. Among other properties, this
scenario allows the saturation of the present observational bound of either the
tensor/scalar ratio r (in the intermediate regime) or the non-Gaussianity f_NL
(in the ultra-relativistic regime), but not both.Comment: 31 pages, 12 figures; typo correcte
Cosmology of the Tachyon in Brane Inflation
In certain implementations of the brane inflationary paradigm, the exit from
inflation occurs when the branes annihilate through tachyon condensation. We
investigate various cosmological effects produced by this tachyonic era. We
find that only a very small region of the parameter space (corresponding to
slow-roll with tiny inflaton mass) allows for the tachyon to contribute some
e-folds to inflation. In addition, non-adiabatic density perturbations are
generated at the end of inflation. When the brane is moving relativistically
this contribution can be of the same order as fluctuations produced 55 e-folds
before the end of inflation. The additional contribution is very nearly
scale-invariant and enhances the tensor/scalar ratio. Additional
non-gaussianities will also be generated, sharpening current constraints on
DBI-type models which already predict a significantly non-gaussian signal.Comment: 30 pages, 2 figures; v3, minor revision, JCAP versio
Is Brane Inflation Eternal?
In this paper, we show that eternal inflation of the random walk type is
generically absent in the brane inflationary scenario. Depending on how the
brane inflationary universe originated, eternal inflation of the false vacuum
type is still quite possible. Since the inflaton is the position of the
D3-brane relative to the anti-D3-brane inside the compactified bulk with finite
size, its value is bounded. In DBI inflation, the warped space also restricts
the amplitude of the scalar fluctuation. These upper bounds impose strong
constraints on the possibility of eternal inflation. We find that eternal
inflation due to the random walk of the inflaton field is absent in both the
KKLMMT slow roll scenario and the DBI scenario. A more careful analysis for the
slow-roll case is also presented using the Langevin equation, which gives very
similar results. We discuss possible ways to obtain eternal inflation of the
random walk type in brane inflation. In the multi-throat brane inflationary
scenario, the branes may be generated by quantum tunneling and roll out the
throat. Eternal inflation of the false vacuum type inevitably happens in this
scenario due to the tunneling process. Since these scenarios have different
cosmological predictions, more data from the cosmic microwave background
radiation will hopefully select the specific scenario our universe has gone
through.Comment: 32 pages; v2: references and comments adde
DBI Inflation using a One-Parameter Family of Throat Geometries
We demonstrate the possibility of examining cosmological signatures in the
DBI inflation setup using the BGMPZ solution, a one-parameter family of
geometries for the warped throat which interpolate between the Maldacena-Nunez
and Klebanov-Strassler solutions. The warp factor is determined numerically and
subsequently used to calculate cosmological observables including the scalar
and tensor spectral indices, for a sample point in the parameter space. As one
moves away from the KS solution for the throat the warp factor is qualitatively
different, which leads to a significant change for the observables, but also
generically increases the non-Gaussianity of the models. We argue that the
different models can potentially be differentiated by current and future
experiments.Comment: 17 pages, 10 figures; v2: section 4 expanded, references added; v3:
typos fixe
Non-gaussianity from the inflationary trispectrum
We present an estimate for the non-linear parameter \tau_NL, which measures
the non-gaussianity imprinted in the trispectrum of the comoving curvature
perturbation, \zeta. Our estimate is valid throughout the inflationary era,
until the slow-roll approximation breaks down, and takes into account the
evolution of perturbations on superhorizon scales. We find that the
non-gaussianity is always small if the field values at the end of inflation are
negligible when compared to their values at horizon crossing. Under the same
assumption, we show that in Nflation-type scenarios, where the potential is a
sum of monomials, the non-gaussianity measured by \tau_NL is independent of the
couplings and initial conditions.Comment: 15 pages, uses iopart.sty. Replaced with version accepted by JCAP;
journal reference adde
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
Natural Inflation, Planck Scale Physics and Oscillating Primordial Spectrum
In the ``natural inflation'' model, the inflaton potential is periodic. We
show that Planck scale physics may induce corrections to the inflaton
potential, which is also periodic with a greater frequency. Such high frequency
corrections produce oscillating features in the primordial fluctuation power
spectrum, which are not entirely excluded by the current observations and may
be detectable in high precision data of cosmic microwave background (CMB)
anisotropy and large scale structure (LSS) observations.Comment: 20 pages, 11 figures. To appear in Int J Mod. Phys.
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