The bispectrum of matter perturbations from cosmic strings

We present the first calculation of the bispectrum of the matter perturbations induced by cosmic strings. The calculation is performed in two different ways: the first uses the unequal time correlators (UETCs) of the string network - computed using a Gaussian model previously employed for cosmic string power spectra. The second approach uses the wake model, where string density perturbations are concentrated in sheet-like structures whose surface density grows with time. The qualitative and quantitative agreement of the two gives confidence to the results. An essential ingredient in the UETC approach is the inclusion of compensation factors in the integration with the Green's function of the matter and radiation fluids, and we show that these compensation factors must be included in the wake model also. We also present a comparison of the UETCs computed in the Gaussian model, and those computed in the unconnected segment model (USM) used by the standard cosmic string perturbation package CMBACT. We compare numerical estimates for the bispectrum of cosmic strings to those produced by perturbations from an inflationary era, and discover that, despite the intrinsically non-Gaussian nature of string-induced perturbations, the matter bispectrum is unlikely to produce competitive constraints on a population of cosmic strings

Dynamical compactification from de Sitter space

We show that D-dimensional de Sitter space is unstable to the nucleation of non-singular geometries containing spacetime regions with different numbers of macroscopic dimensions, leading to a dynamical mechanism of compactification. These and other solutions to Einstein gravity with flux and a cosmological constant are constructed by performing a dimensional reduction under the assumption of q-dimensional spherical symmetry in the full D-dimensional geometry. In addition to the familiar black holes, black branes, and compactification solutions we identify a number of new geometries, some of which are completely non-singular. The dynamical compactification mechanism populates lower-dimensional vacua very differently from false vacuum eternal inflation, which occurs entirely within the context of four-dimensions. We outline the phenomenology of the nucleation rates, finding that the dimensionality of the vacuum plays a key role and that among vacua of the same dimensionality, the rate is highest for smaller values of the cosmological constant. We consider the cosmological constant problem and propose a novel model of slow-roll inflation that is triggered by the compactification process.Comment: Revtex. 41 pages with 24 embedded figures. Minor corrections and added reference

Reconstruction of the Primordial Power Spectrum by Direct Inversion

We introduce a new method for reconstructing the primordial power spectrum, $P(k)$, directly from observations of the Cosmic Microwave Background (CMB). We employ Singular Value Decomposition (SVD) to invert the radiation perturbation transfer function. The degeneracy of the multipole $\ell$ to wavenumber $k$ linear mapping is thus reduced. This enables the inversion to be carried out at each point along a Monte Carlo Markov Chain (MCMC) exploration of the combined $P(k)$ and cosmological parameter space. We present best--fit $P(k)$ obtained with this method along with other cosmological parameters.Comment: 23 pages, 9 figure

Model selection applied to reconstruction of the Primordial Power Spectrum

The preferred shape for the primordial spectrum of curvature perturbations is determined by performing a Bayesian model selection analysis of cosmological observations. We first reconstruct the spectrum modelled as piecewise linear in \log k between nodes in k-space whose amplitudes and positions are allowed to vary. The number of nodes together with their positions are chosen by the Bayesian evidence, so that we can both determine the complexity supported by the data and locate any features present in the spectrum. In addition to the node-based reconstruction, we consider a set of parameterised models for the primordial spectrum: the standard power-law parameterisation, the spectrum produced from the Lasenby & Doran (LD) model and a simple variant parameterisation. By comparing the Bayesian evidence for different classes of spectra, we find the power-law parameterisation is significantly disfavoured by current cosmological observations, which show a preference for the LD model.Comment: Minor changes to match version accepted by JCA

The Inflationary Wavefunction and its Initial Conditions

We explore the effect of initial conditions on the inflationary wavefunction and their consequences for the observed spectrum of primordial fluctuations. In a class of models with a sudden transition into inflation we find that, for a reasonable set of assumptions about the reheat temperature and the number of e-foldings, it is possible for initial conditions set by a pre-inflationary epoch to have an observable effect.Comment: 17 pages, 1 figure, numerical example and analysis thereof added in this versio

