Santiago Casas, Dr. rer. nat.

Large Scale Structure and the Hubble Parameter

RedH0T Project - IDL WPs

Interview

  santiagocasas                               www.santicasas.xyz        

3 Months Internship

Laboratorio Nacional de Luz Sincrotron,

Campinas, Brazil

Tonale Winter School of Cosmology Organizer 2016-2021

My trajectory

• MICIT scholarship, Universidad de Costa Rica
• LNLS Brazil scholarship, U. Campinas
• STAR prize winner 2019
• Summa cum laude
• More than 40 seminar talks
• 5 invited speakers and plenary talks in last 2 years

• 91 peer-reviewed articles with the Euclid Collaboration, 2 as first author, 25 papers as lead author.
• 26 papers outside of collaboration
• Referee for 5 different journals
• 2 published reviews in cosmology

Euclid

EC Internal Communication Management

EC Copenhagen 2023:  Builder Status

EC Rome: Plenary Speaker

2 STAR Prizes

Theory-Likelihood package co-lead

2025

CLOE-org Official Maintainer

Theory

Observables

Simulations

The four pillars of cosmology

Statistics

Broad expertise in all pillars

The matter power spectrum

• Fork github.com/santiagocasas/MGCAMB in f(R):
  Casas+2306.11053
• SKA x Euclid synergy:
  Casas+2210.05705
• Higgs-dilaton inflation+Dark Energy: Casas+1712.04956 

• CLASS 1-loop: Linde+2402.09778 
• Gaussian streaming in RSD:
  Bose+1911.04391
• Sensitivity to Neutrinos: 
  Archidiacono, Lesgourgues, Casas+
  +2405.06047 

• Stage-IV Forecasts for non-linear DE: Casas+1703.01271
• Relativistic N-body, GNQ: Casas+
  1608.02358 
• Fitting functions from f(R) Nbody: Winther, Casas+1903.08798 

I have expertise on all the different scales!

Likelihoods

Euclid: lnterscience Taskforce on Non-linearities, Key Paper, Carrilho, Casas, in prep.

wrong theory

CLASS-Oneloop+Montepython

Test of prior-dependence through Analytical Marginalization - DESI settings

• I am an expert in Fisher Matrices and Bayesian parameter estimation

• As the go-to person for Fisher matrices: They are nothing else than error propagation!!

• Still important to test assumptions,  systematics (nuisance) and pipeline robustness!

My pipeline: CosmicJellyFish

Using symbolic-regression emulators + Nautilus IS+NN. Achieve results in ~O(3hr) vs. days

Public Codes

github.com/santiagocasas/cosmicfishpie

github.com/DifferentiableUniverseInitiative/jax_cosmo

github.com/brinckmann/montepython_public

github.com/cloe-org

Euclid: Validation of the MontePython forecasting tools, Casas, Lesgourgues, Schöneberg, et al.; 2303.09451 

Authored or contributed

https://github.com/santiagocasas/topo-cobaya

Model-independent constraints

Model-independent determination of gravitational anisotropic stress using: BAO+Cosmic Chronometers+RSD and Lensing and Gaussian Processes

Pinho, Casas, Amendola; Model-independent reconstruction of the linear anisotropic stress, ηarXiv:1805.00027 

Amendola, Bettoni, Pinho, Casas; Model-independent measures of gravity at large scales, ηarXiv:1902.06978

Sakr, Zheng, Casas;  Model-independent forecasts for the cosmological anisotropic stress from a combination of Euclid and DESI like surveys: DOI: 10.1093/mnras/staf1111

Model-independent variables, free of assumptions about initial conditions, DM properties:

further reduce dependence on shape of primordial power spectrum:

TOPO-Cobaya

• Uses hash-functions and merkle-trees
• Useful for blinding, reducing human-biases, reproducible and mathematically provable verification of output
• Similar techniques are important if we want to ensure a systematic replication of cosmological analysis

github.com/santiagocasas/topo-cobaya

Casas, Fidler; Time Ordered Provable Outputs arXiv:2411.00072

WP3: Sound Horizon angular and comoving scales from galaxy redshift surveys

WP4: Broadband, additional compressed information from LSS surveys

WP5: Full-modeling of LSS statistics

RedH0T Project:

