Cosmological inference at the field-level

Hugo SIMON-ONFROY,
PhD student supervised by
Arnaud DE MATTIA and François LANUSSE

DPhP, 2025/01/16

Current estimation

A toy example

$\Omega := \{ \Omega_c, \Omega_b, \Omega_\Lambda, H_0, \sigma_8, n_s,...\}$

Linear matter spectrum

Structure growth

Cosmological modeling and inference

$\Omega$

$\delta_L$

$\delta_g$

$\Omega$

$\delta_g$

DESI2024VI

inference

$$\boldsymbol{p}(\Omega \mid \delta_g) \propto \int \boldsymbol{p}(\Omega, \delta_L, \delta_g) \;\mathrm d \delta_L$$

$\Omega := \{ \Omega_c, \Omega_b, \Omega_\Lambda, H_0, \sigma_8, n_s,...\}$

Linear matter spectrum

Structure growth

Can't integrate? Then compress

$\Omega$

$\delta_L$

$\delta_g$

$P$

Power spectrum $P(\delta_g)$ allows to analytically compute $$\boldsymbol{p}(\Omega \mid P) \propto \int \boldsymbol{p}(\Omega, \delta_L, P) \;\mathrm d \delta_L$$

Compression

If $\delta_g$ is Gaussian, $P$ is a lossless compression and then $$\boldsymbol{p}(\Omega \mid P) = \boldsymbol{p}(\Omega \mid \delta_g)$$

But...

At large scales, matter field almost Gaussian so power spectrum is almost lossless compression
At smaller scales however, matter field is non-Gaussian