Méga-analyse: inférence
bayésienne standard et au niveau du champ
Arnaud de Mattia, Christophe Yèche
CEA Saclay, Irfu/DPhP
Stage IV experiments: DESI
2021 - 2025: 40M redshifts at \(0 < z < 3\) over \(14 000 \; \mathrm{deg}²\)
Mayall Telescope at Kitt Peak, AZ
5000 robotically-positioned spectroscopic fibers
robotic positioners
Taken from Zhao et al. (2020)
DESI
Credit: NSF
Taken from Zhao et al. (2020)
DESI focal plane
DESI cosmological constraints
Measuring dark energy
\(\Lambda\)
2024
2025
DESI cosmological constraints
GR
Measuring dark energy
\(\Lambda\)
Testing general relativity
What do we measure?
We measure angular positions (right ascension (R.A.), declination
(Dec.)) and redshifts (\(z\)) of \(\mathcal{O}(10^6)\) galaxies.
What to do with this data?
SDSS data. Credits: EPFL
DESI Y5 galaxy samples
Bright Galaxies: 14M (SDSS: 600k)
0 < z < 0.4
LRG: 8M (SDSS: 1M)
0.4 < z < 1.1
ELG: 16M (SDSS: 200k)
0.6 < z < 1.6
QSO: 3M (SDSS: 500k)
Lya \(1.8 < z\)
Tracers \(0.8 < z < 2.1\)
Y5 (DR1-DR2-DR3) \(\sim 40\)M galaxy redshifts!
\(z = 0.4\)
\(z = 0.8\)
\(z = 0\)
\(z = 1.6\)
\(z = 2.0\)
\(z = 3.0\)
(Isotropic) correlation function
separation between galaxies
correlation function
excess probability that 2 galaxies are close
\(<0\) as \(\int d^3s \xi(s) = 0\)
excess probability that 2 galaxies are close
(Isotropic) power spectrum
power spectrum
wavenumber
small scales
large scales
Likelihood
Taken from Zhao et al. (2020)
We usually assume a Gaussian likelihood
\ln{p(\mathbf{d} | \mathbf{\theta})} \propto -\frac{1}{2} (\mathbf{d} - \orange{\mathbf{t}}(\red{\mathbf{\theta}}))^T \green{\mathrm{C}}^{-1} (\mathbf{d} - \orange{\mathbf{t}}(\red{\mathbf{\theta}}))
theory model
data vector
(\(P_\ell(k)\) or \(\xi_\ell(s)\))
parameters
covariance matrix
- Full Shape fit: \(A_\mathrm{s} \text{ or }\sigma_8, \omega_\mathrm{cdm}, h, n_\mathrm{s}\)
- BAO fit: \(\alpha_\mathrm{iso}, \alpha_\mathrm{ap}\)
+ bias or "nuisance" parameters
analytic or based on fast simulations
We sample the posterior \(p(\red{\mathbf{\theta}} | \mathbf{d}) \propto p(\mathbf{d} | \red{\mathbf{\theta}}) \red{p(\mathbf{\theta})}\)
prior
In a nutshell
Taken from Zhao et al. (2020)
galaxy catalog
galaxy power spectrum (or correlation function)
cosmological constraints
compression = "we measure specific features"
e.g. BAO model \(\Rightarrow\) \(\alpha_\mathrm{iso}, \alpha_\mathrm{ap}\)
"variance of the density field as a function of scale"
Full Shape
Mega-analysis
Taken from Zhao et al. (2020)
- In addition to galaxy clustering analyses, cosmological constraints can be obtained with correlations of galaxy clustering and galaxy and CMB lensing
- For the DESI Y5 sample (timeline: within 2 years)
- Requires mocks simulating jointly galaxy clustering and lensing
Field-level inference
Fit the observed (discretized) field
Sample the initial cosmic density field
initial density
final density
Field-level inference (benchmark)
more efficient
gradient-based samplers
Field-level inference (benchmark)
gradient-based samplers
more efficient
efficiency almost constant with dimension
\(10^6\) parameters \(\simeq 8\) GPU hours
Field-level inference (PNG)
Goal: measure primordial non-Gaussianity with DESI data
Spectroscopic galaxy surveys
imaging surveys (2014 - 2019) + WISE (IR)
target selection
spectroscopic observations
spectra and redshift measurements
- two steps: photometry and spectroscopy ⇒ selection effects
- catalog of angular positions \(\mathrm{R.A.}, \mathrm{Dec.}\) and redshifts \(z\)
Survey selection function
specify the survey selection function \(\bar{n}\) \(\Rightarrow\) account for systematic effects due to photometry/spectroscopy
Expected density without clustering = angular & radial footprint
Survey selection function \(\bar{n}\)
survey selection function \(\bar{n}\)
Taken from DESI Collaboration et al. 2024
mega_analysis_thesis_2025
By Arnaud De Mattia
