An exploration of physics beyond the standard model with next generation cosmological observations

Santiago Casas

Postdoctoral Researcher

TTK, RWTH Aachen University

     @santiagocasas                                                                                        @sant87casas

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

Modified Gravity and Dark Energy

• Add a scalar degree of freedom to the Einstein-Hilbert action
• (Non-)Minimal coupling, Kinetic terms

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

The Matter Power Spectrum

Slides provided by: Guadalupe Cañas-Herrera

spectroscopic GC

photometric WL and GC

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

Vera Rubin LSST

21cm Intensity mapping

• Novel probe for cosmology in the 21st century
• Access to yet unexplored redshifts
• Very different systematics, hybrid of techniques between CMB and GCsp

• Tracer of DM-Halos where neutral H resides
• Information about dark ages
• Very good redshift resolution, bad angular resolution

Vera Rubin LSST

Square kilometer array (SKAO)

• SKA Phase 1: SKA1-Low and SKA1-Mid
• SKA1-Low: 130,000 dipole antennas, 65km max. baseline (Australia)
• SKA1-Mid: ~200 dishes of ~15m diameter, max. baseline 150km (South Africa)
• Precursors: ASKAP, MEERKAT, HERA...
   
• €1.3 Billion, 16 countries, 710 Petabytes, 8 years construction

https://www.skao.int/

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

Vera Rubin LSST

Square kilometer array (SKAO)

SC, Carucci, Pettorino et al (2022) 2210.05705

• WL is better at measuring \(\Sigma\)
• GC is better at measuring \(\mu\)
• SKAO-all-probes constrains at 3% already

• 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

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!

BACKUP

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