Redshift surveys in a nutshell
Learning summary statistics with machine learning
Carolina Cuesta-Lazaro
13th December 2021 - MPA
Collaborators: Cheng-Zong Ruan, Yosuke Kobayashi, Alexander Eggemeier, Pauline Zarrouk, Sownak Bose, Takahiro Nishimichi, Baojiu Li, Carlton Baugh
(\vec{\theta}_i, z_i)
z_i = z_{\mathrm{Cosmological} }
+ z_{\mathrm{Doppler}}
\chi(z) = \int_0^z \frac{dz'}{H(z')}
+ \frac{v_{\mathrm{pec}}}{aH(a)}
\chi_i
Fifth forces modify structure growth
GROWTH
- GRAVITY
- FIFTH FORCE
+ EXPANSION
Credit: Cartoon depicting Willem de Sitter as Lambda from Algemeen Handelsblad (1930).
Cosmology =
\{\vec{c}\}
Main Assumptions
1) Galaxies don't impact dark matter clustering
2) Number of galaxies depends on halo mass only -> Assembly bias?
1) We don't know the Initial Conditions
2) Data is very high dimensional
3) Impact of unknowns (baryonic physics)
4) N-body sims extremely slow to run!
Cosmology =
Galaxy =
\{\vec{c}\}
\{\vec{g}\}
\Omega_M
Summarise the data
1. Modelling Redshift Space Distortions
The Streaming Model
1+\xi^S(s_\perp, s_\parallel) = \int dr_\parallel \left(1 + \xi^R(r)\right) \red{\mathcal{P}(v_\parallel=s_\parallel-r_\parallel|r_\perp, r_\parallel)}
PAIRWISE VELOCITY
DISTRIBUTION
r
v_{\parallel,1}
v_{\parallel,2}
v_{\parallel} = v_{\parallel,1} - v_{\parallel,2}
s
s_{\parallel} = v_{\parallel} + r_{\parallel}
\xi(r)
\xi(s_\perp, s_\parallel)
Probability of finding a pair of galaxies at distance r
v_\parallel < 0
INFALL
v_\parallel > 0
OUTFLOW
1+\xi^S(s_\perp, s_\parallel) = \int dr_\parallel \left(1 + \xi^R(r)\right) \red{\mathcal{P}(v_\parallel=s_\parallel-r_\parallel|r_\perp, r_\parallel)}
\xi^S(s_\perp, s_\parallel) \approx \xi^R(s) + \sum_n \frac{(-1)^n}{n!} \frac{d^n}{d s_\parallel^n} \left( (1+ \xi^R(s)) m_n(s) \right)
On large scales,
slowly varying function of
r_\parallel
v_\parallel < 0
INFALL
v_\parallel > 0
OUTFLOW
Two representative MG models f(R) and nDGP:
- The background expansion is the same as LCDM
- One parameter to describe deviations from LCDM
(same large scale real space clustering)
1+\xi^S(s_\perp, s_\parallel) = \int dr_\parallel \left(1 + \blue{\xi^R(r)}\right) \red{\mathcal{P}(v_\parallel=s_\parallel-r_\parallel|r_\perp, r_\parallel)}
How do these vary with cosmological parameters on small scales?
Described by four parameters
2. Simulation-based models
Cosmology =
\{\vec{c}\}
\vec{c}_i
Neural Network Emulator
\vec{c}, \mathrm{redshift}, M_h
\xi^R_{hh}(r|M_h)
v_{hh}(r|M_h)
1) Very fast -> MCMC
2) Halo-Galaxy mapping modelled very accurately
3) Allows for flexible implementations of Halo-Galaxy connection
4) Modelling RSD through the Streaming Model simplifies the functions the emulator needs to learn
\xi^R_{hh}(r|c_i, M_h)
v_{hh}(r|c_i, M_h)
Galaxy =
\{\vec{g}\}
\xi_{gg} \propto \int d M_h W(\vec{g}_j, M_h) \xi_{hh}(M_h)
\xi_{gg} \propto \int d M_h W(\vec{g}_j, M_h) \xi_{hh}(M_h)
WORK IN PROGRESS
3. Complementary summary statistics
Simplify the model by separating different environments
Voids
Clusters
r [h^{-1} \mathrm{Mpc}]
Assumed density splits identified in real space
How much information is still missing??
\Omega_M
\Omega_\Lambda
\sigma_8
Input
x
Neural network
f
Representation
(Summary statistic)
r = f(x)
Output
o = g(r)
Invariance to known unknowns
Increased interpretability through structured inputs
Modelling cross-correlations
Conclusions
- Redshift Space Distortions allow us to constrain gravity models
- We need to account for the non-Gaussian real to redshift space mapping to correctly model deviations from GR
- Can we learn the optimal summary statistic through Machine Learning?
- Current constrains can be improved by extending models to smaller pair separations through N-body simulations
- How limited are we by our Halo-Galaxy connection assumptions?
MPA
By carol cuesta
