Validity of the kink approximation to the tunneling action

Coleman tunneling in a general scalar potential with two non-degenerate minima is known to have an approximation in terms of a piecewise linear triangular-shaped potential with sharp 'kinks' at the place of the local minima. This approximate potential has a regime where the existence of the bounce solution needs the scalar field to 'wait' for some amount of Euclidean time at one of the 'kinks'. We discuss under which conditions a kink approximation of locally smooth 'cap' regions provides a good estimate for the bounce action.Comment: 7 pages, 4 figures, title changed in version 2 to match published versio

Roulette Inflation with K\"ahler Moduli and their Axions

We study 2-field inflation models based on the ``large-volume'' flux compactification of type IIB string theory. The role of the inflaton is played by a K\"ahler modulus \tau corresponding to a 4-cycle volume and its axionic partner \theta. The freedom associated with the choice of Calabi Yau manifold and the non-perturbative effects defining the potential V(\tau, \theta) and kinetic parameters of the moduli bring an unavoidable statistical element to theory prior probabilities within the low energy landscape. The further randomness of (\tau, \theta) initial conditions allows for a large ensemble of trajectories. Features in the ensemble of histories include ``roulette tractories'', with long-lasting inflations in the direction of the rolling axion, enhanced in number of e-foldings over those restricted to lie in the \tau-trough. Asymptotic flatness of the potential makes possible an eternal stochastic self-reproducing inflation. A wide variety of potentials and inflaton trajectories agree with the cosmic microwave background and large scale structure data. In particular, the observed scalar tilt with weak or no running can be achieved in spite of a nearly critical de Sitter deceleration parameter and consequently a low gravity wave power relative to the scalar curvature power.Comment: Version submitted to Phys.Rev.D. 29 pages, 12 Figures, minor change

Surprising phenomena in a rich new class of inflationary models

We report on a new class of fast-roll inflationary models. In a huge part of its parameter space, inflationary perturbations exhibit quite unusual phenomena such as scalar and tensor modes freezing out at widely different times, as well as scalar modes reentering the horizon during inflation. In another, narrower range of parameters, this class of models agrees with observations. One specific point in parameter space is characterized by extraordinary behavior of the scalar perturbations. Freeze-out of scalar perturbations as well as particle production at horizon crossing are absent. Also the behavior of the perturbations around this quasi-de Sitter background is dual to a quantum field theory in flat space-time. Finally, the form of the primordial power spectrum is determined by the interaction between different modes of scalar perturbations.Comment: 12 pages, 5 figures, 1 table, references + comments added, errors corrected, conclusions unchanged, version published in JCA

The Virtues of Frugality - Why cosmological observers should release their data slowly

Cosmologists will soon be in a unique position. Observational noise will gradually be replaced by cosmic variance as the dominant source of uncertainty in an increasing number of observations. We reflect on the ramifications for the discovery and verification of new models. If there are features in the full data set that call for a new model, there will be no subsequent observations to test that model's predictions. We give specific examples of the problem by discussing the pitfalls of model discovery by prior adjustment in the context of dark energy models and inflationary theories. We show how the gradual release of data can mitigate this difficulty, allowing anomalies to be identified, and new models to be proposed and tested. We advocate that observers plan for the frugal release of data from future cosmic variance limited observations.Comment: 5 pages, expanded discussion of Lambda and of blind anlysis, added refs. Matches version to appear in MNRAS Letter

CMBPol Mission Concept Study: Probing Inflation with CMB Polarization

We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B-mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super-Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale-dependence and non-Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters.Comment: 107 pages, 14 figures, 17 tables; Inflation Working Group contribution to the CMBPol Mission Concept Study; v2: typos fixed and references adde

An Exact Tunneling Solution in a Simple Realistic Landscape

We present an analytical solution for the tunneling process in a piecewise linear and quadratic potential which does not make use of the thin-wall approximation. A quadratic potential allows for smooth attachment of various slopes exiting into the final minimum of a realistic potential. Our tunneling solution thus serves as a realistic approximation to situations such as populating a landscape of slow-roll inflationary regions by tunneling, and it is valid for all regimes of the barrier parameters. We shortly comment on the inclusion of gravity.Comment: RevTeX 4.1, 4 pages, 5 figure

Constraints on the Topology of the Universe: Extension to General Geometries

We present an update to the search for a non-trivial topology of the universe by searching for matching circle pairs in the cosmic microwave background using the WMAP 7 year data release. We extend the exisiting bounds to encompass a wider range of possible topologies by searching for matching circle pairs with opening angles 10 degree < \alpha < 90 degree and separation angles 11 degree < \theta < 180 degree. The extended search reveal two small anomalous regions in the CMB sky. Numerous pairs of well-matched circles are found where both circles pass through one or the other of those regions. As this is not the signature of any known manifold, but is a likely consequence of contamination in those sky regions, we repeat the search excluding circle pairs where both pass through either of the two regions. We then find no statistically significant pairs of matched circles, and so no hints of a non-trivial topology. The absence of matched circles increases the lower limit on the length of the shortest closed null geodesic that self-intersects at our location in the universe (equivalently the injectivity radius at our location) to 98.5% of the diameter of the last scattering surface or approximately 26 Gpc. It extends the limit to any manifolds in which the intersecting arcs of said geodesic form an angle greater than 10^o.Comment: 11 pages, 11 figure

The Overshoot Problem in Inflation after Tunneling

We show the absence of the usual parametrically large overshoot problem of small-field inflation if initiated by a Coleman-De Luccia (CDL) tunneling transition from an earlier vacuum in the limit of small inflationary scale compared to the tunneling scale. For low-power monomial exit potentials $V(\phi)\sim\phi^n, n<4$, we derive an expression for the amount of overshoot. This is bounded from above by the width of the steep barrier traversed after emerging from tunneling and before reaching a slow-roll region of the potential. For $n\geq 4$ we show that overshooting is entirely absent. We extend this result through binomials to a general potential written as a series expansion, and to the case of arbitrary finite initial speed of the inflaton. This places the phase space of initial conditions for small-field and large-field inflation on the same footing in a landscape of string theory vacua populated via CDL tunneling.Comment: 14 pages, 4 figure