https://www.pablocarlosbudassi.com/2021/02/the-infographic-and-artistic-work-named.html

Planck 2018 CMB Temperature map (Commander) .  wiki.cosmos.esa.int/planck-legacy-archive/index.php/CMB_maps

Large Scale Structure

Illustris Simulation: www.nature.com/articles/nature13316

• $\Lambda$CDM is best fit to observations.
• Predictive model with few free parameters.

Concordance Cosmology:

• Lensing
• CMB
• Clustering
• Supernovae
• Clusters

https://www.cosmos.esa.int/web/planck/publications

68% Dark Energy

5% Baryons

27% Dark Matter

Textures created with DALL-E

• $\Lambda$CDM is still best fit to observations.
• Some questions remain:
• $\Lambda$ and CDM.
• CDM hasn't been found
• Cosmological Constant Problem:

doi: 10.1146/annurev.nucl.012809.104521

Age of the Universe

Temperature of the Universe

• Planck measurements, essentially cosmic-variance limited in TT
• Percent precision in cosmological parameters
• Degeneracies in $\Omega_k$, $\Omega_m$ and $H_0$ broken with BAO and lensing
• $H_0 = 67.37 \pm 0.54 \, \textrm{km/s/Mpc}$

Planck 2018 results. VI. Cosmological parameters https://arxiv.org/abs/1807.06209

https://www.cosmos.esa.int/web/planck

• In general: confidence on the distance ladder
• Concerns on calibration, anchors dust or
  metallicity, have basically
  faded out
• Riess et al 2022*:
  $H_0 = 73.30 \pm 1.04 \, \textrm{km/s/Mpc}$
  
  using Cepheids and
  high-z SNIa

* The Astrophysical Journal Letters, 934:L7 (52pp), 2022 July 20

Tensions IN $\Lambda$CDM

$H_0$ tension at 5$\sigma$

• Tensions between local and recombination-based measurements

Freedman et al

SH0ES, Riess et al

Planck 2018, VI

How to measure:

• Positions of galaxies in the sky (angles)

• Redshifts of galaxies (photo or Spectro)

• Shapes (ellipticities of galaxies)

Tension with Planck in the
$\sigma8$ - $\Omega_m$ plane

Lange et al. arXiv: 2301.08692

• So called "lensing is low" 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

Tension with Planck in the
$\sigma8$ - $\Omega_m$ plane

Lange et al. arXiv: 2301.08692

• So called "lensing is low" 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

Tensions IN $\Lambda$CDM

Possible solutions and new directions

• $\Lambda$ ?
• Inflation ?
   
• $m_{\nu}$ ?
   
• LSS  ?
  
   
• Big data?

Outline of working fields

• Coupled Quintessence
• Higgs-Dilaton
• Modified Gravity
• Horndeski/EFToDE
   
• EFToLSS
• Emulators
   
• Machine Learning
• Variational inference
• Stage-IV surveys
  Radio and Optical

First Step: Modify Gravity

Ezquiaga, Zumalacárregui, Front. Astron. Space Sci., 2018

a SCALAR-tensor theory

• Horndeski theory: most general theory for an extra scalar degree of freedom, with second order equations of motion in 4D and no ghosts
• 5 Lagrangian terms, which have been largely ruled out by:
  • Late-ISW
  • GW170817
  • No self-acceleration -> uninteresting

the road ahead of horndeski

The "surviving Horndeski" Lagrangian:

In the EFT formalism, FLRW, linear and
(unitary gauge time $\rightarrow \phi$ ) :

Parametrize free functions and check for stability in solutions

We have shown that certain classes of models will not be distinguishable from LCDM, even with future surveys,  at 1$\sigma$, while others will be measured with 10%-60% precision in their parameters

Frusciante, Peirone, SC, Lima, 1810.10521, Phys.Rev.D 99

Classifying by screening

• Modified Gravity theories should recover GR at small scales, especially in dense regions, screening needed!

Brax, SC, Desmond, Elder 2201.10817  Universe 8

• Perturbations of $\phi$ and matter coupled in Jordan frame -> Yukawa-like fifth forces:

Different types of screening:

• Chameleon: The mass $m(\phi_0)$ increases sharply inside matter
• Damour-Polyakov: The coupling $\beta(\phi_0)$ vanishes inside matter
• K-mouflage and Vainshtein: $Z(\phi_0) \gg 1$

Classifying by screening

Brax, SC, Desmond, Elder 2201.10817  Universe 8

Screening mechanisms can be characterized by the inequality:

• Chameleon: $k=0$ (surface N. potential is large)
• K-mouflage: $k=1$ (N. acceleration is large)
• Vainshtein: $k=2$ (curvature is large)

• $f(R)$ Hu-Sawicki  (see later)
• $k$-essence + univ. coupling
• nDGP (3+1)d brane embedded in 5d

For DE applications and under some assumptions:

• Chameleon screens everything above a certain potential threshold
• K-mouflage does not screen galaxy clusters
• Vainshtein screens all structures that turn non-linear

Parametrized modified gravity

Beyond $\Lambda$CDM the two linear gravitational potentials $\Psi$ and $\Phi$ are not equal to 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 ($a$)

Only two independent functions!

