Tensions in the $\Lambda$CDM model

• $\Lambda$CDM is still best fit to observations.
• Some questions remain:
• H0 tension, now ~5$\sigma$

L.Verde, et al 2019. arXiv:1907.10625

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 $\sigma$

DES DRY3 arxiv:2207.05766

Alternatives to $\Lambda$CDM

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

Alternatives to $\Lambda$CDM

Gregory Horndeski
https://www.horndeskicontemporary.com/works

And in the Lorentz Institute seminar room!

Costa Rica - Arenal Volcano

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

Gregory Horndeski
https://www.horndeskicontemporary.com/works

Can we test more general models?

Cosmology of surviving Horndeski theory: The road ahead, N.Frusciante, S. Peirone, S. Casas, N. Lima, arXiv:1810.10521

Gregory Horndeski
https://www.horndeskicontemporary.com/works

And in the Lorentz Institute seminar room!

Parametrized modified gravity

In $\Lambda$CDM the two linear gravitational potentials $\Psi$ and $\Phi$ are equal to each other

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

Only two independent functions

Late-time parametrization: Planck constraints

• 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
• $\mathcal{O}(100\%)$ relative errors

Planck 2015 results XIV, arXiv:1502.01590

Planck 2018 results VI, arXiv:1807.06209

Late-time parametrization: Forecasts

2017 Forecasts for Stage-IV : Euclid, DESI, SKA1, SKA2, only GC and WL no cross-correlation

• 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

Casas et al (2017), arXiv:1703.01271

SKAO Probes

Image credit: Isabella Carucci

• Continuum emission:  Allows detection of position and shapes of galaxies.

• Line emission of neutral Hydrogen (HI, 21cm):

1. Using redshifted HI line -> spectroscopic galaxy survey

2. Intensity Mapping: Large scale correlations in HI brightness temperature -> very good redshift resolution,
good probe of structures

SKAO Probes

Image credit: Isabella Carucci

• Continuum emission:  Allows detection of position and shapes of galaxies.

• Line emission of neutral Hydrogen (HI, 21cm):

1. Using redshifted HI line -> spectroscopic galaxy survey

2. Intensity Mapping: Large scale correlations in HI brightness temperature -> very good redshift resolution,
good probe of structures

3x2pt recipe

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

Directly constrains MG function $\Sigma$ through Weyl potential

Galaxy Clustering Recipe

BAO

Clustering

RSD

Euclid Collaboration, IST:Forecasts, arXiv: 1910.09273

Intensity Mapping

• IM probes the underlying matter power spectrum.
• Density bias given by the HI mass contained in dark matter halos.
• 21cm brightness temperature depends on cosmological background & the energy fraction of neutral Hydrogen in the Universe $\Omega_{HI}$.
• $P_{\delta\delta,zs}(z,k)$ is the redshift space matter power spectrum

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

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

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

Jolicoeur et al (2020) arXiv:2009.06197

Carucci et al (2020) arXiv:2006.05996

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

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

Intensity Mapping x GCsp

• Cross correlation combines  one term of brightness T with one K term for each "redshift sample".
• Same underlying matter power spectrum for both probes.
• A combined z-error (damping along the line of sight), where "sp" dominates, since the IM resolution is 1-2 orders of magnitude better.

$b_{\rm g}(z) =$ fit to simulations for given galaxy sample

Jolicoeur et al (2020) arXiv:2009.06197

Wolz et al (2021) arXiv:2102.04946

$\sigma_i(z) = \frac{c}{H(z)}(1+z) \delta_z$

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

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

Intensity Mapping

• $P_{gg}$ underlying galaxy power spectrum.
• $P_{IM}/T_{b}^2$:  IM power spectrum.
• $P_{IM,g}/T_{b}^2$ cross-spectrum.
• Angle-dependent beam effect is in the signal*, damps accross the l.o.s.
• Along the l.o.s. damping due to FoG, but higher amplitude due to Kaiser.

