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Register a new userFast Estimation of Gravitational and Primordial Bispectra in Large Scale Structures
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Marcel M. Schmittfull
Publication date
2012
fields
Physics
and research's language is
English
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We present the implementation of a fast estimator for the full dark matter bispectrum of a three-dimensional particle distribution relying on a separable modal expansion of the bispectrum. The computational cost of accurate bispectrum estimation is negligible relative to simulation evolution, so the isotropic bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated. As an application we measure the evolution of gravitational and primordial dark matter bispectra in $N$-body simulations with Gaussian and non-Gaussian initial conditions of the local, equilateral, orthogonal and flattened shape. The results are compared to theoretical models using a 3D visualisation, 3D shape correlations and the cumulative bispectrum signal-to-noise, all of which can be evaluated extremely quickly. Our measured bispectra are determined by $mathcal{O}(50)$ coefficients, which can be used as fitting formulae in the nonlinear regime and for non-Gaussian initial conditions. In the nonlinear regime with $k<2h,mathrm{Mpc}^{-1}$, we find an excellent correlation between the measured dark matter bispectrum and a simple model based on a `constant bispectrum plus a (nonlinear) tree-level gravitational bispectrum. In the same range for non-Gaussian simulations, we find an excellent correlation between the measured additional bispectrum and a constant model plus a (nonlinear) tree-level primordial bispectrum. We demonstrate that the constant contribution to the non-Gaussian bispectrum can be understood as a time-shift of the constant mode in the gravitational bispectrum, which is motivated by the one-halo model. The final amplitude of this extra non-Gaussian constant contribution is directly related to the initial amplitude of the constant mode in the primordial bispectrum. We also comment on the effects of regular grid and glass initial conditions on the bispectrum.
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We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies the multiscale topology of a data set, in our context unifying the contributions of clusters, filament loops, and cosmic voids to cosmological constraints. We describe how this method captures the imprint of primordial local non-Gaussianity on the late-time distribution of dark matter halos, using a set of N-body simulations as a proxy for real data analysis. For our best single statistic, running the pipeline on several cubic volumes of size $40~(rm{Gpc/h})^{3}$, we detect $f_{rm NL}^{rm loc}=10$ at $97.5%$ confidence on $sim 85%$ of the volumes. Additionally we test our ability to resolve degeneracies between the topological signature of $f_{rm NL}^{rm loc}$ and variation of $sigma_8$ and argue that correctly identifying nonzero $f_{rm NL}^{rm loc}$ in this case is possible via an optimal template method. Our method relies on information living at $mathcal{O}(10)$ Mpc/h, a complementary scale with respect to commonly used methods such as the scale-dependent bias in the halo/galaxy power spectrum. Therefore, while still requiring a large volume, our method does not require sampling long-wavelength modes to constrain primordial non-Gaussianity. Moreover, our statistics are interpretable: we are able to reproduce previous results in certain limits and we make new predictions for unexplored observables, such as filament loops formed by dark matter halos in a simulation box.
We use the binned bispectrum estimator to determine the bispectra of the dust, free-free, synchrotron, and AME galactic foregrounds using maps produced by the Commander component separation method from Planck 2015 data. We find that all of these peak in the squeezed configuration, allowing for potential confusion with in particular the local primordial shape. Applying an additional functionality implemented in the binned bispectrum estimator code, we then use these galactic bispectra as templates in an $f_mathrm{NL}$ analysis of other maps. After testing and validating the method and code with simulations, we show that we detect the dust in the raw 143 GHz map with the expected amplitude (the other galactic foregrounds are too weak at 143 GHz to be detected) and that no galactic residuals are detected in the cleaned CMB map. We also investigate the effect of the mask on the templates and the effect of the choice of binning on a joint dust-primordial $f_mathrm{NL}$ analysis.
The understanding of the primordial mechanism that seeded the cosmic structures we observe today in the sky is one of the major goals in cosmology. The leading paradigm for such a mechanism is provided by the inflationary scenario, a period of violent accelerated expansion in the very early stages of evolution of the Universe. While our current knowledge of the physics of inflation is limited to phenomenological models which fit observations, an exquisite understanding of the particle content and interactions taking place during inflation would provide breakthroughs in our understanding of fundamental physics at high energies. In this review, we summarize recent theoretical progress in the modelling of the imprint of primordial interactions in the large scale structures of the Universe. We focus specifically on the effects of such interactions on the statistical distribution of dark matter halos, providing a consistent treatment of the steps required to connect the correlations generated among fields during inflation all the way to the late-time correlations of halos.
Cross-correlations between Cosmic Microwave Background (CMB) temperature and polarization anisotropies and $mu$-spectral distortions have been considered to measure (squeezed) primordial scalar bispectra in a range of scales inaccessible to primary CMB bispectra. In this work we address whether it is possible to constrain tensor non-Gaussianities with these cross-correlations. We find that only primordial tensor bispectra with anisotropies leave distinct signatures, while isotropic tensor bispectra leave either vanishing or highly suppressed signatures. We discuss how the kind of anisotropies and the parity state in primordial bispectra determine the non-zero cross-correlations. By employing the so-called BipoSH formalism to capture the observational effects of these anisotropies, we make Fisher-forecasts to assess the detection prospects from $mu T$, $mu E$ and $mu B$ cross-correlations. Observing anisotropies in squeezed $langle gamma gamma gammarangle$ and $langle gamma gamma zetarangle$ bispectra is going to be challenging as the imprint of tensor perturbations on $mu$-distortions is subdominant to scalar perturbations, therefore requiring a large, independent amplification of the effect of tensor perturbations in the $mu$-epoch. In absence of such a mechanism, anisotropies in squeezed $langle zeta zeta gammarangle$ bispectrum are the most relevant sources of $mu T$, $mu E$ and $mu B$ cross-correlations. In particular, we point out that in models where anisotropies in $langle zeta zeta zeta rangle$ leave potentially observable signatures in $mu T$ and $mu E$, the detection prospects of anisotropies in $langle zeta zeta gammarangle$ from $mu B$ are enhanced.
The covariance matrix $boldsymbol{Sigma}$ of non-linear clustering statistics that are measured in current and upcoming surveys is of fundamental interest for comparing cosmological theory and data and a crucial ingredient for the likelihood approximations underlying widely used parameter inference and forecasting methods. The extreme number of simulations needed to estimate $boldsymbol{Sigma}$ to sufficient accuracy poses a severe challenge. Approximating $boldsymbol{Sigma}$ using inexpensive but biased surrogates introduces model error with respect to full simulations, especially in the non-linear regime of structure growth. To address this problem we develop a matrix generalization of Convergence Acceleration by Regression and Pooling (CARPool) to combine a small number of simulations with fast surrogates and obtain low-noise estimates of $boldsymbol{Sigma}$ that are unbiased by construction. Our numerical examples use CARPool to combine GADGET-III $N$-body simulations with fast surrogates computed using COmoving Lagrangian Acceleration (COLA). Even at the challenging redshift $z=0.5$, we find variance reductions of at least $mathcal{O}(10^1)$ and up to $mathcal{O}(10^4)$ for the elements of the matter power spectrum covariance matrix on scales $8.9times 10^{-3}<k_mathrm{max} <1.0$ $h {rm Mpc^{-1}}$. We demonstrate comparable performance for the covariance of the matter bispectrum, the matter correlation function and probability density function of the matter density field. We compare eigenvalues, likelihoods, and Fisher matrices computed using the CARPool covariance estimate with the standard sample covariance estimators and generally find considerable improvement except in cases where $Sigma$ is severely ill-conditioned.
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