An Observational Test of Two-field Inflation

We study adiabatic and isocurvature perturbation spectra produced by a period of cosmological inflation driven by two scalar fields. We show that there exists a model-independent consistency condition for all two-field models of slow-roll inflation, despite allowing for model-dependent linear processing of curvature and isocurvature perturbations during and after inflation on super-horizon scales. The scale-dependence of all spectra are determined solely in terms of slow-roll parameters during inflation and the dimensionless cross-correlation between curvature and isocurvature perturbations. We present additional model-dependent consistency relations that may be derived in specific two-field models, such as the curvaton scenario.Comment: 6 pages, latex with revtex, no figures; v2, minor changes, to appear in Physical Review

Density Perturbations in the Ekpyrotic Scenario

We study the generation of density perturbations in the ekpyrotic scenario for the early universe, including gravitational backreaction. We expose interesting subtleties that apply to both inflationary and ekpyrotic models. Our analysis includes a detailed proposal of how the perturbations generated in a contracting phase may be matched across a `bounce' to those in an expanding hot big bang phase. For the physical conditions relevant to the ekpyrotic scenario, we re-obtain our earlier result of a nearly scale-invariant spectrum of energy density perturbations. We find that the perturbation amplitude is typically small, as desired to match observation.Comment: 36 pages, compressed and RevTex file, one postscript figure file. Minor typographical and numerical errors corrected, discussion added. This version to appear in Physical Review

Equation of motion for a domain wall coupled to gravitational field

The equation of motion for a domain wall coupled to gravitational field is derived from the Nambu-Goto action. The domain wall is treated as a source of gravitational field. The perturbed equation is also obtained with gravitational back reaction on the wall motion taken into account. For general spherically symmetric background case, the equation is expressed in terms of the gauge-invariant variables.Comment: 13 pages, latex, no figures, uses REVTe

Gravitational Waves in Open de Sitter Space

We compute the spectrum of primordial gravitational wave perturbations in open de Sitter spacetime. The background spacetime is taken to be the continuation of an O(5) symmetric instanton saddle point of the Euclidean no boundary path integral. The two-point tensor fluctuations are computed directly from the Euclidean path integral. The Euclidean correlator is then analytically continued into the Lorentzian region where it describes the quantum mechanical vacuum fluctuations of the graviton field. Unlike the results of earlier work, the correlator is shown to be unique and well behaved in the infrared. We show that the infrared divergence found in previous calculations is due to the contribution of a discrete gauge mode inadvertently included in the spectrum.Comment: 17 pages, compressed and RevTex file, including one postscript figure fil

The shape of the CMB lensing bispectrum

Lensing of the CMB generates a significant bispectrum, which should be detected by the Planck satellite at the 5-sigma level and is potentially a non-negligible source of bias for f_NL estimators of local non-Gaussianity. We extend current understanding of the lensing bispectrum in several directions: (1) we perform a non-perturbative calculation of the lensing bispectrum which is ~10% more accurate than previous, first-order calculations; (2) we demonstrate how to incorporate the signal variance of the lensing bispectrum into estimates of its amplitude, providing a good analytical explanation for previous Monte-Carlo results; and (3) we discover the existence of a significant lensing bispectrum in polarization, due to a previously-unnoticed correlation between the lensing potential and E-polarization as large as 30% at low multipoles. We use this improved understanding of the lensing bispectra to re-evaluate Fisher-matrix predictions, both for Planck and cosmic variance limited data. We confirm that the non-negligible lensing-induced bias for estimation of local non-Gaussianity should be robustly treatable, and will only inflate f_NL error bars by a few percent over predictions where lensing effects are completely ignored (but note that lensing must still be accounted for to obtain unbiased constraints). We also show that the detection significance for the lensing bispectrum itself is ultimately limited to 9 sigma by cosmic variance. The tools that we develop for non-perturbative calculation of the lensing bispectrum are directly relevant to other calculations, and we give an explicit construction of a simple non-perturbative quadratic estimator for the lensing potential and relate its cross-correlation power spectrum to the bispectrum. Our numerical codes are publicly available as part of CAMB and LensPix.Comment: 32 pages, 10 figures; minor changes to match JCAP-accepted version. CMB lensing and primordial local bispectrum codes available as part of CAMB (http://camb.info/

