Growth rate from SNIa peculiar velocity and galaxy density field

Corentin Ravoux - CNRS/LPCA Clermont-Ferrand

 

ACCEL² simulation

with Bastien Carreres, Julian Bautista, Damiano Rosselli and many others

Measuring fσ8

Peculiar velocities (PV)

Redshift Space Distortions (RSD)

  • Direct estimation of velocities

 

 

  • Need an estimate of redshift (      ) and distance (decoupling       from     )
  • Compute statistics from PV
1 + z_{\mathrm{obs}} = (1 + z_{\mathrm{cos}})(1 + v_{\mathrm{p}}/c)
  • Impact of PV on measurements
  • Example: galaxy auto-correlation, void cross-correlation, ...
z_{\mathrm{obs}}
z_{\mathrm{cos}}
v_{\mathrm{p}}

Ravoux et al. 2022

He et al. 2018

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

fσ8 constraints

  • Constrain modified gravity models
  • RSD very effective for high redshift
  • PV for low redshift
  • Improvement with method combination

from Julian Bautista

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Type Ia supernovae

  • Distance modulus:
\mu_{\mathrm{obs},i}=m_{\mathrm{B},i}-M_{\mathrm{B},i}

Betoule et al. 2014

  • SNe Ia standardization = Tripp relation
M_{\mathrm{B},i} = M_{0} - \alpha x_{1,i} + \beta c_i + (\mathrm{opt})

Light-curve stretch

SN color

Parameters common for all SN Ia

"Redder is fainter"

"Luminous fade slowly"

  • SNe Ia:  Thermonuclear explosion a white dwarf reaching Chandrasekhar mass
\sigma_{D} / D \sim 7 \%

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Type Ia supernovae

  • Hubble residuals:
\begin{align*} \Delta \mu_i &= \mu_{\mathrm{obs},i} - \mu_{\mathrm{model}}(z_{\mathrm{obs},i}) \\ &= \mu_{\mathrm{obs},i} - 5 \log\left({\frac{d_{\mathrm{L}}(z_{\mathrm{obs},i})}{10 \mathrm{pc}}}\right) \end{align*}
  • Velocity estimator:
\hat{v}_i=-\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

Carreres et al. 2023

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Likelihood-based field-level inference

ACCEL² simulation

ACCEL² simulation

Carreres et al. 2023

Ravoux et al. 2025

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Likelihood-based field-level estimator

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

Velocity from SNe Ia

Field covariance matrix computed from theory and coordinates

Parameters

Velocity example:

  • Purpose: Maximizing or sampling a likelihood computed from all coordinates of the data
  • p = fitted parameters: simultaneously cosmology (fσ8) and field parameters (e.g., Hubble diagram parameters α, β, M0 for SN)

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Computing the field covariance

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Combining densities (RSD) 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_{vg}\right)

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

General covariance calculation

  • Objective: Improve/Extend the likelihood-based modeling
  • General form of field power spectrum
  • Algorithmically-oriented calculations (Hankel transforms)
  • Wide-angle effect accounted in the integration
C_{\mathrm{ab}}(\mathbf{r_a}, \mathbf{r_b}) = \frac{1}{(2 \pi)^3} \int_{\mathbf{k}} P_{\mathrm{ab}}(k, \mu_{\mathrm{a}}, \mu_{\mathrm{b}}) e^{i \mathbf{k}.\mathbf{r}} d^3 \mathbf{k}
P_{\mathrm{ab}}(k, \mu_{\mathrm{a}}, \mu_{\mathrm{b}}) = \sum_{n} w_{\mathrm{ab},n} F_{\mathrm{ab},n} (k, \mu_{\mathrm{a}}, \mu_{\mathrm{b}}) \mathcal{P}_{\mathrm{ab},n}(k)

gg, gv, vv

Parameters to fit

Terms to integrate analytically

Power spectra terms to integrate numerically

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

flip Field Level Inference Package

  •  python package for likelihood-based field-level inference:

 

 

https://github.com/corentinravoux/flip

  • Fast generation of field covariance
  • Symbolic code generation for covariance model
  • MCMC and Minuit to fit fσ8
  • General expression for vectors (SNIa, density, log distance, TF, FP...)
  • Survey geometry-dependent Fisher forecast

