@santiagocasas                                                                                                        santicasas.xyz

Large Scale Structure of the Universe

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

The Standard $\Lambda$CDM model

• $\Lambda$CDM is still best fit to observations.
• Some questions remain:
• $\Lambda$ and CDM.
• Cosmological Constant Problem:

O(100) orders of magnitude wrong
(Zeldovich 1967, Weinberg 1989, Martin 2012).
 Composed of naturalness and coincidence
sub-problems, among others.

Quantum Gravity?

String Theory Swampland?

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

The Evolution of the Universe and the Dark Ages

Complementarity of probes

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

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:  $5000 \, \rm{deg}^2$

Galaxy Clustering Recipe

BAO

Clustering

RSD

Euclid Collaboration, IST:Forecasts, arXiv: 1910.09273

3x2pt recipe

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

Directly constrains MG function $\Sigma$ through Weyl potential

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:  $20000 \,\rm{deg}^2$

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.

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

Euclid Propaganda

#52weeks of Euclid in space

https://www.euclid-ec.org/euclid-anniversary/

instagram: @euclidconsortium

Exciting new science, but also too many new challenges!

Galaxy Clustering - IM Synergies

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

*No Euclid results today, political reason, paper in prep.

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.

SKAO  + optical

Proposals for the Science Book Chapter (and beyond)

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

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"

SKAO  + optical + CMB

Euclid Preparation: Sensitivity to Neutrino parameters, 2405.06047,  Archidiacono, Lesgourgues, SC, Pamuk, et al.

Can SKAO contribute to these constraints?

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