SKAO GC Surveys

HI galaxies spectroscopic survey

1. GCsp: HI galaxy spec. redshift survey: $0.0 < z < 0.5$
   probes 3D matter power spectrum in Fourier space.

SKA1 Redbook 2018, arXiv:1811.02743

SKA1 Medium Deep Band 2:  $5000 \, \rm{deg}^2$

SKAO Angular Surveys

1. GCsp: HI galaxy spec. redshift survey: $0.0 < z < 0.5$
   probes 3D matter power spectrum in Fourier space
2. GCco + WL + XCco (Continuum): $0.0 < z < 3.0$
   probes angular clustering of galaxies, Weak Lensing (Weyl potential) and galaxy-galaxy-lensing.
   Angular number density:
   $n \approx 3.2 \rm{arcmin}^{-2}$
    

SKA1 Redbook 2018, arXiv:1811.02743

Continuum galaxy survey

SKA1 Medium Deep Band 2:  $5000 \, \rm{deg}^2$

SKAO Angular Surveys

1. GCsp: HI galaxy spec. redshift survey: $0.0 < z < 0.5$
   probes 3D matter power spectrum in Fourier space
2. GCco + WL + XCco (Continuum): $0.0 < z < 3.0$
   probes angular clustering of galaxies, Weak Lensing (Weyl potential) and galaxy-galaxy-lensing.
   Angular number density:
   $n \approx 3.2 \rm{arcmin}^{-2}$
3. For comparison: Stage-IV:
   $n \approx 30 \rm{arcmin}^{-2}$

*kindly provided by Stefano Camera

Continuum galaxy survey

SKA1 Medium Deep Band 2:  $5000 \, \rm{deg}^2$

SKAO IM Surveys

• IM: Intensity mapping survey
  $0.4 < z < 2.5$
• Very good redshift resolution:  $\Delta z \approx \mathcal{O}(10^{-3})$
• We use: 11 redshift bins
• Single dish mode:
  $N_d = 197$
  $t_{obs} = 10000 \, \rm{hr}$
  We limit to the scales
  $0.001 < k < 0.25 \, [h/\rm{Mpc}]$
   

SKA1 Medium Deep Band 1:  $20000 \,\rm{deg}^2$

Stage-IV surveys

• 14 000 square degrees in the sky

• 30 million accurate galaxy spectra
• Redshifts: 0 < z < 2

• 13245 square degrees in the sky

• 20~30 million accurate galaxy spectra
• 2 billion galaxy shapes
• with ground-based photometry
• Redshifts: 0 < z < 3

Euclid

DESI

Vera Rubin Obs. LSST

• 18 000 square degrees in the sky

• ~10 billion photo-z galaxies and shapes
• 11 years observations
• Redshifts: 0 < z < 3

Galaxy Clustering - IM Synergies

• GCsp-IM Cross-correlation in overlapping bins
• Addition in disjoint bins
• No GCsp-GCsp cross-correlation

Fisher Matrix forecasts

Given a likelihood function L, representing the probability of the data d, given the model parameters $\Theta$ , the Fisher matrix is defined as the Hessian of the L:

Assuming that L is a multivariate Gaussian distribution with a covariance matrix C independent of $\Theta$ :

The explicit form of F, depends on the given observational probe and the physical model assumption, for example for GCsp:

Fisher Matrix forecasts

What do we expect from the forecasts before doing them, just by looking at the formulas and the specs?

• SKAO (Phase1) has more independent probes but less statistical power (n(z) and area) -> less constraining power than Stage-IV
• WL and 3x2pt better at constraining $\Sigma$
• GCsp and IM better at constraining $\mu$
• GCsp x IM cross-corr. improves constraints on parameters?

Let's see the results !

SKAO  Results

• GC-IM probes measure $\mu$ at small $z$, where $\mu$ becomes important.

• Continuum probes measure better $\Sigma$ ; Weyl potential is important.

SKAO  Results

• Blue: Combined GCsp+IM (3D)
   
• Yellow: Combined continuum probes (2D: angular)
   
• Purple: Combination of 3D and angular probes
   
• Constraints on $\mu$ are good in angular, due to the XC contribution from GCco clustering.

SKAO  Results

SKAO  x DESI cross-correlation

• GCxIM probes do not improve constraints on MG parameters,
  but improvement on $h$ and $\sigma_8$

DESI_E : high-z Emission Line Galaxies

DESI_B: low-z Bright Galaxy Sample

SKAO GCsp: low-z HI Galaxies

SKAO  x DESI cross-correlation

• However, when combined with angular probes, there is a larger gain.

Galaxy Clustering - IM Synergies

Work in progress:

Same but with Euclid!

However, Euclid DR3 + SKAO AA4 is too far in the future!

SKAO  + optical

1. Have a unified open-source collaborative pipeline for forecasts and analysis
2. Optical GCsp x SKAO IM +HI GC + SKAO continuum 3x2pt
3. SKAO IM + HI GC + Optical 3x2photo + CMB XC?
4. A set of minimal MG models (parametrized + binning/PCA) to explore
5. Treatment of non-linear scales important!  (Are we sensitive here to baryonification?) 1-loop Pk, Bispectrum (Dyonisis talk)?
6. Neutrino mass, DM (Marco Regis talk), N_effective?

