A new probe of the large-scale structure of theUniverse
Joaquín Armijo, Carlton Baugh, Peder Norberg, Nelson PadillaHow to test gravity at large-scale?
Elephant simulations (Li et al. 2012)• The distribution of matter at late times forms afilamentary structure known as the cosmic web.
• At low-redshift, galaxies group in a large-scale networkof nodes, filaments, walls and voids.
• The large-scale structures are mainly shaped by gravity
and the late cosmic acceleration, creating different
environments where galaxies live.

𝑧=0500 Mpc ℎ−1

The galaxy two-point correlation function

White & Padmanabhan 2008

• Currently, galaxy redshift surveys offer accurate measurements ofthe distribution of galaxies at large-scales.
• Mock galaxy catalogues should reproduce both the number density
𝑛(𝑧) and the projected 2-point clustering.

• The match between these metrics between the observation and thesimulations permits the study of gravity on large-scale structureswith detail.
• The tuning of HOD parameters can be used to generate galaxy
catalogues that include such observational constraints (Cautun etal. 2017, Paillas et al. 2018).

Cautun et al. 2017

The marked correlation function
Mark defined by local density•

When the two-point correlation function does not
exhaust all the information of the data, marked statistic
is a viable option.

•“Marks" can be used in two-point statistics to upweightmodels given a density environmental property.

• The mark choice to upweight MG models can be and the
local density of galaxies the mass of the dark matter
halos (Armijo et al. 2018).
• The marked correlation function has been used to
distinguish between standard GR and MG (HernandezAguayo et al. 2018).

White & Padmanabhan 2008

The marked correlation function
Mark defined by halo mass:•

When the two-point correlation function does not
exhaust all the information of the data, marked statistic
is a viable option.

•“Marks" can be used in two-point statistics to upweightmodels given a density environmental property.

• The mark choice to upweight MG models can be and thelocal density of galaxies the mass of the dark matter
halos (Armijo et al. 2018).
• The marked correlation function has been used todistinguish between standard GR and MG (HernandezAguayo et al. 2018).
Armijo et al. 2018

Galaxy & cluster samples
SDSS-III BOSS LOWZ

Survey footprint DR12
NGC:5836 deg 2
SGC: 2501 deg 2

Luminous red galaxies (LRGs)𝑟cmod < 13.5 + 𝑐‖ /0.3𝑐⊥ < 0.2
LOWZ 𝑛𝑔 ~ 3 × 10−4 Mpc −3 ℎ3

16 < 𝑟cmod < 19.6
𝑟psf − 𝑟cmod > 0.3
Reid et al. 2015

This number density is close to optimal forlarge-scale cosmological studies (e.g., Kaiser1986)

Galaxy & cluster samples
SDSS-IV SPIDERS: The SPectroscopic IDentification of EROSITA Sources

CODEX subsample~4600 Clusters

𝑑𝑛/𝑑𝑧

Area normalized to 1

Lindholm et al. 2020

Clerc et al. 2016

• The final CODEX sample is obtained by using original X-ray
catalogue and the red-sequence finder redMaPPer. The
optical/X-ray association provides confident measurements
for the redshift 𝑧 and mass 𝑀200𝑐 of each cluster.

Halo occupation distribution

HOD mock catalogues

𝑁𝑐𝑒𝑛 =Elephant simulations (Li et al. 2012)
HOD galaxies

1log 𝑀𝑚𝑖𝑛 − 𝑀
1 + erf
2𝜎log 𝑀𝑚𝑖𝑛

𝑁𝑠𝑎𝑡 = 𝑁𝑐𝑒𝑛

𝑀 − 𝑀0𝑀1𝑁 = 𝑁𝑐𝑒𝑛 + 𝑁𝑠𝑎𝑡

• HOD parameters are tuned to obtain the same numberdensity 𝑛𝑔 = 2.9 × 10−4 ℎ3 Mpc −3 and 𝑤𝑝 than the LOWZ
sample.
• The best parameters are obtained using MCMC fitting.

𝛼New probes for large-scale structure

0.20 < 𝑧 < 0.25
CODEX clusters

Dec (deg )What we propose?
Marked statistic using the projected correlation function.

ℳ𝑝𝑟𝑝

1 + 𝑊(𝑟𝑝 )=1 + 𝑤𝑝 (𝑟𝑝 )RA (deg )Best mark choices fromArmijo et al. 2018:• Voronoi tessellation densityestimation on 2D.
• 𝑀200𝑐 to mark high mass
haloes (clusters).

log 𝑉/𝑉തNew probes for large-scale structure
What we propose?

Cross-correlation Cluster-galaxy

Marked statistic using the projected correlation function.

ℳ𝑝𝑟𝑝

1 + 𝑊(𝑟𝑝 )=1 + 𝑤𝑝 (𝑟𝑝 )Best mark choices from
Armijo et al. 2018:• Voronoi tessellation density
estimation on 2D.
• 𝑀200𝑐 to mark high mass
haloes (clusters).

Summary and future work
• Use marked statistic to test gravity on large-scales and constrain the late accelerated expansion of theUniverse.
• Large extragalactic surveys have the key information to perform such tests. The sample of luminous redgalaxies from SDSS and the CODEX galaxy clusters that trace the distribution of matter in the Universe.
• Environmental properties like the local density and halo masses are good choices to mark galaxies andclusters. Test density dependent features like the screening mechanism in MG theories.
• HOD mock catalogues to model the effect of systematics errors in the sample to see how this affects theestimation of the marked correlation function.

Thank you for your attention!

Galaxy & cluster samples• Optical Richness is estimated using theredMaPPer cluster-finder.

• The tracer members correspond to red
sequence galaxies with full spectroscopic
information from SDSS.
• Richness-Mass relation are calibrated using
dynamical information (Jeans equation).
• This offers a catalogue with reliablemeasurements of halo mass to mark clusters.
𝑧 0.8
exp 𝜆 > 22(Richness cut)
0.15
𝜆 ≡ ln(SDSS Richness)
Rykoff et al. 2014

Richness-Mass relation (Capasso et al. 2019):
𝜆 = 𝐴𝜆𝑀200𝑐𝑀piv

B𝜆1+z
1 + z𝑝𝑖𝑣𝛾𝜆Halo weights

Halo occupation distribution

𝑁𝑐𝑒𝑛 =1log 𝑀𝑚𝑖𝑛 − 𝑀
1 + erf
2𝜎log 𝑀𝑚𝑖𝑛

𝑁𝑠𝑎𝑡 = 𝑁𝑐𝑒𝑛

𝑀 − 𝑀0𝑀1𝛼

𝑁 = 𝑁𝑐𝑒𝑛 + 𝑁𝑠𝑎𝑡

𝑀𝑚𝑖𝑛

𝑀0𝑀1𝛼𝑀𝑚𝑖𝑛

𝑀0𝑀1𝜎