Another approach:

Parametrized modified gravity

• Using Planck satellite data in 2015 and 2018, constraints were obtained on these two functions $\mu$ and $\eta$.
• Late-time parametrization: dependent on Dark Energy fraction

Parametrized modified gravity

Forecasts for Stage-IV : Euclid, DESI, SKA1, SKA2, only GC and WL

SC, Kunz, Martinelli, Pettorino, Phys.Dark Univ. 18 1703.01271

• Study more general case of free $\mu$, $\eta$ functions at each bin
• Non-linearities crucial for constraints
• Z-PCA decorrelation
• Constraints on $\mu$, $\eta$ of O(10%)

• For late-time and early-time scenario:
  Constraints on $\mu$, $\eta$ of O(3%)
• When combining GC+WL+Planck priors

Stage IV Surveys

• Stage IV surveys get their name from the fourth generation of cosmological surveys

• Provide constraints on cosmological parameters, at least one order of magnitude better than current data

• Euclid, LSST (Vera Rubin Obs), WFIRST (Nancy Roman Telescope), SKAO, CMB S-IV, DESI

Euclid Space Satellite

ESA class M2 space mission

Currently in Cannes, waiting to be shipped to Cape Canaveral

https://www.esa.int/Science_Exploration/Space_Science/Euclid

Sun-Earth Lagrange point 2, 1.5 million km from Earth

Launch vehicle: SpaceX Falcon 9

Euclid Space Satellite

• Two instruments:
•  VIS (visible photometer): shape and orientation of ~1.5 billion galaxies!
•  NISP (near infrared spectrograph): ~30 million galaxy spectra !

• 15 000 square degrees in the sky
•  16 countries, ~1500 members
•  ~170 Petabyte of data!

photometric primary probe

Euclid will measure the photometric 3x2pt function

Directly constrains MG function $\Sigma$ through Weyl potential

spectroscopic probe

BAO

Clustering

RSD

Euclid Collaboration, IST:Forecasts, arXiv: 1910.09273

Euclid will also measure the 2pt corr-func of spectroscopic galaxies in redshift space

The Matter Power Spectrum

Euclid: IST:Forecasts

Awardees of the Euclid STAR Prize Team 2019

Euclid preparation: VII. Forecast validation for Euclid cosmological probes.  arXiv:1910.09273

IST:F (forecasting taskforce), spent a few years refining, validating and comparing recipes, codes and forecasts

Euclid was commissioned to measure $w_0, w_a , \gamma$

Vera Rubin LSST

• Located in Chile, 8.4m telescope
• 20 billion galaxies
• Redshifts: 0 < z ~< 3  (photometric)
• 18,000 square degrees
• 11 years of observation
• 3x2pt, clusters, SNIa

Vera Rubin LSST

DESI telescope

• 14 000 square degrees in the sky
• 30 million accurate galaxy spectra
• Redshifts: 0 < z < 2 (spectroscopic)
• Quasars up to z~3.5
• 5 years of observation
• Starting 2021
• Power spectra, Bispectra, Corr. Func.

Vera Rubin LSST

Euclid vs. DESI+Rubin

• Forecasts for Modfied Gravity parametrizations
• Euclid using spectroscopic and photometric probes, is roughly as powerful as Rubin+DESI

Fisher Matrix Forecasts

Euclid preparation: VII. Forecast validation for Euclid cosmological probes.  arXiv:1910.09273

Bayes Theorem:

Probability of the model parameters given the data

Fisher Information Matrix:

Curvature (Hessian) of the Likelihood

Gaussian Likelihood in data space:

How do we actually perform those forecasts?

J. Schaffmeister

Fisher Matrix Forecasts

Euclid preparation: VII. Forecast validation for Euclid cosmological probes.  arXiv:1910.09273

Fisher Matrix for a Gaussian likelihood of angular power spectra:

Parameter covariance:

Defines an ellipse:

CosmicFish Code

Code: CosmicFish

S.Casas, M.Martinelli and M.Raveri

Soon to be released: New full pythonic version

https://github.com/CosmicFish/CosmicFish

Neutrino forecasts for Euclid

Plots by: Sabarish Sabarish Venkataramani

Euclid Full:

GC spectro + 3x2pt photo

Code: CosmicFish

S.Casas and M.Martinelli

Neutrino constraints from Planck

Planck 2018 results VI, arXiv:1807.06209

MASSIVE Neutrinos in Cosmology

Froustey et al, arXiv:2008.01074, arXiv: 2110.11296

• If neutrinos are massless: relativistic, dilute as $a^{-4}$
• If massive: non-relativistic, one has to follow the Friedmann function evolution

• Neutrinos and Photons initially at thermal equilibrium
• Neutrinos decouple at $\approx$ 1MeV
• Energy injection into photons from $e^+ e^-$ annihilation

massive Neutrinos: Free streaming

• Neutrinos free stream below a scale of $k_{FS}$
• They do not cluster below that scale
• Suppression of the total power spectrum
• The non-relativistic transition imposes a minimum in $k_{FS}$
• Cosmology-dependent

Suppression of the power spectrum, at first order depends on energy density ratios

Likelihood Sampling

• Recent Euclid SP paper (SC, Lesgourgues, Schöneberg, et al) validating MontePython Fishers against IST:F results (in internal review)
• Validation of Einstein-Boltzmann codes CLASS and CAMB using CosmicFish
• Good agreement between Fisher matrices and MCMC contours for Euclid specs.
• Tools used now in several Euclid KP and SP papers.

