We study the matter bispectrum of the large-scale structure by comparing different perturbative and phenomenological models with measurements from N -body simulations obtained with a modal bispectrum ...estimator. Using shape and amplitude correlators, we directly compare simulated data with theoretical models over the full three-dimensional domain of the bispectrum, for different redshifts and scales. We review and investigate the main perturbative methods in the literature that predict the one-loop bispectrum: standard perturbation theory, effective field theory, resummed Lagrangian and renormalized perturbation theory, calculating the latter also at two loops for some triangle configurations. When calibrated on the simulations, this three-shape benchmark model accurately describes the bispectrum on all scales and redshifts considered, providing a prototype bispectrum Halofit-like methodology that could be used to describe and test parameter dependencies.
Despite numerous efforts, the search for oscillatory signatures in primordial spectra has not produced any convincing evidence for feature models to date. We undertake a thorough search for ...signatures of sharp features in the WMAP9 power spectrum and bi-spectrum as well as in the Planck power spectrum. For the first time, we carry out searches in both the power spectrum and bi-spectrum simultaneously, employing well-defined look-elsewhere statistics to assess significances in a rigorous manner. Developing efficient methods to scan power spectrum likelihoods for oscillatory features, we present results for the phenomenological bare sine and cosine modulations, allowing validation against existing Planck likelihood surveys, as well as templates that include the correct sharp feature scaling. In particular, we study degeneracies between feature and cosmological parameters. We use and slightly generalize statistics developed in previous work to reliably judge the significance of large feature model amplitude estimates. We conclude that our results are entirely consistent with a featureless realization of a Gaussian cosmic microwave background.
The simplest inflationary models present us with few observable parameters to discriminate between them. A detection of features in the spectra of primordial density perturbations could provide ...valuable insights and lead to stringent tests of models of the early Universe. So far, searches for oscillatory features have not produced statistically significant results. In this work we consider a combined search for features in the power spectrum and bispectrum. We show that possible dependencies between the estimates of feature model amplitudes based on the two- and three-point correlators are largely statistically independent under the assumption of the null hypothesis of a nearly Gaussian featureless cosmic microwave background. Building on this conclusion we propose an optimal amplitude estimator for a combined search and study the look-elsewhere effect in feature model surveys. In particular we construct analytic models for the distribution of amplitude estimates that allow for a reliable assessment of the significance of potential findings. We also propose a well-behaved integrated statistic that is designed to detect evidence for models exhibiting features at multiple frequencies.
We develop an analytic model to quantitatively describe the evolution of superconducting cosmic string networks. Specifically, we extend the velocity-dependent one-scale (VOS) model to incorporate ...arbitrary currents and charges on cosmic string world sheets under two main assumptions, the validity of which we also discuss. We derive equations that describe the string network evolution in terms of four macroscopic parameters: the mean string separation (or, alternatively, the string correlation length) and the root mean square velocity which are the cornerstones of the VOS model, together with parameters describing the averaged timelike and spacelike current contributions. We show that our extended description reproduces the particular cases of wiggly and chiral cosmic strings, previously studied in the literature. This VOS model enables investigation of the evolution and possible observational signatures of superconducting cosmic string networks for more general equations of state, and these opportunities will be exploited in a companion paper.
The direct evaluation of manifestly optimal, cut-sky cosmic microwave background (CMB) power spectrum and bispectrum estimators is numerically very costly, due to the presence of inverse-covariance ...filtering operations. This justifies the investigation of alternative approaches. In this work, we mostly focus on an inpainting algorithm that was introduced in recent CMB analyses to cure cut-sky suboptimalities of bispectrum estimators. First, we show that inpainting can equally be applied to the problem of unbiased estimation of power spectra. We then compare the performance of a novel inpainted CMB temperature power spectrum estimator to the popular apodized pseudo-Cl (PCL) method and demonstrate, both numerically and with analytic arguments, that inpainted power spectrum estimates significantly outperform PCL estimates. Finally, we study the case of cut-sky bispectrum estimators, comparing the performance of three different approaches: inpainting, apodization and a novel low-l leaning scheme. Providing an analytic argument of why the local shape is typically most affected we mainly focus on local-type non-Gaussianity. Our results show that inpainting allows us to achieve optimality also for bispectrum estimation, but interestingly also demonstrate that appropriate apodization, in conjunction with low-l cleaning, can lead to comparable accuracy.
We report on an extensive study of the evolution of domain wall networks in Friedmann-Lemaitre-Robertson-Walker universes by means of the largest currently available field-theory simulations. These ...simulations were done in 4096 super(3) boxes and for a range of different fixed expansion rates, as well as for the transition between the radiation and matter eras. A detailed comparison with the velocity-dependent one-scale model shows that this cannot accurately reproduce the results of the entire range of simulated regimes if one assumes that the phenomenological energy loss and momentum parameters are constants. We therefore discuss how a more accurate modeling of these parameters can be done, specifically by introducing an additional mechanism of energy loss (scalar radiation, which is particularly relevant for regimes with relatively little damping) and a modified momentum parameter which is a function of velocity (in analogy to what was previously done for cosmic strings). We finally show that this extended model, appropriately calibrated, provides an accurate fit to our simulations.
We study the matter bispectrum of large-scale structure by comparing the predictions of different perturbative and phenomenological models with the full three-dimensional bispectrum from N-body ...simulations estimated using modal methods. We show that among the perturbative approaches, effective field theory succeeds in extending the range of validity furthest on intermediate scales, at the cost of free additional parameters. By studying the halo model, we show that although it is satisfactory in the deeply nonlinear regime, it predicts a deficit of power on intermediate scales, worsening at redshifts z>0. By comparison with the N-body bispectrum on those scales, we show that there is a significant squeezed component underestimated in the halo model. On the basis of these results, we propose a new “three-shape” model, based on the tree-level, squeezed and constant bispectrum shapes we identified in the halo model; after calibration this fits the simulations on all scales and redshifts of interest. We extend this model further to primordial non-Gaussianity of the local and equilateral types by showing that the same shapes can be used to describe the additional non-Gaussian component in the matter bispectrum. This method provides a halofit-like prototype of the bispectrum that could be used to describe and test parameter dependencies and should be relevant for the bispectrum of weak gravitational lensing and wider applications.
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