Constraining modifications of gravity using Galaxy Clustering, Weak Lensing and Intensity Mapping with SKA-1

Santiago Casas,

Isabella Carucci, Valeria Pettorino,

Stefano Camera, Matteo Martinelli

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, 15.04.21

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, 15.04.21

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, 15.04.21

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

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Alternatives to \(\Lambda\)CDM

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

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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

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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:

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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, 15.04.21

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, 15.04.21

SKA Probes

Image credit: Isabella Carucci

Continuum emission: Allows detection of position and shapes of galaxies.
Line emission of neutral Hydrogen (HI, 21cm):

Using redshifted HI line -> spectroscopic galaxy survey

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

Santiago Casas, 15.04.21

SKA Probes

Image credit: Isabella Carucci

Continuum emission: Allows detection of position and shapes of galaxies.
Line emission of neutral Hydrogen (HI, 21cm):

Using redshifted HI line -> spectroscopic galaxy survey

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

Santiago Casas, 15.04.21

SKA1 Surveys

HI galaxies spectroscopic survey

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, 15.04.21

Galaxy Clustering Recipe

BAO

Clustering

RSD

Spec-z

Euclid Collaboration, IST:Forecasts, arXiv: 1910.09273

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SKA1 Surveys

GCsp: HI galaxy spec. redshift survey: \(0.0 < z < 0.5\)
probes 3D matter power spectrum in Fourier space
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, 15.04.21

SKA1 Surveys

GCsp: HI galaxy spec. redshift survey: \(0.0 < z < 0.5\)
probes 3D matter power spectrum in Fourier space
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:
\( n \approx 3.2 \rm{arcmin}^{-2}\)

*kindly provided by Stefano Camera

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

Continuum galaxy survey

Santiago Casas, 15.04.21

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, 15.04.21

SKA 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, 15.04.21

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

\(P^{\rm IM}(z,k) = \bar{T}_{IM}(z)^2[b_{\rm IM}(z)^2+f(z)\mu^2]^2P_{\delta\delta,zs}(z,k) \)

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

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

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

Jolicoeur et al (2020) arXiv:2009.06197

Carucci et al (2020) arXiv:2006.05996

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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

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

\(P^{{\rm IM} \times \rm{GC}}(z,k) = \bar{T}_{\rm IM}(z) [b_{\rm IM}(z)^2+f(z)\mu^2] \times [b_{\rm g}(z)^2+f(z)\mu^2] P_{\delta\delta,zs}(z,k) \times \exp[-\frac{1}{2} k^2 \mu^2 (\sigma_{\rm IM}(z)^2+\sigma_{\rm sp}(z)^2)] r_{\rm IM,opt} \)

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Intensity Mapping

\(P_{gg}\) underlying galaxy power spectrum.
\(P_{HI}/T_{HI}^2\) IM power spectrum.
\(P_{noise} \) for single dish mode in SKA1-MID Band 1 survey.
Angle-dependent beam effect is in the signal.

Santiago Casas, 15.04.21

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, 15.04.21

Euclid space satellite

Santiago Casas, 15.04.21

Euclid space satellite

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

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Galaxy Clustering - IM Synergies

SKA1 and Euclid probe complementary redshifts in spectroscopic GC.
IM and GC cross-correlation offers gain in information and reduction of systematics

Santiago Casas, 15.04.21

SKA1 Results

Euclid GCsp
+
SKA1 GCsp (HI galaxies)

Improved constraints on \(\mu\) since it covers a larger redshift range at small \(z\) where \(\mu\) becomes important.

PRELIMINARY

Santiago Casas, 15.04.21

SKA1 Results

SKA1:

GCsp (HI galaxies)

WL (Continuum)

WL is more constraining on \(\Sigma\) as expected.

PRELIMINARY

Santiago Casas, 15.04.21

SKA1 Results

SKA1:

GCsp (HI galaxies)

(21cm HI)

IM is more constraining in almost all parameters. Except \(h\), where GCsp is better.

PRELIMINARY

Santiago Casas, 15.04.21

SKA1 Results

SKA1:

GCsp (HI galaxies)+IM (HI 21cm)

vs.

