Probing f(R) gravity with PLANCK data on cluster pressure profiles

ΛCDM Extended Theories of Gravity SZ effect Data and Methodology Results Conclusions and future perspectives

Probing f (R)-gravity with PLANCK data oncluster pressure profiles

Ivan de Martino

Universidad de Salamanca

ERE 2014University of Valencia, 1st-5th of September 2014

I. de Martino, et al., MNRAS, 2014, 442, 921.

Ivan de Martino Universidad de SalamancaProbing f (R)-gravity with PLANCK data on cluster pressure profiles 1 / 25


Overview

1 Standard Cosmological Model

2 Extended Theories of Gravity

3 Sunyaev-Zeldovich effect

4 Data and Methodology

5 Results

6 Conclusions and future perspectives



Observational Datasets Dark Energy Dark Matter Shortcomings

Standard Cosmological Model

During the last four decades, the increased number and precision of as-tronomical observations allowed cosmologists to put forward a standardmodel for the evolution of the Universe, known as concordance model. Itis based on

1 General Relativity: the Friedmann Equations describe the evolutionof the Universe as a whole

H2 =8πG3c2 ρ+

Λc23 −

Kc2a2 ,

3H2 + 2H = −4πG3c2 (ρ+ 3p) +

Λc23 .




2 Hubble’s lawvr = H0d .

3 Cosmic Microwave Background

Planck 2013 results. XV: CMB power spectra and likelihood. A&A, accepted. ArXiv:1303.5075

4 Primordial NucleosynthesisIvan de Martino Universidad de SalamancaProbing f (R)-gravity with PLANCK data on cluster pressure profiles 4 / 25



Observational Datasets

The concordance model is favored by different observational datasets.

Amanullah et al., (2010), ApJ, 716:712.




Observational Datasets

In April 2013, the first data release of Planck Satellite become publiclyavailable. The results have favored the concordance model.

Dark Energy

Dark Matter

Ord inary Matter

Planck 2013 results. XVI: Cosmological parameters. A&A accepted. ArXiv:1303.5076.




Dark Energy

Measurements based on SN Type Ia, have indicated that the Universehas entered a period of accelerated expansion driven by a cosmologicalconstant.

Union 2.1: Suzuki et al. (2012), ApJ, 746:85.Ivan de Martino Universidad de SalamancaProbing f (R)-gravity with PLANCK data on cluster pressure profiles 7 / 25



Dark Matter

The missing matter problem comes out comparing dynamical estimates ofmasses of astrophysical systems like stellar cluster, galaxies, and cluster ofgalaxies with observations.




Shortcomings

Due to its simplicity and capacity to explain large datasets, the ΛCDMmodel is considered the standard model in Cosmology.

X Solar System tests that are experimentally well measured.X Galactic dynamics.X Emergence of Large Scale Structure in the Universe, the

cosmological expansion rate, the density parameters, age,etc.

× Quantum theory of gravity.× Initial conditions (fine tuning).




Shortcomings

× What is Dark Matter?MAssive Compact Halo Objects (MACHOs);Really Massive Baryon Objects (RAMBOs);Sub-luminous compact objects (or clusters of objects)like BHs and NSs;Weakly Interacting Massive Particles (WIMPs);Axions;...

× What is Dark Energy?Cosmological Constant, Λ;Quintessence;String Theory;Brane Cosmology;Holographic Principle;...



Yukawa-like potential

Extended Theories of Gravity

Extended Theories of Gravity (ETGs) are generalizations of GR obtained byincluding in the Lagrangian higher-order curvature invariants (such as R2,RµνRµν , RµναβRµναβ , R �R, or R �kR) and minimally or non-minimallycoupled terms between scalar fields and geometry (such as φ2R).

S =

∫d4x√−g[F (R,�R,�2R, ..�kR, φ)− ε

2gµνφ;µφ;ν + 2κL(m)

],

The approach described above is the most generic. We shall concentratein f (R)-theories

Sf (R) =

∫d4x√−g f (R).




Yukawa-like correction to Newtonian gravitational potential

Field Equations in f (R)-gravity:

f ′(R)Rµν − 12 f (R)gµν − f ′(R);µν + gµν�f ′(R) = X Tµν

f (R)-Lagrangian:

f (R) =+∞∑n=0

f n(R0)

n!(R − R0)n = f0 + f ′0R + f ′′0 R2 + f ′′′0 R3 + ... ,

To evaluate the Post-Newtonian limit, we need to take into account cor-rections at the fourth order in the perturbation expansion of the metric.