Inverse Distance Ladder

RedH0T Project:

Inverse Distance Ladder

WP3: Sound Horizon angular and comoving scales from galaxy redshift surveys

WP4: Broadband, additional compressed information from LSS surveys

WP5: Full-modeling of LSS statistics

gain statistical constraining power

activate more model assumptions

increased epistemic risks

systematics could dominate error budget

more nuisance parameters

WP3: Sound Horizon angular and comoving scales from galaxy redshift surveys

WP4: Broadband, additional compressed information from LSS surveys

WP5: Full-modeling of LSS statistics

Ensuring firm footing on assumptions, error propagation, and robustness before increasing model/method complexity

RedH0T Project:

Inverse Distance Ladder

WP3: Sound Horizon angular and comoving scales from galaxy redshift surveys

• Understanding how robust BAO observables are to reconstruction (nonlinear) choices
• Choice of fiducial cosmology templates
• Poorly understood effects: relativistic corrections, velocity biases
• How these choices impact constraints downstream

Main previous experience: Co-leading the full-shape vs. model-independent (BAO+RSD -> projection) approaches of the GCsp probe in the Euclid IST:Forecasting, understanding of h-units

Euclid preparation: VII. Forecast validation for Euclid cosmological probes, Blanchard et al. arXiv:1910.09273

github.com/santiagocasas/fishermathica

RedH0T Project:

Inverse Distance Ladder

• Defining and validating compressed summaries
• Broadband, RSD, BAO, ShapeFit
• Define model-independent quantities and project them (including errors) into parameters
• Explore model-agnostic approaches, Machine-Learning approaches (Gaussian Processes)
• Understand sensitivity of constraints
• Create DESI-Euclid likelihoods for compressed obs.

Main previous experience: Model-independent constraints, Linear-point observable, Euclid GC Working Group, Theory extensions of CLOE

WP4: Broadband, additional compressed information from LSS surveys

Sakr, Zheng, Casas;  Model-independent forecasts for the cosmological anisotropic stress from a combination of Euclid and DESI like surveys: DOI: 10.1093/mnras/staf1111

RedH0T Project:

Inverse Distance Ladder

Euclid: CLOE paper 5: Extensions beyond the standard modelling of theoretical probes and systematic effects; Goh, (incl. Casas), et al.; 2510.09147 

• Careful study of EFT prior-dependence
• Unify approaches: non-linear bias treatment, redshift-space implementation
• Kernel structure beyond LCDM assumptions
• Unify codes and pipelines: less is more!
• Mock-challenges but focused on H0
• Make use of auto-differentiability to properly study nuisances and propagation of errors

Main previous experience: Working on EFTofLSS, TRG, Class-Oneloop, PBJ, IST:Nonlinear, several cosmological inference pipelines, DESI, Euclid forecasts for GCsp, jax-cosmo

WP5: Full-modeling of LSS statistics

CLASS-OneLoop: accurate and unbiased inference from spectroscopic galaxy surveys; Linde, Moradinezhad, Rademacher, Casas, Lesgourgues; arXiv:2402.09778 

JAX-COSMO: An End-to-End Differentiable and GPU Accelerated Cosmology Library, Campagne, Lanusse (incl Casas) et al., arXiv:2302.05163

RedH0T Project:

Inverse Distance Ladder

Research Data Management ideas

for RedH0T project

• Always had strong interest for Open and Reproducible Science
  • Open Science Foundation
  • Proper use of Github repos
  • Maintainer of code and documentation
• At DLR: Road to FAIR (https://www.nature.com/articles/sdata201618)
  • Findable, Accessible, Interoperable, Reproducible
  • https://www.go-fair.org
• RedH0T project: Red, Blue teams
  • White team needs special care of these aspects. Useful to have a professional documentation and management strategy from the start.
     