GC+WL+XC (Continuum)

The combination of WL and angular galaxy correlations, (3x2pt) is very good at constraining \(\Sigma\) as expected, but not so good in \(h\), which is constrained by the Pk probes.

PRELIMINARY

Santiago Casas, 15.04.21

SKA1 Results

SKA1:

GCsp (HI galaxies) +

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

HI galaxies at small z, IM at higher z and angular resolution of continuum galaxies provide good complementary constraints.

PRELIMINARY

Santiago Casas, 15.04.21

SKA1 Results

SKA1:

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

Combined constraints on \(\mu\)-\(\Sigma\) ~ 3%

PRELIMINARY

Santiago Casas, 15.04.21

SKA1 Results

SKA1:

GC+WL+XC (Continuum) +
IM (HI 21cm) + GCsp(HI)
and Planck'15

Planck provides information on \(\Omega_{b}, \, \Omega_{m}\) but also on the MG parameter \(\Sigma\).
In the \(\mu\)-\(\Sigma\) plane it complements very well with the IM constraints

PRELIMINARY

Santiago Casas, 15.04.21

SKA1 Results

SKA1:

GC+WL+XC (Continuum) +
IM (HI 21cm) + GCsp(HI)
+ Planck'15

Planck provides information on \(\Omega_{b}, \, \Omega_{m}\) but also on the MG parameter \(\Sigma\).
In the \(\mu\)-\(\Sigma\) plane it complements very well with the IM constraints.
Combined constraints on \(\Sigma\) ~ 1.5%

PRELIMINARY

Santiago Casas, 15.04.21

SKA1 vs Euclid and Planck

SKA1-All+Planck:

\(\sigma\)[\(\mu\)-\(\Sigma\)] ~ [3, 1.5]%

Euclid-All+Planck:

\(\sigma\)[\(\mu\)-\(\Sigma\)] ~ [1.8, 0.5]%

*Optimistic scenario

PRELIMINARY

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Bonus: w0waCDM

PRELIMINARY

SKA1:

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

Some updated constraints on LCDM and w0waCDM, since all combinations cannot be found on the redbook.
Preliminary numbers:
\(\sigma(w_0)\approx 0.05,\sigma(w_a) \approx 0.1 \)

Santiago Casas, 15.04.21

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.
SKA1 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, including cross-correlations are promising (work in progress).
Using the good z-resolution of SKA1 HI could place tight constraints on redshift-binned parametrizations.

Santiago Casas, 15.04.21

SKA1 vs Euclid

SKA1:

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

Euclid

(Gcsp+GCph+WL+XCph)

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

SKA FG Synergies

By Santiago Casas

SKA FG Synergies

Constraining modified gravity with SKA1 probes and its synergies with optical surveys

Santiago Casas

Cosmologist, Physicist, Data Scientist.

sant87casas

Constraining modifications of gravity using Galaxy Clustering, Weak Lensing and Intensity Mapping with SKA-1

The Standard \(\Lambda\)CDM model

The Standard \(\Lambda\)CDM model

Tensions in the \(\Lambda\)CDM model

Alternatives to \(\Lambda\)CDM

Parametrized modified gravity

Late-time parametrization: Planck constraints

Late-time: Old SKA1, Euclid forecasts

Late-time: Old SKA1, Euclid forecasts

SKA Probes

SKA Probes

SKA1 Surveys

Galaxy Clustering Recipe

SKA1 Surveys

SKA1 Surveys

Weak Lensing

SKA Surveys

Intensity Mapping

Intensity Mapping x GCsp

Intensity Mapping

Intensity Mapping Noise Terms

Euclid space satellite

Euclid space satellite

Galaxy Clustering - IM Synergies

SKA1 Results

SKA1 Results

SKA1 Results

SKA1 Results

SKA1 Results

SKA1 Results

SKA1 Results

SKA1 Results

SKA1 vs Euclid and Planck

Bonus: w0waCDM

Conclusions

SKA1 vs Euclid

SKA FG Synergies

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