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

Oscillations in the Primordial Bispectrum: Mode Expansion

We consider the presence of oscillations in the primordial bispectrum, inspired by three different cosmological models; features in the primordial potential, resonant type non-Gaussianities and deviation from the standard Bunch Davies vacuum. In order to put constraints on their bispectra, a logical first step is to put these into factorized form which can be achieved via the recently proposed method of polynomial basis expansion on the tetrahedral domain. We investigate the viability of such an expansion for the oscillatory bispectra and find that one needs an increasing number of orthonormal mode functions to achieve significant correlation between the expansion and the original spectrum as a function of their frequency. To reduce the number of modes required, we propose a basis consisting of Fourier functions orthonormalized on the tetrahedral domain. We show that the use of Fourier mode functions instead of polynomial mode functions can lead to the necessary factorizability with the use of only 1/5 of the total number of modes required to reconstruct the bispectra with polynomial mode functions. Moreover, from an observational perspective, the expansion has unique signatures depending on the orientation of the oscillation due to a resonance effect between the mode functions and the original spectrum. This effect opens the possibility to extract informa- tion about both the frequency of the bispectrum as well as its shape while considering only a limited number of modes. The resonance effect is independent of the phase of the reconstructed bispectrum suggesting Fourier mode extraction could be an efficient way to detect oscillatory bispectra in the data.Comment: 17 pages, 12 figures. Matches published versio

Aspects of Dark Matter Annihilation in Cosmology

Cosmic microwave background (CMB) constraints on dark matter annihilation are a uniquely powerful tool in the quest to understand the nature of dark matter. Annihilation of dark matter to Standard Model particles between recombination and reionization heats baryons, ionizes neutral hydrogen, and alters the CMB visibility function. Surprisingly, CMB bounds on dark matter annihilation are not expected to improve significantly with the dramatic improvements in sensitivity expected in future cosmological surveys. In this paper, we will present a simple physical description of the origin of the CMB constraints and explain why they are nearly saturated by current observations. The essential feature is that dark matter annihilation primarily affects the ionization fraction which can only increase substantially at times when the universe was neutral. The resulting change to the CMB occurs on large angular scales and leads to a phenomenology similar to that of the optical depth to reionization. We will demonstrate this impact on the CMB both analytically and numerically. Finally, we will discuss the additional impact that changing the ionization fraction has on large scale structure.Comment: 22 pages, 11 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

Squeezing down the Theory Space for Cosmic Inflation

An updated search for primordial gravitational waves has not found asignal, which implies that some popular early Universe models arebecoming less viable

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

Minimal cut-off vacuum state constraints from CMB bispectrum statistics

In this short note we translate the best available observational bounds on the CMB bispectrum amplitudes into constraints on a specific scale-invariant New Physics Hypersurface (NPH) model of vacuum state modifications, as first proposed by Danielsson, in general models of single-field inflation. As compared to the power spectrum the bispectrum constraints are less ambiguous and provide an interesting upper bound on the cut-off scale in general models of single-field inflation with a small speed of sound. This upper bound is incompatible with the power spectrum constraint for most of the parameter domain, leaving very little room for minimal cut-off vacuum state modifications in general single-field models with a small speed of sound.Comment: 9 pages, 1 figur