• Topo-Cobaya example of strong reproducibility.
• Good databases, linkable, clear definitions (almost Ontological)

RedH0T project

based on: A tale of many H0; Verde et al.; arXiv:2311.13305v1

idea for a linked database>

Conclusions

Merci!

Profile

• Senior cosmologist with a strong background in large-scale structure inference and theory. Strong experience in large-collaboration work and leadership roles.

• Expertise spanning all scales of LSS modeling - from BAO to Full-Shape

• Focus on robustness, speed, error propagation, and model dependence in Bayesian cosmological inference

Contribution to RedH0T (IDL WP3–WP5)

• Holistic view of H0 inference across LSS observables

• Ability to interface between theory, data analysis, and numerical pipelines (community)

• Primary role: testing assumptions, understanding sensitivity to modeling choices, and quantifying robustness - based on pipeline experience

• Contributing to consistency and interoperability of IDL deliverables

• Experience mentoring junior researchers within collaborative projects (3 Bachelors, 6 Master and 1 PhD between RWTH, Saclay, and Heidelberg) -> Synergy team

Further ideas for open discussion

• Bayesian hierarchical models and likelihood "free" inference: a compromise between likelihood modeling (especially covariance) and forward-modeling all observational effects
• Prior-sensitivity and assumption-sensitivity map for H0 based on WP3-WP5 probes. What is the possible space?
• Meta-analysis of error budget for Inverse Distance Ladder
• Reproducibility studies: Which BAO+RSD+LSS (and other) constraints can be replicated systematically End2End?
• Variational inference for SNIa+LSS likelihoods
• Linked interoperable database of all current results
• Are there possible relationships between DE and H0 tension?
• More exploration with Dark Sirens and other future probes (cross-WPs) arXiv:2510.08699 
• Can AI accelerate progress? github.com/santiagocasas/clapp

Backup slides

Future plans and support for future missions

https://www.skao.int/

First forecast for MG using Radio x Optical: Constraining gravity with synergies between radio and optical cosmological surveys, Casas et al (2022), Phys.Dark.Univ. 2210.05705

The power of combining Euclid + CMB-S4: Euclid preparation. Sensitivity to Neutrino parameters. Archidiacono, Lesgourgues, Casas, Pamuk, et al (2024) 2405.06047

Supervision of students

• 1 PhD student in Heidelberg:
  • Ana Marta Pinho, gravitational slip
• 2 internship students at CEA :
  • Senwen Deng, inflation-dark-energy
  • Raphael Baena, GP, OT, PCA, emulators.
• 5 Master students at RWTH Aachen (12 months projects each) :
  • Sabarish V.M. + Sefa Pamuk on MontePython.
  • Dennis Linde + Christian Rademacher: CLASS-1loop.
  • Johanna Schafmeister: accuracy-aware emulators
• 2 Bachelor students
  • Jakob Kramp: JAX-Variational inference.
  • Yun Ling: Neutrino N-body forecasts.
    Image credits: Yun Ling, Jeppe Dakin,
    CONCEPT code.

Much of this work has been thanks to excellent collaborators and students over the years!

• Model-independent test of the gravitational slip using Gaussian Processes. Amendola, Pinho, Casas (2018), 1805.00027.
   
• Quintessential $\alpha$-attractor inflation: forecasts for Stage IV galaxy surveys, Akrami, Deng, Casas (2020), 2010.15822.
• Looti Emulator: github.com/santiagocasas/looti  (GP, PCA, Optimal Transport).
   
• Euclid: Validation of the MontePython forecasting tools, Casas, Sabarish V.M. +(2023), 2303.09451
• Euclid: Sensitivity to neutrino parameters, Archidiacono, Lesgourgues, Casas, Pamuk (2024), 2405.06047.
• CLASS-OneLoop: Accurate and Unbiased Inference from Spectroscopic Galaxy Surveys, Linde+Rademacher (2024) 2402.09778.
•  Bayesian NNs: github.com/schafmeister/bayesian_nn

