A new framework totesting modified
gravity using galaxysurveys
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Joaquin Armijo-Torres. IPMU postdoc colloquium

Hello!

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New postdoc started inOctober!
I’m at A049, please pass by.
Interested in cosmology andthe large-scale structure ofthe Universe.

Outline of my talk.
Cold dark matter universe with and without cosmologicalconstant: ΛCDM vs Modified gravity.
GR and MG simulations and mock galaxy catalogues.

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Probes for modified gravity: what does the LSS tell us beyond
2-point statistics? A new approach.

01

ΛCDM vs. Modified gravity

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The ΛCDM Universe

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𝚲 drives dark energy which accounts
for ~70% energy density budget. The
rest comes from matter (25% darkmatter, 5% baryons).
What about modified gravity?

Modified gravity
Ezquiaga & Zumalacarregui (2017)

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Modified gravity● Modified gravity can explain the cosmic acceleration without aSLIDESMANIA.COM

cosmological constant.
● Scalar field coupled to matter or extra term in the Einstein-Hilbert action
triggers extra fifth force that enhances gravity.
● Screening mechanism (Chameleon in f(R)) hides the fifth force in highdensity regions. This is needed to make observationally viable theory (solarsystem scale).
● The fifth force is screened in the early Universe (CMB is unchanged).
● Gravity needs to be probed at cosmic scale using the Large-scale
structure.

Modified gravity
Matter density at 𝒛~𝟎highly non-linear.

isIt shows galaxies but not
mass.

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We understand roughly how
galaxies populate the dark
matter but with some few
parameters.

𝑓(𝑅) gravity
Replace the cosmological constant by 𝒇(𝑹) in the action:

𝑺 = ' 𝒅𝟒 𝒙

𝟏−𝒈𝑹+𝒇 𝑹
𝟐𝟐𝜿+ ℒ𝒎

where a modified Poisson equation can be obtained (varying the Action):𝛁 𝟐 𝚽 = 𝟒𝝅𝑮𝒂𝟐 𝜹𝝆𝒎 −𝒅𝒇

𝟏 𝟐
𝛁 𝒇𝑹
𝟐SLIDESMANIA.COMThe new term 𝒇𝑹 ≡(the scalaron) is understand a new potential which mediates a new𝒅𝑹
effective “fifth force”. In the limit
lim 𝒇(𝑹) = 𝐜𝐨𝐧𝐬𝐭.
𝑹→%
When 𝒇𝑹 → 𝟎, 𝒇 𝑹 = 𝟐𝚲, which is the first condition for viable 𝒇(𝑹). The second limit is for𝒇𝑹 → 𝟎 when 𝝆𝒎 → ∞ (Chameleon mechanism).
The Hu & Sawicki model satisfy these conditions with 𝑓(𝑅) constant in the backgroundcosmology throughout cosmic history.

The Hu & Sawicki model𝑹 𝒏
𝒎𝟐𝟐𝑹 𝒏𝒄𝟐 𝟐 )𝟏𝒎

The function 𝒇(𝑹) takes the form:𝒇 𝑹 = −𝒎𝒄𝟏, (Hu and Sawicki 2007)

Satisfying the previous limit for high curvature we can expand and solve for the backgroundcosmology:

𝒇 𝑹

𝒄𝟏 𝟐
𝒄𝟏 𝟐 𝒎𝟐≈ 𝒎 + 𝟐𝒎𝒄𝟐
𝑹𝒄𝟐𝒏

𝛀𝒄𝒄𝟏, with 𝟏 = 𝚲,𝟎 and 𝟏𝟐 = −𝒄𝟐
𝛀𝒎,𝟎𝒏𝒄𝟐𝟑

𝛀𝟏 + 𝟒 𝚲,𝟎𝛀𝒎,𝟎𝒏)𝟏𝒇𝑹𝟎 .

We can constraint the model based in 2 free parameters. For n=1 we obtain 𝒇𝑹𝟎 < 𝟏𝟎.𝟒
(Schmidt et al. 2009). Current constraints using abundance of clusters and weak lensing give𝒇𝑹𝟎 < 𝟏𝟎.𝟓
New scalaronmodifies gravity

Newtonian potential 𝚽SLIDESMANIA.COM𝒇𝑹𝟎Deep 𝚽GR recovered
Screened regime

02

GR and MG simulations

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Modified gravity
simulations
Fully non-linear equations of motion forgravity 𝚽 and the scalaron 𝒇𝑹 (Poissonequation).
Solutions to these equations using theECOSMOG code (Li et al. 2012) and MGGADGEGT (Arnold et al. 2018).

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Simulations for GR and 𝒇 𝑹 models with
𝒇𝑹𝟎 < 𝟏𝟎.𝟓 , 𝟏𝟎.𝟔 (F5, F6).
Simulations start from the same initialconditions.

The MG lightcone project (Arnold et al. 2018)𝑧 = 0, 𝐿!"# = 768 Mpc ℎ$%Modified gravity simulations
Chameleon mechanism: Gravity is modified, however screened in high-density regions(e.g. inside a large mass halo)

GRF5GR − F5SLIDESMANIA.COM

Screened region

Testing gravity using the cosmic web● The distribution of matter at latetimes forms large-scale structures.