Contributors: Bastien Carreres, Damiano Rosselli and Alex G. Kim

Flip article: arxiv:2501.16852

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Field covariance models

  • Model comparison on a regular coordinate grid (Adams & Blake 2017, Adams & Blake 2020, Lai et al. 2022)

 

  • New wide-angle model developed (RC25): improved stability in integration and for wider fitting parameter ranges

Ravoux et al. 2025

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Combining DESI galaxy density and ZTF SNIa velocities on simulation

ACCEL² simulation

ACCEL² simulation

 

 

Ravoux et al. in prep

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

ACCEL² simulation

Zwicky Transient Facility (ZTF)

  • ZTF = high-cadence photometric telescop in the Palomar observatory
  • Very large field of view (47 deg²)
  • Observing 3/4 of the sky every nights with 3 filters (g, r, i)
  • Transient sky: Supernovae, gamma ray burst, tidal distruptive events, comets, asteroids

  • Dedicated spectroscopic telescope measuring transient spectra (SEDmachine)

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

SN Ia simulation and analysis

SN Ia simulator

Survey parameters

SN Ia model

N-body host simulation

Realistic SN Ia light curves

Quality cuts

(Detection, spec-z selection, light curve quality...)

Light curve fit (SALT2)

Velocity estimation and simultaneous fit of fσ8 and velocity parameters

f\sigma_8

Simulation

Analysis

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

snsim

https://github.com/bastiencarreres/snsim

  • Survey parameters: Cadence (ZTF, LSST), CCD gain, zero point, sky noise
  • SN Ia model: Rate, SED, color, stretch, intrinsic scattering distributions, light-curve parameters
  • Host catalog: Use velocities and associated clustering from N-body simulation

Flux

Phase

Phase

Phase

Carreres et al. 2023

Main contributors: Bastien Carreres, Damiano Rosselli

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

DESI x ZTF simulation

  • 27 simulations from AbacusSummit (Maksimova et al. 2019)
  • Density: DESI Bright Galaxy Survey (BGS) clustering matching for DR3 (J. Bautista, A. Smith)
  • Velocity: ZTF SNIa Y6 simulation performed (following Carreres et al. 2023)

from Julian Bautista

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Galaxy field

Supernovae velocities

  • Runs of SNsim to mimic ZTF SNIa Y6 data set (following Carreres et al. 2023)
  • AbacusSummit mocks matching DESI DR3 (5 years) BGS clustering and footprint

Ravoux et al. in prep.

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Model for density & velocity fit

  • Use of the RC25 wide-angle model implemented in flip:
P_{\mathrm{vv}} = (aHf)^2 \frac{\mu_1 \mu_2}{k^2} P_{\mathrm{\theta\theta}}(k) D_u^2(k, \sigma_u)
P_{\mathrm{gg}}=\left[b^2 P_{\mathrm{mm}}(k)+b f (\mu_1^2 + \mu_2^2) P_{\mathrm{m\theta}}(k)+f^2 \mu_1^2 \mu_2^2 P_{\theta \theta}(k)\right] \exp \left[\frac{-k^2 (\mu_1^2 + \mu_2^2) \sigma_{\mathrm{g}}^2}{2}\right]
P_{\mathrm{gv}} = iaH \frac{\mu_2}{k^2} \left(bf P_{\mathrm{m\theta}}(k) + f^2 \mu_1^2 P_{\mathrm{\theta\theta}}(k) \right) \exp \left[\frac{-k^2 \mu_1^2 \sigma_{\mathrm{g}}^2}{2}\right] D_u(k, \sigma_u)
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}

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

ZTF velocity fit

  • Velocity fit including Hubble diagram parameters to reproduce Carreres et al. 2023
  • Variation of analysis parameters (max redshift, SNIa density...)

Ravoux et al. in prep.

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

DESI density fit

  • Density grid with pypower
  • Test varying all density gridding parameters: grid size, mesh cell size, interpolation scheme (NGC, CIC, TSC, PCS), footprint (DESI DR3 or no cut)
  • Mean minuit fit on 27 mocks with average error bar

Ravoux et al. in prep.