Students moved on to excellent PhDs

Outreach

• Member of the Euclid Consortium Internal Communications team (ECICOM):
  • Newsletter (+ J. Brinchmann, G. Cañas-Herrera): www.euclid-ec.org/science/newsletter/
• EC Education and Public Outreach member (ECEPO):
  • Social media team, manager of @euclidconsortium instagram's account.
• Funding member of alpha-Cen :  First Central-American association of astrophysics. Webinars, Remote-internships, mentoring, (Virtual) Summer Schools for underrepresented students .
• Podcasts :  Podcastination (with CosmoStat members)
  
   
• Big Think, Starts with a Bang
• TV-appearances : Teleantioquia y Telemedellin
• CNRS 80-years anniversary: Euclid stand at Gif-Sur-Yvette.
• Science Communication Summer School: Alexander von Humboldt Foundation, Berlin, 2021.
  Declaration handed in to German Bundestag, including chapters on inclusion and diversity.

An example of the complexity in analyzing and constraining a cosmological model

Project led by K.Koyama, me and my student Sefa Pamuk

• Fitting formulae not accurate enough against N-body simulations
• Emulators / Halo-model strong differences among each other

We can describe general modifications of gravity (of the metric) at the linear perturbation level with 2 functions of scale (\(k\)) and time (\(a\))

Euclid primary observables

Casas, Kunz, Martinelli, Pettorino (2017); Phys.Dark Univ. 18 1703.01271

Updated forecasts for SKAO, LSST(Rubin), DESI : 
Casas, Carucci, Pettorino,  Camera, Martinelli (2023); Phys. Dark Univ.,  2210.05705;  

Lensing and Clustering

very complimentary probes

What makes Stage-IV galaxy surveys particularly well-suited for testing Modified Gravity?

The power spectrum: summary statistics

• Fourier transform of 2-point correlation function
• Linear scales predicted by Einstein-Boltzmann codes
• Intermediate scales predicted by perturbation theory

Archidiacono, Lesgourgues, Casas et al., Euclid preparation - LIV. Sensitivity to neutrino parameters, 2405.06047

• Dark energy and modify gravity can enhance growth
• Neutrino suppresses growth
• Baryonic feedback complicates small scales

• The power spectrum can be obtained through Galaxy Clustering and Weak Lensing (Euclid probes)

• Non-linear scales -> expensive simulations, Machine Learning emulators

• Good agreement between Fisher Matrix (Casas+2023) and MCMCs with MontePython,  synthetic data == model
   
• Synthetic data is FORGE (MG-Arepo) : observe parameter bias in the estimation.

Weak Lensing, 6years Euclid data,

IST:F validated MontePython likelihoods: github.com/Sefa76/photometric_fofR/ 

• What is \(\Lambda\) ?
• What is CDM ?

Projet de Recherche: Disentangle neutrinos, modified gravity and nonlinearities using Euclid and cross-correlations with other surveys

DESI cosmological results (2024, 2025) -> Not a cosmological constant?

Casas et al., Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes, 2306.11053 

Archidiacono, Lesgourgues, Casas et al., Euclid preparation - LIV. Sensitivity to neutrino parameters, 2405.06047

• Modified gravity -> increases growth, enhances power spectrum

• Neutrinos -> suppress growth and power
• Baryonic feedback -> dissipate clustering
• Strong degeneracy

Weak Lensing, optimistic, with BCEmu as baryonic-feedback model

• When baryonic feedback parameters are left free, the situation degrades!
   
• When estimating lower bound on \(\log f_{R0}\) we quickly hit the prior. Contours are far from Gaussian.

• Use Bayes ratios to compute prior-independent bounds.
   
• Large degeneracy in parameter space between cosmology and baryonic parameters, causes projection-effects.
   
• Used the PROSPECT (Holm+2023) profiling tool to find the profile likelihood: github.com/AarhusCosmology/prospect_public

We included theoretical errors (Audren+2012) to mitigate biases

github.com/Sefa76/photometric_fofR/

Forecasting the constraining power of Euclid and other Stage-IV surveys

Code: CosmicFishPie 

S. Casas, M. Martinelli and M. Raveri

S. Pamuk, Sabarish V.M. and friends

github.com/santiagocasas/cosmicfishpie

New pythonic version: I have been main developer on forecasts for:

SKAO (21cm IM), DESI (GCsp), Vera Rubin LSST (3x2photo), Euclid (GCsp+3x2photo), CMB (TT+TE+EE)

Fisher matrix for the photometric 3x2pt observable in angular space

Recurring Challenge: Modified Gravity in the nonlinear regime

Credit: CoDECS simulations

Simulations of MG are

expensive, need for fitting functions or Emulators.

