63 research outputs found
Constraining Inflation
Slow roll reconstruction is derived from the Hamilton-Jacobi formulation of
inflationary dynamics. It automatically includes information from sub-leading
terms in slow roll, and facilitatesthe inclusion of priors based on the
duration on inflation. We show that at low inflationary scales the
Hamilton-Jacobi equations simplify considerably. We provide a new
classification scheme for inflationary models, based solely on the number of
parameters needed to specify the potential, and provide forecasts for likely
bounds on the slow roll parameters from future datasets. A minimal running of
the spectral index, induced solely by the first two slow roll parameters
(\epsilon and \eta) appears to be effectively undetectable by realistic Cosmic
Microwave Background experiments. However, we show that the ability to detect
this signal increases with the lever arm in comoving wavenumber, and we
conjecture that high redshift 21 cm data may allow tests of second order
consistency conditions on inflation. Finally, we point out that the second
order corrections to the spectral index are correlated with the inflationary
scale, and thus the amplitude of the CMB B-mode.Comment: 32 pages. v
Primordial Black Holes, Eternal Inflation, and the Inflationary Parameter Space after WMAP5
We consider constraints on inflation driven by a single, minimally coupled
scalar field in the light of the WMAP5 dataset, as well as ACBAR and the
SuperNova Legacy Survey. We use the Slow Roll Reconstruction algorithm to
derive optimal constraints on the inflationary parameter space. The scale
dependence in the slope of the scalar spectrum permitted by WMAP5 is large
enough to lead to viable models where the small scale perturbations have a
substantial amplitude when extrapolated to the end of inflation. We find that
excluding parameter values which would cause the overproduction of primordial
black holes or even the onset of eternal inflation leads to potentially
significant constraints on the slow roll parameters. Finally, we present a more
sophisticated approach to including priors based on the total duration of
inflation, and discuss the resulting restrictions on the inflationary parameter
space.Comment: v2: version published in JCAP. Minor clarifications and references
adde
Inflation and the Scale Dependent Spectral Index: Prospects and Strategies
We consider the running of the spectral index as a probe of both inflation
itself, and of the overall evolution of the very early universe. Surveying a
collection of simple single field inflationary models, we confirm that the
magnitude of the running is relatively consistent, unlike the tensor amplitude,
which varies by orders of magnitude. Given this target, we confirm that the
running is potentially detectable by future large scale structure or 21 cm
observations, but that only the most futuristic measurements can distinguish
between these models on the basis of their running. For any specified
inflationary scenario, the combination of the running index and unknown
post-inflationary expansion history induces a theoretical uncertainty in the
predicted value of the spectral index. This effect can easily dominate the
statistical uncertainty with which Planck and its successors are expected to
measure the spectral index. More positively, upcoming cosmological experiments
thus provide an intriguing probe of physics between TeV and GUT scales by
constraining the reheating history associated with any specified inflationary
model, opening a window into the "primordial dark age" that follows the end of
inflation.Comment: 32 pages. v2 and v3 Minor reference updates /clarification
Implications of a Running Spectral Index for Slow Roll Inflation
We analyze the weak (2 sigma) evidence for a running spectral index seen in
the three-year WMAP dataset and its implications for single field, slow roll
inflation. We assume that the running is comparable to the central value found
from the WMAP data analysis, and use the Hubble Slow Roll formalism to follow
the evolution of the slow roll parameters. For all parameter choices consistent
with a large, negative running, single field, slow roll inflation lasts less
than 30 efolds after CMB scales leave the horizon. Thus, a definitive
observation of a large negative running would imply that any inflationary phase
requires multiple fields or the breakdown of slow roll. Alternatively, if
single field, slow roll inflation is sources the primordial fluctuations, we
can expect the observed running to move much closer to zero as the CMB is
measured more accurately at small angular scales.Comment: 4 pages; v2 Refs added, some clarifications in discussion, minor
typos fixe
The Lyth Bound and the End of Inflation
We derive an extended version of the well-known Lyth Bound on the total
variation of the inflaton field, incorporating higher order corrections in slow
roll. We connect the field variation to both the spectral index of
scalar perturbations and the amplitude of tensor modes. We then investigate the
implications of this bound for ``small field'' potentials, where the field
rolls off a local maximum of the potential. The total field variation during
inflation is {\em generically} of order , even for potentials with
a suppressed tensor/scalar ratio. Much of the total field excursion arises in
the last e-fold of inflation and in single field models this problem can only
be avoided via fine-tuning or the imposition of a symmetry. Finally, we discuss
the implications of this result for inflationary model building in string
theory and supergravity.Comment: 10 pages, RevTeX, 2 figures (V3: version accepted for publication by
JCAP
Boundary Effective Field Theory and Trans-Planckian Perturbations: Astrophysical Implications
We contrast two approaches to calculating trans-Planckian corrections to the
inflationary perturbation spectrum: the New Physics Hypersurface [NPH] model,
