Maximum likelihood framework for growth rate measurement

Corentin Ravoux - LPCA Clermont-Ferrand, France

with Julian Bautista, Bastien Carreres, Damiano Rosselli, Alex Kim and others

 

 

 

 

December 2024 - DESI Collaboration meeting

 

 

Maximum likelihood

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Maximal likelihood estimator

\begin{aligned} \mathcal{L}(p) \propto & \exp\left[-\frac{1}{2} v^T(p) C_{vv}(p)^{-1} v(p)\right] \\ \end{aligned}

Data vector

Field covariance matrix computed from theory and coordinates

  • Purpose: Minimize a likelihood computed from all coordinates of the data
  • p = parameters: contains cosmology and vector parameters

Parameters

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Combining densities and peculiar velocities

\begin{aligned} \mathcal{L}(p) \propto & \exp\left[-\frac{1}{2} \right. \end{aligned}

Velocities

Density field from galaxy surveys

Full field covariance matrix

\delta
\delta
v
v
\Bigg]
-1
T
\left(C_{gg}\right)
\left(C_{gv}\right)
\left(C_{vv}\right)
\left(C_{gv}\right)

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Computing the field covariance

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

General covariance calculation

  • Objective: Improve/Extend the Maximum likelihood modeling
  • General form of field power spectrum
  • Algorithmically-oriented calculations (Hankel transforms)
  • Modeling with and without wide-angle
C_{\mathrm{ab}}(\mathbf{r_1}, \mathbf{r_2}) = \frac{1}{(2 \pi)^3} \int_{\mathbf{k}} P_{\mathrm{ab}}(k, \mu_1, \mu_2) e^{i \mathbf{k}.\mathbf{r}} d^3 \mathbf{k}
P_{\mathrm{ab}}(k, \mu_1, \mu_2)
P_{\mathrm{ab}}(k, \mu)

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

flip Field Level Inference Package

  •  python package for maximum likelihood estimator:

 

 

https://github.com/corentinravoux/flip

  • Symbolic code generation for covariance model
  • Fast generation of covariance
  • All previous models implemented (AB17, AB20, L22, C23, RC)
  • MCMC and Minuit fitter
  • General expression for vectors (SNIa, density, log distance...)
  • Covariance model evaluation
  • Survey dependent Fisher forecast
  • Paper in preparation: describing flip and comparing models

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Application: combining DESI galaxy density and ZTF SNIa velocities

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Abacus BGS mocks

  • 27 Abacus realization matching to the BGS clustering v0.3 (code of Alex Smith, run by Julian Bautista)

 

  • ZTF SNIa Y6 simulation performed (only accessible to members of both collaboration)

 

  • Objective: Assessing growth rate measurement on a DESI Y5/ ZTF Y6 simulation

Julian's plot

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Galaxy field

  • Runs of SNsim to mimic ZTF Y6
  • Uses ZTF logs files which are private for now

Supernovae velocities

https://github.com/bastiencarreres/snsim

  • DESI Y5 BGS footprint and density field gridding

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Velocity fit only

  • Maximum likelihood model with wide-angle, and no Taylor expansion of nuisance parameters
  • Velocity fit including Hubble diagram parameters (Carreres et al. 2023)

 

 

  • Variation of analysis parameters (max z, SNIa density...)

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

\hat{v}_i\left(\mathbf{p}_{\mathrm{HD}}\right)=-\frac{\ln (10) c}{5}\left(\frac{\left(1+z_i\right) c}{H\left(z_i\right) r\left(z_i\right)}-1\right)^{-1} \Delta \mu_i\left(\mathbf{p}_{\mathrm{HD}}\right)

Density fit only

  • Density grid with pypower
  • Mean fit of 27 mocks with minuit with mean error bar, Y5 footprint
  • Test varying all density gridding parameters: grid size, voxel size, interpolation (ngc, cic, tsc, pcs), footprint (Y5 or full)

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Joint fit

  • ZTF Y6 SNIa velocity fit with Hubble diagram parameters and DESI Y5 BGS density field (Article in preparation)

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Density improves fs8 constraints up to 25%

Application: Test on FP and TF data

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Velocity fit on abacus simulations

  • Start of expanding flip package for infrastructure tasks
  • Implementation of log distance fit
  • True log distance fit with flip:

 

  • Test on existing FP mocks: 20,000 velocities fit, without gridding
\eta \equiv-\log \frac{D\left(z_{\mathrm{cos}}\right)}{D\left(z_{\mathrm{obs}}\right)}
f\sigma_8 = 0.48 \pm 0.04
f\sigma_8 = 0.5 \pm 0.2
(f\sigma_8(\mathrm{fid}) = 0.47)
  • Need help on this
  • Possible improvement: TF/FP fit including standardization parameters, combination TF/FP with SNIa

Corentin Ravoux                                                                                                                                                             DESI Cancun meeting 2024 - 12 Dec.

Conclusion

  • flip = Framework for maximum likelihood inference
  • Growth rate analysis on abacus BGS mocks with ZTF SNIa
  • Start extension for FP and TF with flip