Baldi (2011);
Casas+(2015) 1508.07208; Winther, Casas+ (2019)1903.08798

Credits: Yun Ling

CONCEPT forecasts,

Ling, Casas, Dakin, in prep.

Are neutrino suppressions degenerate with MG enhancements?

Peel+(2018)

What about baryons??

Euclid standard project: f(R)+Mnu
Casas, Parimbelli in prep.

Is the fifth force screened at Halo, Clusters and galaxy level?

Different types of screening:

Chameleon, Damour-Polyakov, K-mouflage, Vainshtein

Review: Testing Screened Modified Gravity; Brax, Casas, Desmond, Elder (2021), 2201.10817.

Can we compute very nonlinear dynamics that backreacts into the Friedmann equation?

Growing Neutrino Quintessence,

Casas, Pettorino, Wetterich (2016), Phys. Rev. D 1608.02358

Ongoing research

Induces changes in the gravitational potentials -> fifth force

Casas et al., Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes, 2306.11053 

"Fifth-force" scale for cosmological densities

\(f_{R0}=(5.0^{+ 0.58}_{-0.52} \times 10^{-6})\)

Emulator differences sometimes larger than Euclid error bars

f(R) Hu-Sawicki model

Koyama, Pamuk, Casas et al., Euclid preparation. Simulations and nonlinearities beyond $\Lambda$CDM. 4. Constraints on $f(R)$ models from the photometric primary probes, 2409.03524

Archidiacono, Lesgourgues, Casas et al., Euclid preparation - LIV. Sensitivity to neutrino parameters, 2405.06047

Effect of neutrino mass on matter clustering

IST:Forecasting

Recipe, comparison and final Fisher matrices.
One of the few validated Galaxy Clustering + Weak Lensing codes

My main contributions:

Euclid preparation: VII. Forecast validation for Euclid cosmological probes, Blanchard et al. arXiv:1910.09273

Figure of Correlation (FoC), based on:

Casas et al,  (2017) Phys. Dark Univ. 1703.01271

github.com/santiagocasas/cosmomathica

github.com/santiagocasas/fishermathica

Maintainer of public repository.

Plotting scripts for all the figures.

submission to the arXiv

Future avenues of research

Short Term

• Develop a modern likelihood pipeline that contains emulators for modified gravity, neutrinos and baryonic physics
• Lead one of the Euclid Data Release 1 Key Project papers on modified gravity and dark energy
• Thereby helping to understand current cosmological tensions

Medium term

• Develop cross-correlation likelihoods for N-point statistics with different surveys such as SPT and CMB-Stage-IV (S. Galli, K. Benabed at IAP), 21cm Intensity Mapping with SKAO and Dark/Standard Sirens with Gravitational Waves using Einstein Telescope and LISA (French involvement also at IAP)
• Make the likelihood pipeline fully automatically-differentiable
• Investigate the interaction of baryonic physics with modified gravity and neutrinos
• Go beyond 2-point statistics -> field level with Euclid, DESI and LSST (G. Lavaux, F. Leclerq at IAP)

Longer term

• Run a fully modern cosmological analysis with Stage-IV data and its successors
• Develop automatic and agentic AI systems for cosmological discovery
• github.com/santiagocasas/clapp , classclapp.streamlit.app

First forecast for MG using Radio x Optical: Constraining gravity with synergies between radio and optical cosmological surveys, Casas et al (2022), Phys.Dark.Univ. 2210.05705

Vera Rubin LSST

Square kilometer array (SKAO)

• Modelling is very analogous to GCsp, with brightness temperature on top and different biases
• GCsp-IM Cross-correlation in overlapping bins
• DESI : Two galaxy samples
• SKAO: HI Galaxies and 21cm-IM