in which modes are normalized when their physical wavelength first exceeds a
critical value, and the Boundary Effective Field Theory [BEFT] approach, where
the initial conditions for all modes are set at the same time, and modified by
higher dimensional operators enumerated via an effective field theory
calculation. We show that these two approaches -- as currently implemented --
lead to radically different expectations for the trans-Planckian corrections to
the CMB and emphasize that in the BEFT formalism we expect the perturbation
spectrum to be dominated by quantum gravity corrections for all scales shorter
than some critical value. Conversely, in the NPH case the quantum effects only
dominate the longest modes that are typically much larger than the present
horizon size. Furthermore, the onset of the breakdown in the standard
inflationary perturbation calculation predicted by the BEFT formalism is likely
to be associated with a feature in the perturbation spectrum, and we discuss
the observational signatures of this feature in both CMB and large scale
structure observations. Finally, we discuss possible modifications to both
calculational frameworks that would resolve the contradictions identified here.Comment: Reworded commentary, reference added (v2) References added (v3
New Solutions of the Inflationary Flow Equations
The inflationary flow equations are a frequently used method of surveying the
space of inflationary models. In these applications the infinite hierarchy of
differential equations is truncated in a way which has been shown to be
equivalent to restricting the set of models considered to those characterized
by polynomial inflaton potentials. This paper explores a different method of
solving the flow equations, which does not truncate the hierarchy and in
consequence covers a much wider class of models while retaining the practical
usability of the standard approach.Comment: References added, and a couple of comment
Recovering the Inflationary Potential and Primordial Power Spectrum With a Slow Roll Prior: Methodology and Application to WMAP 3 Year Data
We introduce a new method for applying an inflationary prior to a
cosmological dataset that includes relations between observables at arbitrary
order in the slow roll expansion. The process is based on the inflationary flow
equations, and the slow roll parameters appear explicitly in the cosmological
parameter set. We contrast our method to other ways of imposing an inflationary
prior on a cosmological dataset, and argue that this method is ideal for use
with heterogeneous datasets. In particular, it would be well suited to
exploiting any direct detection of fundamental tensor modes by a BBO-style
mission. To demonstrate the practical use of this method we apply it to the
WMAPI+All dataset, and the newly released WMAPII dataset on its own and
together with the SDSS data. We find that all basic classes of single field
inflationary models are still allowed at the 1-2sigma level, but the overall
parameter space is sharply constrained. In particular, we find evidence that
the combination of WMAPII+SDSS is sensitive to effects arising from terms that
are quadratic in the two leading-order slow roll parameters.Comment: v2 adds references and fixes typos. New explanatory material added
clarifying effects that depend on terms that are second order in the slow
roll parameters, and the impact of the beam parametrization and SZ prior on
the central value of n_s v3: Added refs, minor clarifications, title
modified. In press with JCAP v4: New figures, with minor smoothing artifacts
removed. Matches published version. v5 Fixed typo in caption of Figure
Slow Roll Reconstruction: Constraints on Inflation from the 3 Year WMAP Dataset
We study the constraints on the inflationary parameter space derived from the
3 year WMAP dataset using ``slow roll reconstruction'', using the SDSS galaxy
power spectrum to gain further leverage where appropriate. This approach
inserts the inflationary slow roll parameters directly into a Monte Carlo
Markov chain estimate of the cosmological parameters, and uses the inflationary
flow hierarchy to compute the parameters' scale-dependence. We work with the
first three parameters (epsilon, eta and xi) and pay close attention to the
possibility that the 3 year WMAP dataset contains evidence for a ``running''
spectral index, which is dominated by the xi term. Mirroring the WMAP team's
analysis we find that the permitted distribution of xi is broad, and centered
away from zero. However, when we require that inflationary parameters yield at
least 30 additional e-folds of inflation after the largest observable scales
leave the horizon, the bounds on xi tighten dramatically. We make use of the
absence of an explicit pivot scale in the slow roll reconstruction formalism to
determine the dependence of the computed parameter distributions on the pivot.
We show that the choice of pivot has a significant effect on the inferred
constraints on the inflationary variables, and the spectral index and running
derived from them. Finally, we argue that the next round of cosmological data
can be expected to place very stringent constraints on the region of parameter
space open to single field models of slow roll inflation.Comment: 26 pages, 11 figures, JHEP format. v2: version accepted by JCAP:
minor clarifications and references added, 1 figure added, v3: 1 reference
adde
The Fate of the Alpha-Vacuum
de Sitter space-time has a one complex parameter family of invariant vacua
for the theory of a free, massive scalar field. For most of these vacua, in an
interacting scalar theory the one loop corrections diverge linearly for large
values of the loop momentum. These divergences are not of a form that can be
removed by a de Sitter invariant counterterm, except in the case of the
Euclidean, or Bunch-Davies, vacuum.Comment: 15 pages, 6 figures, uses ReVTeX, minor corrections to the time
evolutio
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