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

DESI x ZTF joint fit

  • SNIa velocity fit with Hubble diagram parameters and density field

Adding density improves fs8 constraints up to 50%

Different density configurations

Ravoux et al. in prep.

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Summary of PV estimations on realistic simulations

ZTF + DESI

(this talk)

ZTF (Carreres et al. 2023)

LSST (Rosselli et al. 2025)

Corentin Ravoux                                                                                                                                                                           DESI presentation - June 26

Conclusion

  • Large modeling and simulation preparatory work for ZTF, LSST and combination with DESI density field
  • Dedicated sofware for simulation (snsim, skysurvey) and analysis (flip)
  • DESI ZTF simulation article draft ready

ACCEL² simulation

Hubble diagram

Perfect standard candle in an expanding Universe

from Bastien Carreres

Standard candle = object with fixed luminosity

Hubble diagram

Peculiar velocities

from Bastien Carreres

Perfect standard candle in an expanding Universe

Hubble diagram

Noise sources (intrinsic scatter, local environment, instruments...)

from Bastien Carreres

Standardizable candle in an expanding Universe

Peculiar velocities

Hubble diagram

from Bastien Carreres

High redshifts = dark energy  constraints (w, or w0,wa)

Low redshifts + calibration of the candle luminosity = H0 constraints

Hubble residuals = fσ8 constraints

Dark Energy

  • What is the nature of dark energy ?
  • Cosmological constant model (Λ) not very satisfying

Recent DESI DR2 BAO + CMB + SNIa results: stronger hints for varying dark energy

DESI DR2 BAO 2025

Dark Energy

  • What is the nature of dark energy ?
  • Cosmological constant model (Λ) not very satisfying
  • Other models :
    • Fifth force, additional field ?
    • Modified gravity theories ?
  • Our current objective: Probing large-scale structure formation to constrain dark energy/modified gravity.

Shankaranarayanan et al. 2022

Cosmic web

  • Matter perturbations in the primordial Universe grew to form the cosmic web
  • Static description: matter density contrast (δ) follows a linear power spectrum at large-scales
  • Dynamic description: Cosmic web peculiar velocities (   ) caused by gravitation

Walther et al. 2021

Chabanier et al. 2019

v_p

fσ8 parameter

  • Linear perturbation theory:
\nabla \cdot \mathbf{v}(\mathbf{r}) \propto-a H (f \sigma_8) \hat{\delta}(\mathbf{r})

Cosmic web velocities

Normalized matter overdensity

fσ8 parameter

  • Linear perturbation theory:
\nabla \cdot \mathbf{v}(\mathbf{r}) \propto-a H (f \sigma_8) \hat{\delta}(\mathbf{r})

Cosmic web velocities

Normalized matter overdensity

Logarithmic growth rate of linear perturbations

f=\frac{d \log \delta_{+}}{d \log a} \simeq \Omega_{\mathrm{m}}^{0.55}

8 Mpc/h

Amplitude of the matter perturbations in spheres of 8 Mpc/h comoving radius (matter power spectrum amplitude)

in GR

A word on wide-angle in clustering

\mathbf{r_{1}}
\mathbf{r_{2}}
\mathbf{v_{1}}
\mathbf{v_{2}}
\mathbf{r} = \mathbf{r_{1}} - \mathbf{r_{2}}

Plane parallel models

Wide angle models

\mu = \mu_1 = \mu_2
\mathbf{r_{1}}
\mathbf{r_{2}}
\mathbf{v_{1}}
\mathbf{v_{2}}
\mathbf{r} = \mathbf{r_{1}} - \mathbf{r_{2}}
\theta
\phi
\mu_1 \neq \mu_2
\mu_{i} = \mathbf{k} \cdot \mathbf{r_{i}}
\theta