Pipelines

Code: CosmicFishPie

S.Casas, M.Martinelli and M.Raveri, S. Pamuk and more!

Soon to be released with MCMC support!

Contains:

Euclid (spectro+photo), Planck, LSST, DESI, SKAO IM, HI and continuum

https://github.com/santiagocasas/cosmicfishpie

https://cosmicfishpie.readthedocs.io

jaxcosmo library https://github.com/DifferentiableUniverseInitiative

Campagne, Lanusse, Zuntz, SC, et al, 2302.05163

We still need to develop many parts of a differentiable pipeline!

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

Euclid TH Science Goals

Euclid TH Science Goals

Euclid TH Science Goals

Euclid DR3 vs DR1

MeerKLASS specs

Thankfully provided by Zé

MeerKLASS specs

Thankfully provided by Zé

Now implemented into CosmicFishPie

My ex-student now collaborator Sefa Pamuk is implementing masks into a CF-based code

(now PhD candidate of José Bernal)

Euclid (GCsp) vs SKAO HI-GC + IM

SKAO IM - MCMC

Using Cosmic(Jelly)Fish + Nautilus -> 40min on a laptop

Euclid DR1 (GC-only) vs MeerKLASS

Seems futuristic!

SKAO  + optical

Credit: Guadalupe Cañas, Pedro Carrilho, Santiago Casas, for IST:NL/L, KPs, CLOE papers

Neglecting baryons -> bias!!

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

CLASS 1-loop Code in development in Aachen, RWTH

Validated against CLASS-PT, Velocileptors

Implemented in MontePython, soon in CosmicFishPie for GCsp and IM

in Fourier and "Legendre"

Text

ESA Datalabs - Collaborative Approach

Text

ESA Datalabs - Collaborative Approach

Text

ESA Datalabs - Collaborative Approach

ESA Datalabs Live DEMO

Text

Conclusions

• $\Lambda$CDM is still the best fit to observations, however certain theoretical uncertainties and tensions in data are still of concern.
• Constraining modifications of gravity at the level of perturbations -> hints for alternative models.
• SKAO will be able to probe weak lensing and matter density perturbations in novel and independent ways compared to optical surveys.
• Synergies with optical surveys, like Euclid, DESI and Rubin, including cross-correlations are promising to remove systematics and break degeneracies.
• Using the good z-resolution of SKAO HI IM could place tight constraints on redshift-binned parametrizations.

Santiago Casas

SKA1  vs Euclid

SKA1:

GC+WL+XC (Continuum) +
IM (HI 21cm) + GCsp(HI)

vs

Euclid

(Gcsp+GCph+WL+XCph)

vs

Euclid

(Gcsp+GCph+WL+XCph)+SKA1 Pk-probes.

Unfortunately, the $\mu$ constraints from Euclid alone dominate over the improvement that SKA1 "Pk-probes" add

Santiago Casas, 06.12.22

Late-time: Old SKA1, Euclid forecasts

• Old SKA1 forecasts contain only WL continuum and GCsp from HI galaxies
• Linear GCsp formalism and no IA params in WL

Santiago Casas, 06.12.22

Late-time: Old SKA1, Euclid forecasts

• However, we do roughly recover the same contour orientations and constraints with the new WL SKA1 forecasts.
• Deeply non-linear Pk recipe is the same, using an interpolation to recover GR at small scales.

Santiago Casas, 02.11.21

The Square Kilometer Array Obs. (SKAO)

• Next-generation Radioastronomy observatory
• Largest radiotelescope in the world: eventually 1km^2 area.
• 15 countries + partners
• Australia + South Africa installations
• ~2 billion Euros up to 2030.
• 5Tbps data rate and 250 Pflops needed for computation

Santiago Casas, 06.12.22

The Square Kilometer Array Obs. (SKAO)

• 15,000-20,000 square degrees in the sky
• Precursors: 10^7, SKA-phase1: 10^8, SKA-phase2: 10^9 galaxies
• SKA1-MID: 0 < z  < 3
• SKA1-Low: 3 < z < ~ 20
• Cosmology is just one small area, Exoplanets, Craddle of Life, Reionization, Cosmic Magnetism....

Santiago Casas, 06.12.22

Intensity Mapping Noise Terms

Number of dishes

Effective beam

$\beta_{SD} = \exp[-\frac{k_\perp r(z)^2 \theta_b (z)^2}{8 \ln 2}]$

$\alpha_{SD}  = \frac{1}{N_d}$

Jolicoeur et al (2020) arXiv:2009.06197