Enrique Paillas, Pauline Zarrouk, Yan-Chuan Cai, Will Percival, Sesh Nadathur, Mathilde Pinon, Arnaud de Mattia, Florian Beuler

Constraining vΛCDM:

 beyond two-point functions

 

Carolina Cuesta-Lazaro

IAIFI fellow

arXiv:2209.04310

(\vec{\theta}_i, z_i)
P(\mathcal{C}|\,\,\,\,\,\,\,\,\,\,)

?

Early Universe

 ~linear

Gravity

Late Universe

Non-linear 

Credit: S. Codis+16

 

Non-Guassianity

 Second moment not optimal

\delta = \frac{\rho - \bar{\rho}}{\bar{\rho}} << 1
\delta >> 1
\bar{\xi}(R_s)
R_s
1
1
1
2
2
4
5
5
5
3

Autocorrelation

Cross-correlation with haloes

Monopole

Quadrupole

Voids

Clusters

Monopole

Where does the information come from?

?

Show comparison Quijote and GRF

# TODO: ADD GREEN AFTERWARDS

But, can we estimate densities realistically?

?

Autocorrelation of quintiles

Cross-correlation between quintiles and haloes

Monopole

Monopole

Quadrupole

Quadrupole

\theta

Simulated Data

Data

Prior

Posterior

x_\mathrm{obs}
x
P(\theta|x_\mathrm{obs})

Inverse problem

Forwards model

Density Estimation with normalising flows

x = f(z), \, z = f^{-1}(x)
p(\mathbf{x}) = p_z(f^{-1}(\mathbf{x})) \left\vert \det J(f^{-1}) \right\vert

No assumptions on the likelihood (likelihoods rarely Gaussian!)

 

No expensive MCMC chains needed to estimate posterior

\Omega_M
\Omega_\Lambda
\sigma_8

Input

x

 

Neural network

f

Representation

(Summary statistic)

r = f(x)

Output

 

Increased interpretability through structured inputs

Modelling cross-correlations

P(\theta|x_\mathrm{obs})

What ML can do for cosmology

  • ML to accelerate non-linear predictions and density estimation

 

  • Can ML extract **all** the information that there is at the field-level in the non-linear regime?
    • Compare data and simulations, point us to the missing pieces?

cuestalz@mit.edu

Contact me for anything related to Astro and ML!