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We present a pipeline for characterizing and constraining initial conditions in cosmology via persistent homology. The cosmological observable of interest is the cosmic web of large scale structure, and the initial conditions in question are non-Gaussianities (NG) of primordial density perturbations. We compute persistence diagrams and derived statistics for simulations of dark matter halos with Gaussian and non-Gaussian initial conditions. For computational reasons and to make contact with experimental observations, our pipeline computes persistence in sub-boxes of full simulations and simulations are subsampled to uniform halo number. We use simulations with large NG ($f_{rm NL}^{rm loc}=250$) as templates for identifying data with mild NG ($f_{rm NL}^{rm loc}=10$), and running the pipeline on several cubic volumes of size $40~(textrm{Gpc/h})^{3}$, we detect $f_{rm NL}^{rm loc}=10$ at $97.5%$ confidence on $sim 85%$ of the volumes for our best single statistic. Throughout we benefit from the interpretability of topological features as input for statistical inference, which allows us to make contact with previous first-principles calculations and make new predictions.
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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.
Sharp features in the primordial power spectrum are a powerful window into the inflationary epoch. To date, the cosmic microwave background (CMB) has offered the most sensitive avenue to search for these signatures. In this paper, we demonstrate the power of large-scale structure observations to surpass the CMB as a probe of primordial features. We show that the signatures in galaxy surveys can be separated from the broadband power spectrum and are as robust to the nonlinear evolution of matter as the standard baryon acoustic oscillations. As a result, analyses can exploit a significant range of scales beyond the linear regime available in the datasets. We develop a feature search for large-scale structure, apply it to the final data release of the Baryon Oscillation Spectroscopic Survey and find new bounds on oscillatory features that exceed the sensitivity of Planck for a significant range of frequencies. Moreover, we forecast that the next generation of galaxy surveys, such as DESI and Euclid, will be able to improve current constraints by up to an order of magnitude over an expanded frequency range.
We investigate primordial black hole formation in the matter-dominated phase of the Universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zeldovich approximation, Thornes hoop conjecture, and Doroshkevichs probability distribution and subsequently derive the production probability $beta_{0}$ of primordial black holes. The numerical result obtained is applicable even if the density fluctuation $sigma$ at horizon entry is of the order of unity. For $sigmall 1$, we find a semi-analytic formula $beta_{0}simeq 0.05556 sigma^{5}$, which is comparable with the Khlopov-Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for $sigmalesssim 0.05$, while they are comparable with each other for $sigmagtrsim 0.05$. We also discuss how $sigma$ can be written in terms of primordial curvature perturbations.
Primordial magnetic fields lead to non-Gaussian signals in the Cosmic Microwave Background (CMB) even at the lowest order, as magnetic stresses, and the temperature anisotropy they induce, depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arise only as a higher order effect. We propose here a novel probe of stochastic primordial magnetic fields that exploits the characteristic CMB non-Gaussianity that they induce. In particular, we compute the CMB bispectrum ($b_{l_{_1}l_{_2}l_{_3}}$) induced by stochastic primordial fields on large angular scales. We find a typical value of $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} sim 10^{-22}$, for magnetic fields of strength $B_0 sim 3$ nano Gauss and with a nearly scale invariant magnetic spectrum. Current observational limits on the bispectrum allow us to set upper limits on $B_0 sim 35$ nano Gauss, which can be improved by including other magnetically induced contributions to the bispectrum.
A new and powerful probe of the origin and evolution of structures in the Universe has emerged and been actively developed over the last decade. In the coming decade, non-Gaussianity, i.e., the study of non-Gaussian contributions to the correlations of cosmological fluctuations, will become an important probe of both the early and the late Universe. Specifically, it will play a leading role in furthering our understanding of two fundamental aspects of cosmology and astrophysics: (i) the physics of the very early universe that created the primordial seeds for large-scale structures, and (ii) the subsequent growth of structures via gravitational instability and gas physics at later times. To date, observations of fluctuations in the Cosmic Microwave Background (CMB) and the Large-Scale Structure of the Universe (LSS) have focused largely on the Gaussian contribution as measured by the two-point correlations (or the power spectrum) of density fluctuations. However, an even greater amount of information is contained in non-Gaussianity and a large discovery space therefore still remains to be explored. Many observational probes can be used to measure non-Gaussianity, including CMB, LSS, gravitational lensing, Lyman-alpha forest, 21-cm fluctuations, and the abundance of rare objects such as clusters of galaxies and high-redshift galaxies. Not only does the study of non-Gaussianity maximize the science return from a plethora of present and future cosmological experiments and observations, but it also carries great potential for important discoveries in the coming decade.
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