Institut de Physique Théorique
Direction de la Recherche Fondamentale  -  Saclay
UMR 3681 - INP
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ANR COSMO@NLO (F. Bernardeau)


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The Large-Scale Structure of the Universe at Next-to-Leading Order : COSMO@NLO

Scientist in charge : F. Bernardeau - IPhT

Duration : Jan 1st 2013 - Dec 31st 2016


This project aims at developing tools for predicting and computing cosmic density spectra and bispectra (three-point correlation function) for a large set of cosmological models that include non-standard effects such as massive neutrinos or clustering dark energy. More precisely we wish to build theoretical tools for predicting those quantities analytically and with a controlled precision in the quasilinear regime and develop robust and fast numerical codes for computing a set of well defined observables such as those related to cosmic shear observations, redshift space density field, etc. We also wish  to construct more phenomenological models that explore the relationships between the density field (and its various components) and the halo density.

The approaches we favor in this project make use of computation techniques that have been recently put forward in which re-summations of large classes of diagrams can be taken into account. These approaches explicitly, or implicitly, take advantage of the so-called eikonal approximation. Those approaches allow to develop perturbation theory calculations in a controlled way and for a large class of observables such as spectra, bispectra etc. Our project aims at writing and releasing packages - in fortran to make its portability to different systems easier - for the fast computation of perturbation theory spectra and bispectra beyond linear theory. More precisely, we wish to develop codes that compute spectra up to 2 loops (NNLO) and bispectra up to 1 loop (NLO).

State of the art and available codes

Comparison with N-body results at 2-loop order
Figure 1: Analytical predictions up to 2-loop order (solid lines) compared to N-body results (red dots) at z=1. The dotted line is the linear theory prediction, the dashed lines are the 1-loop order results and the solid lines the 2loop results (in the latter cases, top are standard PT, and bottom are Reg-PT predictions). The grey zones depict respectively the 1-loop uncertainties (light grey) and 2-loop uncertainties (dark grey).
Public codes for fast computations of power spectra at 2-loop order are now available. There are currently two proposed versions (see accompanying papers)
MPTBreeze : Code to compute power spectra from multi-point expansions. It is based on the prescription described in  MPTbreeze: A fast renormalized perturbative scheme,
    Lat modified :  08-Jul-2012 15:36
    Code: MPTbreeze-v1.tar.gz
    Readme : readme.txt
RegPT : Code to compute cosmological power spectra using the regularized method based on
Direct and fast calculation of regularized cosmological power spectrum at two-loop order, arXiv:1208.1191. This code also gives the values of the standard PT expansion up to two-loop order.
    Last modified: 2012/8/4
    Code: RegPT.tgz
    Readme: readme_RegPT.pdf
The MPTbreeze and RegPT codes are free software: you can redistribute it and/or modify it at your own risk. This program is distributed in the hope that it will be useful in scientific research, but without any warranty.

Partners and ongoing developments

All project members can be reached via email. At the IPhT collaborators are involved in various aspects of the extension of the methods and content of the universe,
  • F. Bernardeau (IPhT) - Theory, statistical tools, in charge of the project
  • P.  Valageas (IPhT) - theory, PT techniques
  • F.  Vernizzi (IPhT) - modified gravity, Effective theory approaches.
  • Ph. Brax (IPhT) - modified gravity, Chameleon mechanisms, numerical developments
  • Ch. Pichon (IAP) - statistical and topological tools, statitical indicators beyond power spectrum
  • H. Dupuy (IPhT) - PHD student, on massive neutrino effects
  • S. Codis (IAP) - on statistical tools and topological tools.
The project involves also 3 international collaborations. One with
  • Prof. Taruya (U. Tokyo) - encoding and N-body codes
  • Dr. Nishimichi (IPMU, Tokyo) - N-body codes and comparison with numerical simulations
which aims at developing codes in particular for redshift space distortion effects and at comparing results with N-body codes. The theoretical developments are also done in collaboration with,
  • Prof. R Scoccimarro (NYU),
  • Dr. M Crocce (U. Barcelona).

Finally exploration of alternative statistical tools are also done with

  • Prof. D. Pogosyan (U. Alberta, Canada).
The works under progress span,
  • the application of these computations to redshift space distortions and the computations of related power spectra;
  • the computation of covariance matrices;
  • the application of these predictions to cosmic shear observations;
  • the development of alternative statistical indicators.



The next milestones for the collaboration are
  • Kick off and general collabotation meeting : PTChat at Cargese, April 30 - May 3 2013
  • Visit of T. Nishimichi, April 1st 2013 onward
  • Visit of A. Taruya, Feb 11-18 2013

Of special interests for the collaboration :

Previous meeting directly related to the project are listed below. Relevant material can be found on their web sites,

  • PTChat, a workshop on Resummation Methods in Cosmological Perturbation Theory, 20-22 September 2011,
  • Itzykson meeting, Heart of Darkness, dark energy and modified gravity, 18-20 June 2012 IPhT CEA-Saclay



    page n° 674, actualisée le 15-04-2013 21:06:36  par fbernard

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