Optimal CMB estimators for bispectra from excited states

We propose optimal estimators for bispectra from excited states. Two common properties of such bispectra are the enhancement in the collinear limit, and the prediction of oscillating features. We review the physics behind excited states and some of the choices made in the literature. We show that the enfolded template is a good template in the collinear limit, but does poorly elsewhere, establishing a strong case for an improved estimator. Although the detailed scale dependence of the bispectra differs depending on various assumptions, generally the predicted bispectra are either effectively 1 or 2-dimensional and a simple Fourier basis suffices for accurate reconstruction. For an optimal CMB data analysis, combining all n-point functions, the choice for the excited state needs to be the same when computing power spectrum, bispectrum and higher order correlation functions. This has not always been the case, which could lead to wrong conclusions. We calculate the bispectrum for different choices previously discussed for the power spectrum, setting up a consistent framework to search for evidence of excited states in the CMB data.Comment: 19 pages, 9 figure

The Future of Primordial Features with 21 cm Tomography

Detecting a deviation from a featureless primordial power spectrum of fluctuations would give profound insight into the physics of the primordial Universe. Depending on their nature, primordial features can either provide direct evidence for the inflation scenario or pin down details of the inflation model. Thus far, using the cosmic microwave background (CMB) we have only been able to put stringent constraints on the amplitude of features, but no significant evidence has been found for such signals. Here we explore the limit of the experimental reach in constraining such features using 21 cm tomography at high redshift. A measurement of the 21 cm power spectrum from the Dark Ages is generally considered as the ideal experiment for early Universe physics, with potentially access to a large number of modes. We consider three different categories of theoretically motivated models: the sharp feature models, resonance models, and standard clock models. We study the improvements on bounds on features as a function of the total number of observed modes and identify parameter degeneracies. The detectability depends critically on the amplitude, frequency and scale-location of the features, as well as the angular and redshift resolution of the experiment. We quantify these effects by considering different fiducial models. Our forecast shows that a cosmic variance limited 21 cm experiment measuring fluctuations in the redshift range $30\leq z \leq 100$ with a 0.01-MHz bandwidth and sub-arcminute angular resolution could potentially improve bounds by several orders of magnitude for most features compared to current Planck bounds. At the same time, 21 cm tomography also opens up a unique window into features that are located on very small scales.Comment: Matches version accepted for publication. Changes made to forecasting; using k space instead of \ell space. Forecasted constraints significantly improved for some feature

Joint resonant CMB power spectrum and bispectrum estimation

We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large number of simulations to derive the probability density function (PDF) of the feature-amplitude in the Gaussian case. Although these simulations are tractable for the power spectrum, for the bispectrum they require significant computational resources. We show that, by assuming that the PDF is given by a multi-variate Gaussian where the covariance is determined by the Fisher matrix of the sine and cosine terms, we can efficiently produce spectra that are statistically close to those derived from full simulations. By drawing a large number of spectra from this PDF, both for the power spectrum and the bispectrum, we can quickly determine the statistical significance of candidate signatures in the CMB, considering both single frequency and multi-frequency estimators. We show that for resonance models, cosmology and foreground parameters have little influence on the estimated amplitude, which allows to simplify the analysis considerably. A more precise likelihood treatment can then be applied to candidate signatures only. We also discuss a modal expansion approach for the power spectrum, aimed at quickly scanning through large families of oscillating models.Comment: 17 pages, 11 figures. This version: Added refs, fixed typos and some rewrite

Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates

Scanning tunneling spectroscopy (STS) is a useful probe for studying the cuprates in the superconducting and pseudogap states. Here we present a theoretical study of the Z-map, defined as the ratio of the local density of states at positive and negative bias energies, which frequently is used to analyze STS data. We show how the evolution of the quasiparticle interference peaks in the Fourier transform Z-map can be understood by considering different types of impurity scatterers, as well as particle-hole asymmetry in the underlying bandstructure. We also explore the effects of density wave orders, and show that the Fourier transform Z-map may be used to both detect and distinguish between them.Comment: final version published in Phys. Rev.

Hasard et destin dans le Anton Reiser de Karl Philipp Moritz

International audienceThe distinction between literary chance and chance as experience (E. Köhler) allows the originality of Moritz's autobiographical novel to be disengaged. This study of the motif of chance in book II ofAnton Reiser shows the establishment of a narrative method characterized by repressing the literary treatment of chance and maintaining of chance as a category of lived experience. In this text, the fortunate and unfortunate chances do not found the literary necessity of an exemplary destiny, but are the occasion for throwing light on the double determination, exterior and interior, that affects the character's existence, an existence that is experienced under the sign of a radical contingency. It is in this first obscurity that psychological analysis operates, not to establish the horizon of Providence, but to disengage the general lessons of an existence, and to give to its hero, at this moment, the consistency of a novelistic character.La distinction entre les deux catégories du « hasard vécu » (erlebter Zufall) et du « hasard littéraire » (literarischer Zufall), empruntée à Erich Köhler, permet d'aborder l'étude du roman autobiographique de Karl Philipp Moritz, Anton Reiser, en faisant ressortir l'ambivalence d'un projet "romanesque" en un sens nouveau. On montre ici comment le recul de la figuration du hasard littéraire au profit de la figuration du hasard vécu exprime la remise en cause du roman traditionnel et la recherche de nouvelles formes permettant de saisir et de donner forme à la consistance de la vie intérieure