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!
DensitySplit
By carol cuesta