\(P^{\rm IM}(z,k) = \bar{T}_{IM}(z)^2 \rm{AP}(z) K_{\rm rsd}^2(z, \mu; b_{\rm HI}) \)
\(FoG(z,k,\mu_\theta) \\ \times P_{\delta\delta,dw}(z,k)  \)

\( K_{\rm rsd}(z, \mu; b_{\rm HI}) = [b_{\rm HI}(z)^2+f(z)\mu^2] \)

\( b_{\rm HI}(z) = 0.3(1+z) + 0.6 \)

\( \bar{T}_{\mathrm{IM}}(z)= 189h \frac{(1+z)^2 H_0}{H(z)}\Omega_{HI}(z) \,\,{\rm mK} \)

\(\Omega_{HI}  = 4(1+z)^{0.6} \times 10^{-4} \)

Carucci et al (2020) 2006.05996

Jolicoeur et al (2020) 2009.06197

\(P^{{\rm IM} \times \rm{g}}(z,k) = \bar{T}_{\rm IM}(z) {\rm AP} (z) r_{\rm IM,opt}  K_{\rm rsd}(z, \mu; b_{\rm HI}) \)
\( \times K_{\rm rsd}(z, \mu; b_{\rm g}) FoG(z,k,\mu_\theta) P_{\delta\delta,dw}(z,k) \)

\( \times \exp[-\frac{1}{2} k^2 \mu^2 (\sigma_{\rm IM}(z)^2+\sigma_{\rm sp}(z)^2)]  \)

SC, Carucci, Pettorino et al (2022) 2210.05705

Brightness temperature of 21cm emission line

Fraction of neutral hydrogen in the Universe

CosmicFish in the beyond-\(\Lambda\)CDM sea

Casas, Rubio, Pauly et al., 1712.04956 

Higgs-Dilaton inflation: early-late Universe connection

Constraints on Hu-Sawicki \( f(R)\)

Casas, Amendola, Baldi, Pettorino et al., 1508.07208

Coupled Quintessence: DM-DE

Surviving Horndeski EFT

Frusciante, Peirone, Casas, Lima, 1810.10521

Modified Gravity with SKA 21cm-IM

Casas, Cardone, Sapone, et al., 2306.11053 

Casas, Carucci, Pettorino et al 2210.05705 

Atayde, Frusciante, Bose, Casas, Li, 2404.11471 

Forecasts for generalized Cubic Galileons

Important: Take decisions, is it worth analyzing with data?

MCMC sampling with MontePython

Are Fishers a good approximation to the posterior?

in presence of neutrinos

• TTK Aachen group: developed Euclid photometric and spectroscopic likelihoods for MontePython.
• Validated likelihoods against CosmicFish Fishers, 4 different settings: CAMB/CLASS.

Euclid: Validation of the MontePython forecasting tools, Casas, Lesgourgues, Schöneberg, et al.; 2303.09451 

Euclid: Sensitivity to neutrino parameters , Archidiacono, Lesgourgues, Casas, et al.; 2405.06047

w0waCDM

MCMC sampling with MontePython

First up-to-date MCMC forecasts for Euclid+external probes in presence of neutrinos

• TTK Aachen group:  developed Euclid photometric and spectroscopic likelihoods for MontePython.
• Validated likelihoods against CosmicFish Fishers, 4 different settings: CAMB/CLASS.
• MCMC Metropolis-Hastings forecasts to test neutrino sensitivity + CMB + clusters.
• Careful consideration of neutrino effects in solvers.