Plane parallel model

  • Express power spectrum model in a general way:
P_{\mathrm{ab}}(k, \mu) = \sum_{n} w_{\mathrm{ab},n} F_{\mathrm{ab},n} (k, \mu) \mathcal{P}_{\mathrm{ab},n}(k)
  • vv "simple" example:
P_{\mathrm{vv}} = (f\sigma_8)^2 \times \left(a^2 H^2 \frac{\mu^2}{k^2}\right) \times \left(P_{\mathrm{\theta\theta}}(k) D_u^2(k, \sigma_u)\right)

Parameters to fit

Terms to integrate analytically

Power spectra terms to integrate numerically

Plane parallel model

  • Without loosing generality we can express the covariance:
C_{\mathrm{ab}}(\mathbf{r_1}, \mathbf{r_2}) = \sum_n w_{\mathrm{ab},n} \sum_{\ell} N_{\mathrm{ab},\ell}(\phi) \mathcal{H}_\ell\left[\mathcal{P}_{\mathrm{ab},n}(k)M_{\mathrm{ab},n}^{\ell}(k)\right](r)
M_{\mathrm{ab},n}^{\ell}(k) = \frac{1}{2}\int_{-1}^{1}d\mu^\prime F_{\mathrm{ab},n}(k, \mu^\prime)L_{\ell}(\mu^\prime)
N_{\mathrm{ab},\ell}(\phi) =(2\ell +1)L_\ell(\cos\left(\pi - \phi\right))

Plane parallel model

C_{\mathrm{ab}}(\mathbf{r_1}, \mathbf{r_2}) = \sum_n w_{\mathrm{ab},n} \sum_{\ell} N_{\mathrm{ab},\ell}(\phi) \mathcal{H}_\ell\left[\mathcal{P}_{\mathrm{ab},n}(k)M_{\mathrm{ab},n}^{\ell}(k)\right](r)

Linear sum of matrix with parameters to fit as coefficients

  • Without loosing generality we can express the covariance:

Plane parallel model

C_{\mathrm{ab}}(\mathbf{r_1}, \mathbf{r_2}) = \sum_n w_{\mathrm{ab},n} \sum_{\ell} N_{\mathrm{ab},\ell}(\phi) \mathcal{H}_\ell\left[\mathcal{P}_{\mathrm{ab},n}(k)M_{\mathrm{ab},n}^{\ell}(k)\right](r)

Hankel transform

\mathcal{H}_\ell\left[f(k)\right](r) = i^\ell \int_{0}^\infty\frac{k^2 dk}{2\pi^2}j_\ell(kr)f(k)
  • Most important part: Algorithmically optimized way to compute power spectrum integral, with FFTLog algorithm
  • Without loosing generality we can express the covariance:

Plane parallel model

  • Without loosing generality we can express the covariance:
C_{\mathrm{ab}}(\mathbf{r_1}, \mathbf{r_2}) = \sum_n w_{\mathrm{ab},n} \sum_{\ell} N_{\mathrm{ab},\ell}(\phi) \mathcal{H}_\ell\left[\mathcal{P}_{\mathrm{ab},n}(k)M_{\mathrm{ab},n}^{\ell}(k)\right](r)

Terms pre-computed analytically with symbolic code generaltion

  • More complicated formalism derived and implemented for wide-angle
M_{\mathrm{ab},n}^{\ell}(k) = \frac{1}{2}\int_{-1}^{1}d\mu^\prime F_{\mathrm{ab},n}(k, \mu^\prime)L_{\ell}(\mu^\prime)
N_{\mathrm{ab},\ell}(\phi) =(2\ell +1)L_\ell(\cos\left(\pi - \phi\right))