Yukawa-like correction to Newtonian gravitational potential

Spherical simmetry

g00 (ct, r) = 1 + g (2)00 (ct, r) + g (4)

00 (ct, r) , (1)

g11 (ct, r) = −1 + g (2)11 (ct, r) , (2)

g22 (ct, r) = −r2, (3)g33 (ct, r) = −r2 sin θ2, (4)

Modified Newtonian potential

Φ(r) = − GM(r)

(1 + δ)r(1 + δe− r

L),

where

δ = 1− f ′0 L .=

(−6f ′′0

f ′0

)1/2

.

We are able to test dynamics and formation of the astrophysical structures.Ivan de Martino Universidad de SalamancaProbing f (R)-gravity with PLANCK data on cluster pressure profiles 13 / 25


Cluster pressure profiles Cluster pressure profiles in f (R)-gravity

Sunyaev-Zeldovich effect

Clusters of galaxies are the largest virialized objects in the Universe, andmost of baryons in clusters are not in, galaxies but are in the diffuse Intra-Cluster Medium. The incoming CMB photons are inverse Compton scat-tered by the free electrons and gain energy when crossing the potentialwells of clusters. As a result of the interaction, the CMB blackbody spec-trum is distorted and clusters induce secondary temperature anisotropieson the CMB.




Sunyaev-Zeldovich effect

T (n)− T0T0

=

∫ [g(ν)

kBTemec2

+~vcl nc

]dτ

The thermal Sunyaev-Zeldovich (tSZ) effect is the only SZ anisotropy thathas been measured for individual clusters.It is customary to introduce the Comptonization parameter defined as

yc =kBσTmec2

∫ne(r)Te(r)dl =

σTmec2

∫Pe(r)dl

In the non-relativistic limit g(ν) = hν(z)kT (z) coth

(hν(z)

2kBT (z)

)− 4.




Cluster pressure profiles

Several cluster pressure profile have appeared in literature:Universal profile

p(x) ≡ P0

(c500x)γ [1 + (c500x)α](β−γ)/α

Komatsu-Seljak profile

ygas(x) ≡{1− B

[1− ln(1 + x)

x

]}1/(γ−1)

β profilene(r) = ne0

(1 + x2

)−3β/2where x = r

r500 .




Cluster pressure profiles in f (R)-gravity

The dynamical effect of DM in galaxy clusters can be replaced by a Yukawa-like correction to the Newtonian potential in analytical f (R) theories.

Φ(r) = − GM(r)(1+δ)r

(1 + δe− r

L)

dP(r)dr = −ρ(r)

dΦgrav (r)dr

dM(r)dr = 4πρ(r)

P(r) ∝ ργ(r)



X-ray Cluster Catalog Planck data SMICA and NILC

Data and Methodology

We will use Planck data to compare the pressure profiles of 579 X-rayselected galaxy clusters obtained from the Planck foreground clean mapSMICA.

We construct a total of 30,000 models for f (R)-pressure profiles varying

δ = [−1, 1] γ = [1, 5/3]

and two different parameterizations for L

(A) L = ζr500 with ζ = [0.1, 10]

(B) L = [0.1, 50]Mpc




X-ray Cluster Catalog

Our cluster sample contains 579 clusters outside Planck minimal mask.ROSAT-ESO Flux Limited X-ray catalog (REFLEX)extended Brightest Cluster Sample (eBCS)Clusters in the Zone of Avoidance (CIZA)

All three surveys are X-ray selected and X-ray flux limited. The position,flux, X-ray luminosity, angular extent, and redshifts are measured The X-ray temperature was derived from the LX − TX relation




Planck data

First Data Release, April 2013




SMICA and NILC maps




SMICA and NILC maps

Each profile it is convolved with the antenna beam (5 arcminutes) andnormalized to 1. The error bar was computed out of the cluster region,carrying out 1,000 random simulation.



Results



Results

Model (A): δ < [−0.46,−0.10], ζ < [2.5, 3.7] and γ > [1.35, 1.12]

Model (B): δ < [−0.43,−0.08], L < [12, 19] Mpc and γ > [1.45, 1.2]



Conclusions and future perspectives

X The f(R)-theories are a viable way to describe the dynamical measure-ments without introduce any DM component.

⇒ We needs CMB clean maps, or filtered maps to analyze the profilecluster by cluster.

⇒ We need to use frequency information to improve our constraint andto fit the amplitude.

⇒ We need to reduce the error bar of the tSZ effect.


Probing f(R) gravity with PLANCK data on cluster pressure profiles

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