PV group presentation

Growth rate from SNIa peculiar velocity and galaxy density field

Corentin Ravoux

Group presentation - 04/12/25

ACCEL² simulation

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

Corentin Ravoux Group presentation - Dec. 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

Corentin Ravoux Group presentation - Dec. 2025

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

Corentin Ravoux Group presentation - Dec. 2025

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

Corentin Ravoux Group presentation - Dec. 2025

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

Corentin Ravoux Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

fσ8 measurement with peculiar velocities

ACCEL² simulation

Corentin Ravoux Group presentation - Dec. 2025

Hubble diagram

Perfect standard candle in an expanding Universe

from Bastien Carreres

Standard candle = object with fixed luminosity

Corentin Ravoux Group presentation - Dec. 2025

Hubble diagram

Peculiar velocities

from Bastien Carreres

Perfect standard candle in an expanding Universe

Corentin Ravoux Group presentation - Dec. 2025

Hubble diagram

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

from Bastien Carreres

Standardizable candle in an expanding Universe

Peculiar velocities

Corentin Ravoux Group presentation - Dec. 2025

Hubble diagram

from Bastien Carreres

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

Low redshifts + calibration of the candle luminosity = H0 constraints

Hubble residuals = fσ8 constraints

Corentin Ravoux Group presentation - Dec. 2025

"Not-so" standard candles

Tully-Fisher relation

Fundamental plane relation

Spiral galaxies (Late-type)
Absolute magnitude (M) / rotational velocity (W)

Elliptical galaxies (Early-type)
Effective radius (Re) / surface brightness (Ie) / stellar velocity dispersion (σ)

\log R_e=a \log \sigma+b \log I_e+c

\sigma_{D} / D \sim 20 \%

M = a + b \log{W}

Said et al. 2024

Said 2023

Corentin Ravoux Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

Likelihood-based field-level inference

ACCEL² simulation

Carreres et al. 2023

Ravoux et al. 2025

Corentin Ravoux Group presentation - Dec. 2025

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:

Standard inference: compute 2-point correlation functions and fit
Field-level inference: 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 Group presentation - Dec. 2025

Computing the field covariance

Corentin Ravoux Group presentation - Dec. 2025

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

\Bigg]

-1

\left(C_{gg}\right)

\left(C_{gv}\right)

\left(C_{vv}\right)

\left(C_{vg}\right)

Corentin Ravoux Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

Combining DESI galaxy density and ZTF SNIa velocities on simulation

ACCEL² simulation

Ravoux et al. in prep

Corentin Ravoux Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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

Carreres et al. 2023

Main contributors: Bastien Carreres, Damiano Rosselli

Corentin Ravoux Group presentation - Dec. 2025

DESI

4m multi-object spectrograph at Kitt Peak Observatory

DESI collaboration 2022

Corentin Ravoux Group presentation - Dec. 2025

DESI

5 μm positioning in few sec. for 5000 targets
All fibers connected to 10 spectrographs

Silber et al. 2022

Corentin Ravoux Group presentation - Dec. 2025

DESI

BGS: Bright Galaxy Survey
LRG: Luminous Red Galaxy
ELG: Emission Line Galaxy
QSO: Quasar
- z > 2.1: with a Lyman-α forest
- z < 2.1: as tracers

63 million redshifts in 8 years

over 17,000 deg²

Primary science: BAO and RSD measurements

Corentin Ravoux Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

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 Group presentation - Dec. 2025

DESI x ZTF joint fit

SNIa velocity fit with Hubble diagram parameters and density field

Adding density improves fs8 constraints up to 60%

Different density configurations

Ravoux et al. in prep.

Corentin Ravoux Group presentation - Dec. 2025

Growth rate on LSST SNIa simulations

ACCEL² simulation

Carreres et al. 2025

Rosselli et al. 2025

Corentin Ravoux Group presentation - Dec. 2025

Rubin - LSST

Telescope mount assembly

AuxTel: 1.2m atmospheric telescop

Corentin Ravoux Group presentation - Dec. 2025

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)

Corentin Ravoux Group presentation - Dec. 2025

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

Corentin Ravoux Group presentation - Dec. 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

Corentin Ravoux Group presentation - Dec. 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

Corentin Ravoux Group presentation - Dec. 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}}

Corentin Ravoux Group presentation - Dec. 2025

LSST PV Topical team

Creation of a new topical team under the DESC-TD WG
Planned projects:
- Project 1: Modeling LSST's detection efficiency and photometric accuracy for bright targets.
- Project 2: Analyzing filter non-uniformity over focal plane
- Project 3: Evaluating initial forecasts against the DP1 observing logs
- Project 4: Cross-observatory alerts
- Project 5: Velocity-field inference bias using mocks
- Project 6: Compile a list of methodologies used to infer f𝛔8, tabulate (dis)advantages for clear comparison
- Project 7: Develop estimators, covariance matrix formulae, validate higher-order statistics

Corentin Ravoux Group presentation - Dec. 2025

Summary of PV estimations on realistic simulations

ZTF + DESI

(this talk)

ZTF (Carreres et al. 2023)

LSST (Rosselli et al. 2025)

Corentin Ravoux Group presentation - Dec. 2025

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)
Next steps:
- Application on data (Pantheon+, ZTF, DEBASS, ATLAS)
- Simulation of all-sky combination (LSST/4HS+4MOST, ZTF+DESI)
- Combination with other velocity tracers (DESI TF, FP)

ACCEL² simulation

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