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What is next for CMBXlike?

Status and prospects

CMBXC meeting @ INAF-IASF Milano 23-24 Oct 2023

Louis&Margherita

On behalf of the CMBXC:Likelihood team

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Plan

  • Theoretical recipe of CMBXlike
  • Status of the Merge with CLOE (no updates from Copenhaghen)
  • CMBXlike follow-up
  • Status of OU-LE3 discussions
  • Development of independent CMBX likelihood

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CMBXlike: likelihood and covariance matrix

We implement a Gaussian likelihood function,

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with an analytical covariance matrix between the spectra and ,

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assuming cosmic variance limited CMB temperature spectrum and SO noise for CMB lensing

( and follow the CLOE prescription).

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CMBXlike: theoretical recipe

Our theoretical recipe assumes GR, flatness and the Limber approximation, then we write

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where each probe A and B has a specific kernel.

The iSW kernel is given by

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and, the CMB lensing kernel given by

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while the GCphot and WL kernels are reported in S. Ilić et al. (Euclid collab.) 2021.

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Integration of CMBXlike in CLOE

  • CMBXlike is a tool to perform joint analysis of Euclid main probes with CMB observables, iSW and CMB lensing;

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Integration of CMBXlike in CLOE

  • CMBXlike is a tool to perform joint analysis of Euclid main probes with CMB observables, iSW and CMB lensing;
  • We had several meetings/interactions with the IST:Likelihood group to decide on how to implement our modifications; our philosophy has been to make a flexible code, with the same structure as CLOE;

The 7x2pt covariance matrix is loaded when CMBX probes are used.

The 3x2pt block, containing the main probes from Euclid, is the one from IST:Likelihood.

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Integration of CMBXlike in CLOE

  • CMBXlike is a tool to perform joint analysis of Euclid main probes with CMB observables, iSW and CMB lensing;
  • We had several meetings/interactions with the IST:Likelihood group to decide on how to implement our modifications; our philosophy has been to make a flexible code, with the same structure as CLOE;
  • CMBXlike is ready and validated. We are in the “merging” phase. We split the merge into three requests (dubbed MR1, MR2 and MR3) to facilitate the review process.

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Integration of CMBXlike in CLOE

We split the merge into three requests (dubbed MR1, MR2 and MR3) to facilitate the review process. In more details:

  • MR1 concerns extra files that are completely independent from the IST:likelihood work (i.e. cmbx.py, containing definition of a class for the CMBX observables);
  • MR2 concerns semi-independent additions to already existing classes (e.g. adding quantities we need to the cosmo dictionary in the "Cosmology" class in cosmo.py, or adding a function to read the CMBX data in reader.py);
  • MR3 concerns actual modifications to CLOE (i.e. enlarging the covariance, data and theory vectors to include the CMBX observables, and the consequent modifications to the masking routines, or the redshift range for CMB lensing kernel).

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Integration of CMBXlike in CLOE

We split the merge into three requests (dubbed MR1, MR2 and MR3) to facilitate the review process. In more details:

  • MR1 concerns extra files that are completely independent from the IST:likelihood work (i.e. cmbx.py, containing definition of a class for the CMBX observables);
  • MR2 concerns semi-independent additions to already existing classes (e.g. adding quantities we need to the cosmo dictionary in the "Cosmology" class in cosmo.py, or adding a function to read the CMBX data in reader.py);
  • MR3 concerns actual modifications to CLOE (i.e. enlarging the covariance, data and theory vectors to include the CMBX observables, and the consequent modifications to the masking routines, or the redshift range for CMB lensing kernel).

Still waiting for the IST:L to review our code!

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CMBXlike follow-up

  • Take into account both masks: Euclid and Planck (what else?)
  • Refine CMB lensing estimation (see CMB lensing likelihood report)
  • Add iSWxWL cross-correlation
  • Magnification bias
  • Run full MCMC analysis

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Discussions with OU-LE3

From the discussion in Marseille (23-24 March 2023)

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What is the status?

Do we need to set up a common repository with the CMB data we want to use?

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Independent CMBX likelihood

  • Idea is to use the theory spectra from CAMB directly instead of the ones from CLOE
  • Can be used for our development purposes, and merged with CLOE at a much later stage, when CLOE has already been validated for DR1.

Pros:

  • Flexibility (more optimal redshift binning and multipole bins)
  • Faster Cls computation time (?)
  • Stop focusing on updating our code to the last CLOE version
  • Focus on validation of the CMBX likelihood, without depending on the development of CLOE-only part of the likelihood

Cons:

  • Less marginalisation parameters
  • No intrinsic alignment
  • Halofit non linear recipes maybe less accurate?
  • Political issues?
  • Duplication of efforts?

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Simple CMBX likelihood

  • Likelihood which is directly interfaced between Cobaya and CAMB (without CLOE)
  • Cls of iSW, CMB lensing GC, WL and all their Xcorr are given by CAMB
  • Euclid window function are from the Euclid_windows module (developed by the iSW likelihood team, integrated in CAMB)
  • Flexibility to define the redshift bins and the multipole bins
  • Can be used for testing optimal binnings for CMBX
  • Can be used to develop a modular analytical covariance matrix code

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Example demo spectra

These spectra (and all auto and cross) are computed from CAMB, and interfaced in our CMBX likelihood through Cobaya

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What is next for this simple likelihood

  • The covariance matrix is not included yet

To be able to reproduce CLOE:

  • Intrinsic alignment
  • Other biases not in CAMB baseline code ?
  • Marginalisation on bias parameters