Cosmological Imprints of Pre-Inflationary Particles

We study some of the cosmological imprints of pre-inflationary particles. We show that each such particle provides a seed for a spherically symmetric cosmic defect. The profile of this cosmic defect is fixed and its magnitude is linear in a single parameter that is determined by the mass of the pre-inflationary particle. We study the CMB and peculiar velocity imprints of this cosmic defect and suggest that it could explain some of the large scale cosmological anomalies.Comment: 31 pages, 7 figure

Observational Consequences of a Landscape

In this paper we consider the implications of the "landscape" paradigm for the large scale properties of the universe. The most direct implication of a rich landscape is that our local universe was born in a tunnelling event from a neighboring vacuum. This would imply that we live in an open FRW universe with negative spatial curvature. We argue that the "overshoot" problem, which in other settings would make it difficult to achieve slow roll inflation, actually favors such a cosmology. We consider anthropic bounds on the value of the curvature and on the parameters of inflation. When supplemented by statistical arguments these bounds suggest that the number of inflationary efolds is not very much larger than the observed lower bound. Although not statistically favored, the likelihood that the number of efolds is close to the bound set by observations is not negligible. The possible signatures of such a low number of efolds are briefly described.Comment: 21 pages, 4 figures v2: references adde

The extended empirical process test for non-Gaussianity in the CMB, with an application to non-Gaussian inflationary models

In (Hansen et al. 2002) we presented a new approach for measuring non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern, based on the multivariate empirical distribution function of the spherical harmonics a_lm of a CMB map. The present paper builds upon the same ideas and proposes several improvements and extensions. More precisely, we exploit the additional information on the random phases of the a_lm to provide further tests based on the empirical distribution function. Also we take advantage of the effect of rotations in improving the power of our procedures. The suggested tests are implemented on physically motivated models of non-Gaussian fields; Monte-Carlo simulations suggest that this approach may be very promising in the analysis of non-Gaussianity generated by non-standard models of inflation. We address also some experimentally meaningful situations, such as the presence of instrumental noise and a galactic cut in the map.Comment: 15 pages, 6 figures, submitted to Phys. Rev.

Bayesian joint estimation of non-Gaussianity and the power spectrum

We propose a rigorous, non-perturbative, Bayesian framework which enables one jointly to test Gaussianity and estimate the power spectrum of CMB anisotropies. It makes use of the Hilbert space of an harmonic oscillator to set up an exact likelihood function, dependent on the power spectrum and on a set of parameters $\alpha_i$, which are zero for Gaussian processes. The latter can be expressed as series of cumulants; indeed they perturbatively reduce to cumulants. However they have the advantage that their variation is essentially unconstrained. Any truncation(i.e.: finite set of $\alpha_i$) therefore still produces a proper distribution - something which cannot be said of the only other such tool on offer, the Edgeworth expansion. We apply our method to Very Small Array (VSA) simulations based on signal Gaussianity, showing that our algorithm is indeed not biased.Comment: 11pages, 4 figures, submitted to MNRA

Large Scale Pressure Fluctuations and Sunyaev-Zel'dovich Effect

The Sunyaev-Zel'dovich (SZ) effect associated with pressure fluctuations of the large scale structure gas distribution will be probed with current and upcoming wide-field small angular scale cosmic microwave background experiments. We study the generation of pressure fluctuations by baryons which are present in virialized dark matter halos and by baryons present in small overdensities. For collapsed halos, assuming the gas distribution is in hydrostatic equilibrium with matter density distribution, we predict the pressure power spectrum and bispectrum associated with the large scale structure gas distribution by extending the dark matter halo approach which describes the density field in terms of correlations between and within halos. The projected pressure power spectrum allows a determination of the resulting SZ power spectrum due to virialized structures. The unshocked photoionized baryons present in smaller overdensities trace the Jeans-scale smoothed dark matter distribution. They provide a lower limit to the SZ effect due to large scale structure in the absence of massive collapsed halos. We extend our calculations to discuss higher order statistics, such as bispectrum and skewness in SZ data. The SZ-weak lensing cross-correlation is suggested as a probe of correlations between dark matter and baryon density fields, while the probability distribution functions of peak statistics of SZ halos in wide field CMB data can be used as a probe of cosmology and non-Gaussian evolution of large scale structure pressure fluctuations.Comment: 16 pages, 9 figures; Revised with expanded discussions. Phys. Rev. D. (in press