Reconstructing the primordial power spectrum from the CMB

We propose a straightforward and model independent methodology for characterizing the sensitivity of CMB and other experiments to wiggles, irregularities, and features in the primordial power spectrum. Assuming that the primordial cosmological perturbations are adiabatic, we present a function space generalization of the usual Fisher matrix formalism, applied to a CMB experiment resembling Planck with and without ancillary data. This work is closely related to other work on recovering the inflationary potential and exploring specific models of non-minimal, or perhaps baroque, primordial power spectra. The approach adopted here, however, most directly expresses what the data is really telling us. We explore in detail the structure of the available information and quantify exactly what features can be reconstructed and at what statistical significance.Comment: 43 pages Revtex, 23 figure

Holographic analysis of diffraction structure factors

We combine the theory of inside-source/inside-detector x-ray fluorescence holography and Kossel lines/x ray standing waves in kinematic approximation to directly obtain the phases of the diffraction structure factors. The influence of Kossel lines and standing waves on holography is also discussed. We obtain partial phase determination from experimental data obtaining the sign of the real part of the structure factor for several reciprocal lattice vectors of a vanadium crystal.Comment: 4 pages, 3 figures, submitte

Gauge-Invariant Initial Conditions and Early Time Perturbations in Quintessence Universes

We present a systematic treatment of the initial conditions and evolution of cosmological perturbations in a universe containing photons, baryons, neutrinos, cold dark matter, and a scalar quintessence field. By formulating the evolution in terms of a differential equation involving a matrix acting on a vector comprised of the perturbation variables, we can use the familiar language of eigenvalues and eigenvectors. As the largest eigenvalue of the evolution matrix is fourfold degenerate, it follows that there are four dominant modes with non-diverging gravitational potential at early times, corresponding to adiabatic, cold dark matter isocurvature, baryon isocurvature and neutrino isocurvature perturbations. We conclude that quintessence does not lead to an additional independent mode.Comment: Replaced with published version, 12 pages, 2 figure

Oscillations During Inflation and the Cosmological Density Perturbations

Adiabatic (curvature) perturbations are produced during a period of cosmological inflation that is driven by a single scalar field, the inflaton. On particle physics grounds -- though -- it is natural to expect that this scalar field is coupled to other scalar degrees of freedom. This gives rise to oscillations between the perturbation of the inflaton field and the perturbations of the other scalar degrees of freedom, similar to the phenomenon of neutrino oscillations. Since the degree of the mixing is governed by the squared mass matrix of the scalar fields, the oscillations can occur even if the energy density of the extra scalar fields is much smaller than the energy density of the inflaton field. The probability of oscillation is resonantly amplified when perturbations cross the horizon and the perturbations in the inflaton field may disappear at horizon crossing giving rise to perturbations in scalar fields other than the inflaton. Adiabatic and isocurvature perturbations are inevitably correlated at the end of inflation and we provide a simple expression for the cross-correlation in terms of the slow-roll parameters.Comment: 23 pages, uses LaTeX, added few reference

The CMB Bispectrum

We use a separable mode expansion estimator with WMAP data to estimate the bispectrum for all the primary families of non-Gaussian models. We review the late-time mode expansion estimator methodology which can be applied to any non-separable primordial and CMB bispectrum model, and we demonstrate how the method can be used to reconstruct the CMB bispectrum from an observational map. We extend the previous validation of the general estimator using local map simulations. We apply the estimator to the coadded WMAP 5-year data, reconstructing the WMAP bispectrum using $l<500$ multipoles and $n=31$ orthonormal 3D eigenmodes. We constrain all popular nearly scale-invariant models, ensuring that the theoretical bispectrum is well-described by a convergent mode expansion. Constraints from the local model \fnl=54.4\pm 29.4 and the equilateral model \fnl=143.5\pm 151.2 (\Fnl = 25.1\pm 26.4) are consistent with previously published results. (Here, we use a nonlinearity parameter \Fnl normalised to the local case, to allow more direct comparison between different models.) Notable new constraints from our method include those for the constant model \Fnl = 35.1 \pm 27.4 , the flattened model \Fnl = 35.4\pm 29.2, and warm inflation \Fnl = 10.3\pm 27.2. We investigate feature models surveying a wide parameter range in both the scale and phase, and we find no significant evidence of non-Gaussianity in the models surveyed. We propose a measure \barFnl for the total integrated bispectrum and find that the measured value is consistent with the null hypothesis that CMB anisotropies obey Gaussian statistics. We argue that this general bispectrum survey with the WMAP data represents the best evidence for Gaussianity to date and we discuss future prospects, notably from the Planck satellite