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) similar to 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 >= 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.

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.

We present exact bounce solutions and amplitudes for tunneling in i) a piecewise linear-quartic potential and ii) a piecewise quartic-quartic potential. We cross check their correctness by comparing with results obtained through the thin-wall approximation and with a piecewise linear-linear potential. We briefly comment on applications in cosmology.

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 the 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 comment briefly on the inclusion of gravity.

Inflation in an open universe produced by Coleman-De Luccia (CDL) tunneling induces a friction term that is strong enough to allow for successful small-field inflation in models that would otherwise suffer from a severe overshoot problem. In this paper, we present a polynomial scalar potential which allows for a full analysis. This provides a simple model of single-field open inflation on a small-field inflection point after tunneling. We present numerical results and compare them with analytic approximations.

We present an update to the search for a nontrivial topology of the Universe by searching for matching circle pairs in the cosmic microwave background [N. J. Cornish et al. Phys. Rev. Lett. 92, 201 302 (2004)] using the WMAP 7-year data release. We extend the existing bounds to encompass a wider range of possible topologies by searching for matching circle pairs with opening angles 10 degrees <= alpha <= 90 degrees and separation angles 11 degrees <= theta <= 180 degrees. The extended search reveals two small anomalous regions in the cosmic microwave background 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 nontrivial 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 degrees.

It is currently believed that the Standard Model is an effective low energy theory which in principle may contain higher dimensional non-renormalizable operators. These operators may modify the standard model Higgs potential in many ways, one of which being the appearance of a second vacuum. For a wide range of parameters, this new vacuum becomes the true vacuum. It is then assumed that our universe is currently sitting in the false vacuum. Thus the usual second-order electroweak phase transition at early times will be followed by a second, first-order phase transition. In cosmology, a first-order phase transition is associated with the production of gravity waves. In this paper we present an analysis of the production of gravitational waves during such a second electroweak phase transition. We find that, for one certain range of parameters, the stochastic background of gravitational waves generated by bubble nucleation and collision have an amplitude which is estimated to be of order $\Omega_{GW}h^2\sim10^{-11}$ at $f=3\times 10^{-4}$Hz, which is within reach of the planned sensitivity of LISA. For another range of parameters, we find that the amplitude is estimated o be of order $\Omega_{GW}h^2\sim10^{-25}$ around $f=10^3$Hz, which is within reach of LIGO. Hence, it is possible to detect gravity waves from such a phase transition at two different detectors, with completely different amplitude and frequency ranges.

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.

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. 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.

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.

There are things we know, things we know we don't know, and then there are things we don't know we don't know. In this paper we address the latter two issues in a Bayesian framework, introducing the notion of doubt to quantify the degree of (dis)belief in a model given observational data in the absence of explicit alternative models. We demonstrate how a properly calibrated doubt can lead to model discovery when the true model is unknown.

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.

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 Kaehler 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 nonperturbative effects defining the potential V({tau},{theta}) and kinetic parameters of the moduli brings 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 trajectories', with long-lasting inflations in the direction of the rolling axion, enhanced in the 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.

The bottom-up approach to ination reconstructs from available observables the acceleration trajectories (histories) in terms of the Hubble parameter H as a function of the e-folding number N. Assuming a scalar eld driven ination, it also addresses the reconstruction of its potential. We suggest new, numerically fast, methods to scan the space of acceleration trajectories H(N), based on (uniform) function approximations (including Chebyshev polynomials, lters and splines). Assuming mildly broken scale invariant primordial spectra, we map the acceleration trajectories to the 3d space of observables: spectral index ns, its running dns=d lnk and the tensor to scalar ratio r. We show that the space of models is larger relative to that obtained with RG o w methods (? ). With respect to potential reconstruction, we demonstrate that the same spectrum (not necessarily mildly broken invariant) of primordial scalar perturbations corresponds to a a degenerate family of potentials which include both positively and negatively curved potentials. The degeneracy is only broken by constraining the tensor contribution from the model. Ination is fully dened by acceleration with the Hub- ble parameter trajectory H(x;t) monotonically decreas- ing with increasing expansion factora(x;t). It ends when heating occurs and the deceleration parameter trajectory q(x;t) = aa=_ a 2 = d lnHa=d lna passes from negative to positive. Within the single-eld inaton approxima- tion, often valid even when there are many scalar elds present, these dynamical trajectories associated with the gravitational dynamics are all that are needed, driv- ing the evolution of the inaton potential and the var- ious scalar and tensor uctuation power spectra. The usual approach in ination is to specify parameterized scalar eld potentials motivated by fundamental parti- cle physics, proceed to derive the dynamical histories and compare with cosmic observations model by model characterized by only a few parameters, a \top{down" framework. With the increasing emphasis on complex potential landscapes dotted by many local minima with varied structures surrounding them, large ensembles of possible trajectories could arise, viable ones being deter- mined probabilistically, from theoretical \prior" informa- tion and from the data, whether with very broad error bars, as in anthropic considerations, or of the increas- ingly high precision sort oered by the cosmic microwave background and large scale structure observations. This bottom{up view is a phenomenology, based on few a pri- ori assumptions. Although there is much art in deciding what theoretical priors to impose, based on concepts such as \baroqueness" of the eectiv e potentials allowed, it is best to allow the priors to be broadly dened and let the data decide what is allowed and what not. It is a well- trod path in concept and one we develop further in this paper. The bottom{up view is cast here in the context of the Hamilton Jacobi (HJ) formalism, intimately associ- ated with the stochastic ination picture which treats the background elds as long wavelength elds, such as lna(x;t) and H(x;t), upon which are superposed high frequency uctuations within the instantaneous horizon, Ha(x;t). lna(x;t) and H(x;t) are the metric variables that are the analog of scalar elds (x;t) and their mo- menta ( x;t). In this paper we normalize scalar elds as