17 research outputs found
Recommended from our members
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
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
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
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
Estimators for local non-Gaussianities
We study the Likelihood function of data given f_NL for the so-called local
type of non-Gaussianity. In this case the curvature perturbation is a
non-linear function, local in real space, of a Gaussian random field. We
compute the Cramer-Rao bound for f_NL and show that for small values of f_NL
the 3-point function estimator saturates the bound and is equivalent to
calculating the full Likelihood of the data. However, for sufficiently large
f_NL, the naive 3-point function estimator has a much larger variance than
previously thought. In the limit in which the departure from Gaussianity is
detected with high confidence, error bars on f_NL only decrease as 1/ln Npix
rather than Npix^-1/2 as the size of the data set increases. We identify the
physical origin of this behavior and explain why it only affects the local type
of non-Gaussianity, where the contribution of the first multipoles is always
relevant. We find a simple improvement to the 3-point function estimator that
makes the square root of its variance decrease as Npix^-1/2 even for large
f_NL, asymptotically approaching the Cramer-Rao bound. We show that using the
modified estimator is practically equivalent to computing the full Likelihood
of f_NL given the data. Thus other statistics of the data, such as the 4-point
function and Minkowski functionals, contain no additional information on f_NL.
In particular, we explicitly show that the recent claims about the relevance of
the 4-point function are not correct. By direct inspection of the Likelihood,
we show that the data do not contain enough information for any statistic to be
able to constrain higher order terms in the relation between the Gaussian field
and the curvature perturbation, unless these are orders of magnitude larger
than the size suggested by the current limits on f_NL.Comment: 26 pages. v2: added comments about the approximations used, published
JCAP versio
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
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
Non-Gaussianities in Multi-field Inflation
We compute the amplitude of the non-Gaussianities in inflationary models with
multiple, uncoupled scalar fields. This calculation thus applies to all models
of assisted inflation, including N-flation, where inflation is driven by
multiple axion fields arising from shift symmetries in a flux stabilized string
vacuum. The non-Gaussianities are associated with nonlinear evolution of the
field (and density) perturbations, characterized by the parameter . We
derive a general expression for the nonlinear parameter, incorporating the
evolution of perturbations after horizon-crossing. This is valid for arbitrary
separable potentials during slow roll. To develop an intuitive understanding of
this system and to demonstrate the applicability of the formalism we examine
several cases with quadratic potentials: two-field models with a wide range of
mass ratios, and a general N-field model with a narrow mass spectrum. We
uncover that is suppressed as the number of e-foldings grows, and that
this suppression is increased in models with a broad spectrum of masses. On the
other hand, we find no enhancement to that increases with the number
of fields. We thus conclude that the production of a large non-Gaussian signal
in multi-field models of inflation is very unlikely as long as fields are
slowly rolling and potentials are of simple, quadratic form. Finally, we
compute a spectrum for the scalar spectral index that incorporates the
nonlinear corrections to the fields' evolution.Comment: 23 pages; v.3: minor extensions to match version accepted in JCA
Large Non-Gaussianities in Single Field Inflation
We compute the 3-point correlation function for a general model of inflation
driven by a single, minimally coupled scalar field. Our approach is based on
the numerical evaluation of both the perturbation equations and the integrals
which contribute to the 3-point function. Consequently, we can analyze models
where the potential has a "feature", in the vicinity of which the slow roll
parameters may take on large, transient values. This introduces both scale and
shape dependent non-Gaussianities into the primordial perturbations. As an
example of our methodology, we examine the ``step'' potentials which have been
invoked to improve the fit to the glitch in the for ,
present in both the one and three year WMAP data sets. We show that for the
typical parameter values, the non-Gaussianities associated with the step are
far larger than those in standard slow roll inflation, and may even be within
reach of a next generation CMB experiment such as Planck. More generally, we
use this example to explain that while adding features to potential can improve
the fit to the 2-point function, these are generically associated with a
greatly enhanced signal at the 3-point level. Moreover, this 3-point signal
will have a very nontrivial shape and scale dependence, which is correlated
with the form of the 2-point function, and may thus lead to a consistency check
on the models of inflation with non-smooth potentials.Comment: 23 pages JHEP-style, 7 Figures. Updated with improved results.
Accepted for publication by JCA