Wide angle model

\xi_{\mathrm{ab},\ell}^{i}(r) = \sum_j N_{\mathrm{ab},\ell}^{i,j} (\theta, \phi) \left[ i^{\ell} \int_k \frac{k^2 dk}{2 \pi^2} P_{\mathrm{ab},i} (k) M_{\mathrm{ab},\ell}^{i,j} (k) j_{\ell}(k r)\right]
C_{\mathrm{ab}}(\mathbf{r_1}, \mathbf{r_2}) = \sum_i A_{\mathrm{ab},i} \sum_l \xi_{\mathrm{ab},\ell}^{i}(r)
M_{\mathrm{ab},\ell}^{i,j=(\ell_1,\ell_2)} (k) = \int_{\mu_1 = -1}^1 \int_{\mu_2 = -1}^1 \frac{1}{4} L_{\ell_1}(\mu_1)L_{\ell_2}(\mu_2) B_{\mathrm{ab},i} (k, \mu_1, \mu_2) d \mu_1 d \mu_2
N_{\mathrm{ab},\ell}^{i,j=(\ell_1,\ell_2)} (\theta, \phi) = (4 \pi)^2 \sum_{m, m_1, m_2} G_{l, l_1, l_2}^{m, m_1, m_2} Y_{\ell m}(\hat{\mathbf{r}})^* Y_{\ell_1 m_1}(\hat{\mathbf{r_1}})^* Y_{\ell_2 m_2}(\hat{\mathbf{r_2}})^*
G_{m_1, m_2, m_3}^{l_1, l_2, l_3}=\sqrt{\frac{\left(2 l_1+1\right)\left(2 l_2+1\right)\left(2 l_3+1\right)}{4 \pi}} \left(\begin{array}{ccc} l_1 & l_2 & l_3 \\ 0 & 0 & 0 \end{array}\right)\left(\begin{array}{lll} l_1 & l_2 & l_3 \\ m_1 & m_2 & m_3 \end{array}\right)
P_{\mathrm{ab}}(k, \mu_1, \mu_2) = \sum_{i} A_{\mathrm{ab},i} B_{\mathrm{ab},i} (k, \mu_1, \mu_2) P_{\mathrm{ab},i}(k)

linear sum of matrix

flip validations

  • Field covariance comparison with pairV Anthony Carr & David Parkinson
  • Model validated on N-body simulations  Tyann Dummerchat

Disagreement due to different power spectrum model

Ravoux et al. 2025

Ravoux et al. 2025

Survey dependent Fisher forecast

  • Field covariance matrix accounts for survey geometry
  • Comparing ZTF simulation (Carreres et al. 2023) with Fisher forecasts
  • Error ~ 30% closer to likelihood-based than standard Fisher

Howlett et al. 2017

Ravoux et al. 2025

Rubin - LSST

Telescope mount assembly

AuxTel: 1.2m atmospheric telescop

Rubin - LSST: instrument

  • Largest numerical camera in the world: 3.2 Gpixels with 2s readout time
  • 8.4 m primary mirror and 9.6 deg² field of view
  • 6 filters: (u, g, r, i, z, y)
  • 10-year photometric survey of half of the sky (~ 20 000 deg²)

ZTF results

  • SN Ia selection bias causes velocity & fσ8 bias at high redshift
  • No fσ8 error bar improvement even with correction
  • Maximum redshift usable:
z =0.06

Carreres et al. 2023

Carreres et al. 2023

ZTF results

  • fσ8 fit performed with Hubble diagram parameters
  • no fσ8 bias on the 27 simulations
  • 19 % precision measurement with only 1600 SNe Ia

Carreres et al. 2023

Carreres et al. 2023

LSST simulations

  • 10 year simulation from Uchuu-UniverseMachine (Behroozi et al. 2019)
  • Cadence and instrument properties from the observing strategy simulation v3.3

Rosselli et al. 2025

LSST simulations

  • SN host redshift efficiency (C. Ravoux, P. Gris, D. Rosselli, J. Bautista):
    • Use of DC2 LSST simulation with galaxy properties
    • Footprint and efficiency for different spectroscopic survey
    • Considering SNe variety contamination

Rosselli et al. 2025

LSST simulations

  • 33,000 SNe Ia with spectro-z at z < 0.16 (among 1M for the full sample)
  • Photo-typing with SuperNNovae (Moller et al. 2019) gives 0.02% contamination from peculiar SN

Rosselli et al. 2025

LSST results

  • Dedicated study to test BBC framework and check the impact of intrinsic scatter model and nuisance parameter (      = dispersion of velocity position)

Carreres et al. 2025

\sigma_{\mathrm{u}}

LSST results

  • Unbiased fσ8 measurement with full Hubble diagram fit over 3 redshift points
  • How can we do better ? Combine with density field

Rosselli et al. 2025