Galaxy Clustering beyond Linear

Slide by: Dennis Linde

• Start from Vlasov-Poisson system
• Take non-linear terms into Fourier space
• Compute mode-coupling kernels
• Integrate out small scale physics

Text

• Pros: More accuracy, BAO damping, correct bias and RSD expansion
• Cons: Many more free parameters
• Implementing currently into CLASS à la FFTLog  (Simonovic et al, arxiv:1708.08130)

Angulo et al, 1406.4143

Euclid likelihood development IST:L

CLOE team, Oslo 2022

Cosmological Likelihood for Observables in Euclid

• In charge of implementing the likelihood for spectroscopic and photometric observables
• Samplers, emulators, Boltzmann codes
• Theory prediction code
• Data, covariance reader and handler
• Group of ~15 people

Agile: Recently -> 1000 tasks!

Euclid likelihood NONLINEAR IST:NL

• Group of ~10 people
  In charge of implementing the non-linear prescriptions for IST:Likelihood
• GCspectro: EFT 1-loop RSD in multipoles
• 3x2pt photo:
  • Covariance, nonlinear Super-Sample
  • Bias expansion
  • Emulators for nonlinear, HMCode, Halofit, Bacco, EuclidEmu
  • Baryonic Feedback

• Different emulators with systematic offsets
• Euclid optimistic error bars can distinguish them
• Biases in parameter estimation to be resolved
• S.Casas, P. Carrilho, C. Moretti to lead KP papers

other models tested with STAGE-IV

Euclid: SC et al (2022) in review

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

f(R) Hu-Sawicki

scale-independent scalar-tensor theories

Euclid: Frusciante, Pace, Cardone, SC  et al (2022) in review

SC, Rubio, Pauly et al (2017) 1712.04956

Higgs-Dilaton inflation: early-late Universe connection

Model-independent anisotropic-stress $\eta$

Amendola, Pinho, SC 1805.00027

SC, Amendola, Baldi, Pettorino et al 1508.07208

Coupled Quintessence: DM-DE

More exotic models

More exotic models

machine Learning and variational methods

• In era of Big Data (billions of raw data points) and hundreds of possible models and simulations:
  • Important to be as computationally efficient as possible
     
• Likelihood codes for Euclid 2-3s per evaluation, Einstein-Boltzmann codes 1-10 seconds (depending on model)
• Emulators for linear and nonlinear codes (CLASS, N-body, Lensing)
  • Bayesian Neural Networks give also uncertainty estimations
     
•  Automatic-Differentiable (AD) codes: Leverage variational methods, such as Hamilton MC, AD-Variational Inference, Exact Fisher and beyond

Text

Conclusions

• $\Lambda$CDM paradigm still best fit to observations, but tensions, unknowns and discrepancies start to crack the model.
• Several avenues of research important: Modified Gravity, cosmological Neutrinos, Early-Late time interaction.
• Stage-IV surveys, infrarred, optical and radio will improve error bars by one order of magnitude.
• Theoretical modelling (especially at non-linear scales) has to keep up with accuracy.
• Combination and synergies of surveys will break degeneracies.
• Big Data challenge needs to be resolved with ML and AI
• Unexpected unknowns awaiting for us in the data this decade!

Credits: Tobias Liaudat, CosmoStat

Euclid Shape Pipeline

Credits: Rodlophe Cledassou, CNES

Euclid

Neutrinos Masivos en Cosmologia

Neutrinos masivos: Free streaming

CMB angular spectrum and matter power spectrum are both dependent on neutrino mass, N_eff and ordering

Linear Perturbations

Vlasov-Poisson system is a set of diff.eqn. in which all matter-radiation species are coupled

Slides by: Dennis Linde

f(R) Hu-Sawicki model

Text

Modification of the Einstein-Hilbert action

Induces changes in the gravitational potentials *

Scale-dependent growth of matter perturbations

Small changes in lensing potential

Free parameter: $f_{R0}$

Hu, Sawicki (2007)

"Fifth-force" scale for cosmological densities

$\lambda_C =32 \rm{Mpc}\sqrt{|f_{R0}|/10^{-4}}$

Euclid: Casas et al (2022) in preparation

f(R) Hu-Sawicki model

Text

Euclid: Casas et al (2022) in preparation

Codes used: for background and scale-dependent linear perturbations: MGCAMB and EFTCAMB

For non-linear power spectrum:

Winther et al (2019) fitting formula