Euclid: Validation of the MontePython forecasting tools, Casas, Lesgourgues, Schöneberg, et al.; 2303.09451 

Euclid: Sensitivity to neutrino parameters , Archidiacono, Lesgourgues, Casas, et al.; 2405.06047

Vera Rubin LSST

Radio x Optical Cosmology

SC, Carucci, Pettorino et al (2022) 2210.05705

• WL is better at measuring \(\Sigma\) (40% relative error)
• GC is better at measuring \(\mu\) (20% relative error)
• SKAO-all-probes constrains at 3-5% relative error
• At Planck best fits

• DESI(GCsp)xSKAO(IM) helps in \(h, \sigma_8\) but not in MG parameters
• Combination of SKAO + one Stage-IV probe is as good as two Stage-IV
• Different noise and systematics -> break degeneracies

Euclidean Timeline

Joined Interscience Taskforce on Forecasting

2015

STAR prize co-winner, plenary talk

2019

2019

2019

Core member, developer and reviewer of Interscience Taskforce on Nonlinearities and Likelihood

2019

Coordinator of pre-launch Key-Project on beyond standard models

2021

2 Key-papers co-lead

2022

Become Euclid Consortium (EC) member, Theory Science Working Group

2014

Joined EC Internal Communication Management

2023

EC Copenhagen: Achieved Builder Status

2023

EC Rome: Plenary Speaker

STAR prize for EC-Communication

2024

Theory-Likelihood package co-lead

2024

Theory Work Package Forecasting co-lead

nomination STAR prize PhD

2018

EC
social media manager

2025

CLOE-org Maintainer

Galaxy Clustering

Express the excess probabilty of finding another galaxy as a function of scale

Euclid: Fast two-point correlation function covariance through linear construction, Keihänen et al. (2022)

Measured galaxy power spectrum multipoles from mocks. Pezzotta et al. 2024. Compared to a EFToLSS model.

Neutrinos

Weak Lensing

tomography: multiple redshift bins and their cross-correlations

\(z\)

Euclid. I. Overview of the Euclid mission, Euclid collaboration, Mellier et al., 2405.13491

Neutrinos

Neutrinos

Neutrinos

Neutrinos

DESI

In a nutshell: Measure a geometric scale that was imprinted on LSS at recombination

https://data.desi.lbl.gov/doc/papers/

Another tension we need to explain?

spectroscopic probe: Full Shape

Linde, Moradinezhad, Rademacher, SC, Lesgourgues (2402.09778)

• Trade-off: larger error bars, more accuracy, less biasing
• Compared against IST:F model at different scales
• Many free parameters, good fit to ABACUS simulations

Tensions

Tensions IN \(\Lambda\)CDM

\(H_0\) tension at 5\(\sigma\)

• Tensions between local and sound-horizon-based measurements

Freedman et al

SH0ES, Riess et al

Planck 2018, VI

Credits: Yun Ling

CONCEPT N-body simulation, in red Dark Matter, in green-blue neutrinos. Ling, Casas, Dakin, in prep.

The Large Scale Structure of the Universe

• Cosmic web, filaments, halos
• Dark matter 
  clusters strongly, backbone of galaxy formation
• Neutrinos 
  free stream below certain scales

• Theory of gravity and physics predict this cosmic web
• Need very expensive N-body simulations
• Cannot compare 
  theory vs. observations point
  by point ->
  need
  summary!

Tension with Planck in the
\(\sigma8\) - \(\Omega_m\) plane

Lange et al. arXiv: 2301.08692

• \( S_8 = \sigma_8 \sqrt{\Omega_{m,0}/0.3} \)
• So called "lensing is low" problem or S8 problem.
• At the moment just a discrepancy (no tension) at 2-3 \(\sigma\)
• Blind comparisons among surveys can rule out usual systematics below z<0.54 (A. Leauthaud et al.)
• Beyond \(\Lambda\)CDM modelling does not help with current nonlinear analysis

Planck 2018, VI

DES DRY3 arxiv:2207.05766

Tensions IN \(\Lambda\)CDM

Beyond Gaussian, non-Gaussianities

voids, filaments, walls, knots

Minkowski functionals

Bispectrum

Approximate Bayesian Compuation

Euclid's 3x2pt data vector:

~12200 entries long

30 ell-bins

13 n_z bins

GG, GL, LL

DELFI: Denisty estimation likelihood-free inference

Projet de Recherche

Bayesian NN with Schafmeister

https://github.com/schafmeister/bayesian_nn

Stage V:

Backup slides