Constraining modifications of gravity with synergies between radio and optical surveys

 

 

 

Santiago Casas,

Isabella Carucci, Valeria Pettorino,

Stefano Camera, Matteo Martinelli

 

arXiv:2210.05705 accepted in Phys. Dark Univ.

Cosmic Microwave Background

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

Santiago Casas, 06.12.22

The Standard \(\Lambda\)CDM model

  • \(\Lambda\)CDM is still best fit to observations.
  • Predictive model with few free parameters.
  • Lensing
  • CMB
  • Clustering
  • Supernovae
  • Clusters
G_{\mu \nu} + \Lambda g_{\mu \nu} = 8\pi G T_{\mu \nu}

Concordance Cosmology:

Santiago Casas, 06.12.22

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?

G_{\mu \nu} + \Lambda g_{\mu \nu} = 8\pi G T_{\mu \nu}

Santiago Casas, 06.12.22

Tensions in the \(\Lambda\)CDM model

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

Planck, Clusters and Lensing tension on clustering amplitude \(\sigma_8\)

KiDS 1000 Cosmology, arXiv:2010:16416

L.Verde, et al 2019. arXiv:1907.10625

Santiago Casas, 06.12.22

Alternatives to \(\Lambda\)CDM

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

Santiago Casas, 06.12.22

Parametrized modified gravity

\rm{d}s^2 = -(1+2\Psi) \rm{d}t^2 + a^2(1-2\Phi) \rm{d}x^2

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 (\(a\))

\Sigma(a,k) = \frac{1}{2}\mu(a,k)(1+\eta(a,k))

Only two independent functions

Santiago Casas, 06.12.22

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

Planck 2015 results XIV, arXiv:1502.01590

Planck 2018 results VI, arXiv:1807.06209

Casas et al (2017), arXiv:1703.01271

Forecasts for Stage-IV surveys in:

Santiago Casas, 06.12.22

Late-time: Old SKA1, Euclid forecasts

Casas et al (2017), arXiv:1703.01271

  • 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

Casas et al (2017), arXiv:1703.01271

  • 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, 06.12.22

The Evolution of the Universe and the Dark Ages

Santiago Casas, 06.12.22

Complementarity of probes

21cm Intensity Mapping

Image credit: Sunayana Bhargava

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)

  • SKA Phase 1: SKA1-Low and SKA1-Mid
  • SKA1-Low: 130,000 dipole antennas, 65km max. baseline
  • SKA1-Mid: ~200 dishes of ~15m diameter, max. baseline  150km
  • Precursors: ASKAP, MEERKAT, HERA...

Google maps

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

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

Santiago Casas, 06.12.22

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

Santiago Casas, 06.12.22

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:  \(5000 \, \rm{deg}^2\)

Santiago Casas, 06.12.22

Galaxy Clustering Recipe

BAO

Clustering

RSD

Spec-z

Euclid Collaboration, IST:Forecasts, arXiv: 1910.09273

Santiago Casas, 06.12.22

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

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

Continuum galaxy survey

Santiago Casas, 06.12.22

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

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

Continuum galaxy survey

Santiago Casas, 06.12.22

Weak Lensing

  •  Influence of matter-energy: galaxies align and get distorted
  •  Correlation function
    of cosmic shear: information about matter content
    and expansion.

Directly constrains MG function \(\Sigma\) through Weyl potential

-k^2(\Phi(a,k)+\Psi(a,k)) \equiv 8\pi G a^2 \Sigma(a,k)\rho(a)\delta(a,k)

Santiago Casas, 06.12.22

3x2pt analysis (continuum, photometric)

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

Santiago Casas, 06.12.22

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:  \(20000 \,\rm{deg}^2\)

Santiago Casas, 06.12.22

Intensity Mapping

  • IM probes the underlying matter power spectrum.
  • There is a density bias given by the HI mass contained in dark matter halos.
  • 21cm brightness temperature depends on cosmological background evolution and 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

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

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

Santiago Casas, 06.12.22

Intensity Mapping x GCsp

  • The cross correlation combines one term of brightness temperature with one Kaiser term for each "redshift sample".
  • Same underlying matter power spectrum for both probes.
  • A combined redshift 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

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

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

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

Santiago Casas, 06.12.22

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.

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

Santiago Casas, 06.12.22

Stage-IV surveys

Euclid space satellite, now waiting in Cannes

Santiago Casas, 06.12.22

DESI telescope

  • 14 000 square degrees in the sky
  • 30 million accurate galaxy spectra
  • Redshifts: 0 < z < 2
  • Quasars up to z~3.5
  • 5 years of observation

Specialized in Galaxy Clustering

Santiago Casas, 06.12.22

Vera Rubin Observatory

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

Specialized in Photometric Angular Probes: Lensing and Clustering

Santiago Casas, 06.12.22

Galaxy Clustering - IM Synergies

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

Santiago Casas, 06.12.22

SKAO  Results

 

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

 

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

Santiago Casas, 06.12.22

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.

Santiago Casas, 06.12.22

SKAO  Results

  • Combining all SKAO probes (optimistic), 2-3% errors on \(\mu\) and \(\Sigma\).
  • Minor improvement from Planck, mainly through ISW and CMB lensing.

Santiago Casas, 06.12.22

SKAO  x DESI cross-correlation

 

  • GCxIM probes do not improve our MG parameters, but improve \(h\) and \(\sigma_8\)

DESI_E : high-z Emission Line Galaxies

DESI_B: low-z Bright Galaxy Sample

SKAO GCsp: low-z HI Galaxies

Santiago Casas, 06.12.22

SKAO  x DESI cross-correlation

 

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

Santiago Casas, 06.12.22

SKAO  + optical

 

  • SKAO + one Stage-IV survey is as competitive as two Stage-IV surveys

Santiago Casas, 06.12.22

SKAO  + optical

 

  • SKAO + one Stage-IV survey is as competitive as two Stage-IV surveys

Santiago Casas, 06.12.22

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.
  • This will place constraints on deviations of standard gravity at yet unexplored redshifts.
  • 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.

Backup slide

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

 

 

PRELIMINARY

Backup slide

Testing at higher H0 value

Backup slide

Backup slide

Backup slide

Backup slide