Non-perturbative probability distribution function for cosmological counts in cells

We present a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. The PDF is represented as a path integral and is evaluated using the saddle-point method. It factorizes into an exponent given by a spherically symmetri...

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Bibliographic Details
Published in:Journal of cosmology and astroparticle physics 2019-03, Vol.2019 (3), p.9-9
Main Authors: Ivanov, Mikhail M., Kaurov, Alexander A., Sibiryakov, Sergey
Format: Article
Language:English
Subjects:
Clustering
Computer simulation
Cosmology
Density
Distribution functions
Equivalence principle
Fluctuations
Initial conditions
Mathematical analysis
Probability distribution
Probability distribution functions
Red shift
Saddle points
Sensitivity
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Summary:We present a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. The PDF is represented as a path integral and is evaluated using the saddle-point method. It factorizes into an exponent given by a spherically symmetric saddle-point solution and a prefactor produced by fluctuations. The exponent encodes the leading sensitivity of the PDF to the dynamics of gravitational clustering and statistics of the initial conditions. In contrast, the prefactor has only a weak dependence on cosmology. It splits into a monopole contribution which is evaluated exactly, and a factor corresponding to aspherical fluctuations. The latter is crucial for the consistency of the calculation: neglecting it would make the PDF incompatible with translational invariance. We compute the aspherical prefactor using a combination of analytic and numerical techniques. We demonstrate the factorization of spurious enhanced contributions of large bulk flows and their cancellation due to the equivalence principle. We also identify the sensitivity to the short-scale physics and argue that it must be properly renormalized. The uncertainty associated with the renormalization procedure gives an estimate of the theoretical error. For zero redshift, the precision varies from sub percent for moderate density contrasts to tens of percent at the tails of the distribution. It improves at higher redshifts. We compare our results with N-body simulation data and find an excellent agreement.
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2019/03/009