● These structures are shaped mainly

by gravity and the late cosmic
acceleration, creating different
environments where galaxies live.

● Nodes, filaments, walls and voids canbe found in the cosmic web.

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Testing gravity using the cosmic web

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We observe galaxies:● Galaxies trace the underlying matter
distribution assuming a non-linear
and stochastic bias relation 𝜹𝒈 = 𝒃𝜹𝒎 .
● They follow the formation of thesame structures as the cosmic web
formed by matter.
● Studying the connection between
dark matter (haloes) and galaxies
help us to understand thecosmological model.

Galaxy clustering: The 2-point correlation function
1+𝜉 =SLIDESMANIA.COM

𝑠=𝑟+𝐷𝐷𝑅𝑅

Estimator: relates the number of galaxy pairs DD incomparison to a random distribution of pairs RR
𝑤' 𝑟'
1 (= ; 𝑑𝑟) 𝜉(𝑟' , 𝑟) )𝑟'𝑟' $(

1 + 𝑧 𝑣||𝑒̂||𝐻(𝑧)3D pair distance including pairwise‘peculiar’ velocities

The projected-correlation function

SDSS-III BOSS

Large-scale galaxy surveys● Currently 1- and 2-point functions are measured
accurately in a large range of scales.
● When creating mock galaxy catalogues fromsimulations (GR and MG) we are forced to reproduce
both 𝒏(𝒛) and he projected 2-point clustering.

SLIDESMANIA.COM● We can rely in the fine tunning ofparameters of the halo-galaxy
models to generate suchobservational constraints. (Cautunet al. 2017, Armijo et al. 2018, Paillas
et al. 2019)

Can we replicate these results directly in thesimulations? That’s the neat part! Absolutely yes!
We need to create galaxy mock catalogues

The Halo occupation distribution(HOD) model:
Average number of galaxies
inside a dark matter halo as
function of its mass:

𝑁# =1log 𝑀$%& − 𝑀
1 + erf
2𝜎'() *!"#

𝑁+ = 𝑁#SLIDESMANIA.COM

Alam et al. (2016)

𝑀 − 𝑀, .
𝑀-(caveat) the HOD function (5 parameters) is degenerated with
the number density of galaxies 𝒏𝐠𝐚𝐥 and the clustering 𝝃.

03Probes for modified gravity

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Weak lensing in cosmic voids● Finding void regions in the cosmic web and comparing void finders: 7 void finders (4 3D-VF, 3 2D-VF).
● Using galaxies in voids to measure weak lensing statistics and compare it for different gravity
models.

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The SHED collaboration: Cautun et al. 1710.01730; Paillas et al. 1810.02864

𝑓(𝑅) voids: prediction using the spherical top-hat model:
Clampitt et al. 2013 calculate the Newtonian and fifth force for a top-hat empty region
Negative fifth force inside voids acting in opposite
Direction to Newtonian

𝜌(67Stronger for lower internal
density and for small voids

𝜌45

𝐹2
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Void stacked mass profiles

3D voids2D voids
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Testing MG with voids in the LSST era• Lensing can be used to detect 𝒇(𝑹) withLSST especially with 2D VF.
• DM profiles confirm emptier voids in MGmodels.
• These results are found for models evenwith the same 2-point clustering.
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Marked statistics
𝜌 2𝑚=𝜌̅“Marks" can be used in two-point statistics toupweight models given a density environmentalproperty.
• The marked correlation function can be used tobreak degeneracies in HOD modeling (White etal. 2008).
• The marked correlation function has been used
to distinguish between standard GR and MG(Armijo et al. 2018).

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White et al. (2008)

Testing modified gravity using the marked correlation function
Marks:
based in the local density marks defined in White et al. (2016), We estimate the local density using
the Voronoi tessellation method
Project in 2D-plane
Survey data: (RA, Dec, z)

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Testing modified gravity using the marked correlation function
Marks:
based in the local density marks defined in White et al. (2016), We estimate the local density usingthe Voronoi tessellation method
Project in 2D-plane
Survey data: (RA, Dec, z)

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Testing modified gravity using the marked correlation function
Marks:
based in the local density marks defined in White et al. (2016), We estimate the local density using
the Voronoi tessellation method
𝜌 2Project in 2D-plane𝑚=𝜌̅Survey data: (RA, Dec, z)

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Testing modified gravity using the marked correlation function•We measure ℳ(𝒓𝒑) for LOWZ andCMASS. We can constrain the HOD
model with the data but not ruleout modified gravity.

•Although CMASS agrees betterwith GR, some disagreement isfound at 𝟑 < 𝒓𝒑/𝐌𝐩𝐜 𝒉*𝟏 < 𝟓.

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Future LRG sample (DESI survey)
could improve this measurement.

Summary and Conclusions
In the search for the elusive camouflaged fifth force in modified gravity. Looking
into the predicted modified environments where 𝒇(𝑹) gravity acts.

Into the void: emptier voids in MG models might be a key to constraint thefifth force.
Marked statistic to test gravity on large-scales and understand the halo model. It
helps to break the degeneracy between MG and the HOD modelling. Future datasuch DESI-LRG will be relevant for this test.
SLIDESMANIA.COMThank you!

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