In this paper, we propose a self-consistent test for a Hubble constant estimate using galaxy cluster and type Ia supernovae (SNe Ia) observations. The approach consists, in a first step, of obtaining the observational value of the galaxy cluster scaling-relation  $$Y_{SZE}D_{A}^{2}/C_{XSZ}Y_X = C $$  <math> <mrow> <msub> <mi>Y</mi> <mrow> <mi>SZE</mi> </mrow> </msub> <msubsup> <mi>D</mi> <mrow> <mi>A</mi> </mrow> <mn>2</mn> </msubsup> <mo>/</mo> <msub> <mi>C</mi> <mrow> <mi>XSZ</mi> </mrow> </msub> <msub> <mi>Y</mi> <mi>X</mi> </msub> <mo>=</mo> <mi>C</mi> </mrow> </math>   by combining the X-Ray and SZ observations of galaxy clusters at low redshifts ( $$z &lt; 0.1$$  <math> <mrow> <mi>z</mi> <mo>&lt;</mo> <mn>0.1</mn> </mrow> </math>  ) from the first Planck mission all-sky data set ( $$0.044 \le z \le 0.444$$  <math> <mrow> <mn>0.044</mn> <mo>≤</mo> <mi>z</mi> <mo>≤</mo> <mn>0.444</mn> </mrow> </math>  ), along with SNe Ia observations and making use of the cosmic distance duality relation validity. Then, by considering a flat  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model for  $$D_A$$  <math> <msub> <mi>D</mi> <mi>A</mi> </msub> </math>  , the constant C from the first step and the Planck prior on  $$\Omega _M$$  <math> <msub> <mi>Ω</mi> <mi>M</mi> </msub> </math>   parameter, we obtain  $$H_0$$  <math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math>   by using the galaxy cluster data with  $$z&gt;0.1$$  <math> <mrow> <mi>z</mi> <mo>&gt;</mo> <mn>0.1</mn> </mrow> </math>  . As a result, we obtain  $${ H_0=73.014^{+7.435}_{-6.688}}$$  <math> <mrow> <msub> <mi>H</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>73</mn> <mo>.</mo> <msubsup> <mn>014</mn> <mrow> <mo>-</mo> <mn>6.688</mn> </mrow> <mrow> <mo>+</mo> <mn>7.435</mn> </mrow> </msubsup> </mrow> </math>   km/s/Mpc, in full agreement with the latest results from HST + SH0ES team. We also compare our method with that one where the C parameter is obtained from hydrodynamical simulations of massive galaxy clusters.

India

Kamal Bora

Brazil

R. Holanda

The Hubble constant from galaxy cluster scaling-relation and SNe Ia observations: a consistency test

In this work, we discuss a new method to probe the redshift evolution of the gas depletion factor, i.e. the ratio by which the gas mass fraction of galaxy clusters is depleted with respect to the universal mean of baryon fraction. The dataset we use for this purpose consists of 40 gas mass fraction measurements measured at  $$r_{2500}$$  <math> <msub> <mi>r</mi> <mn>2500</mn> </msub> </math>   using Chandra X-ray observations, strong gravitational lensing sub-samples obtained from SLOAN Lens ACS + BOSS Emission-line Lens Survey (BELLS) + Strong Legacy Survey SL2S + SLACS. For our analysis, the validity of the cosmic distance duality relation is assumed. We find a mildly decreasing trend for the gas depletion factor as a function of redshift at about 2.7 $$\sigma $$  <math> <mi>σ</mi> </math>  .

Shantanu Desai

A test of the evolution of gas depletion factor in galaxy clusters using strong gravitational lensing systems

In this paper, we implement a test of the standard law for the dark matter density evolution as a function of redshift. For this purpose, only a flat universe and the validity of the FRW metric are assumed. A deformed dark matter density evolution law is considered, given by  $$\rho _c(z) \propto (1+z)^{3+\epsilon }$$  <math> <mrow> <msub> <mi>ρ</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>∝</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>)</mo> </mrow> <mrow> <mn>3</mn> <mo>+</mo> <mi>ϵ</mi> </mrow> </msup> </mrow> </math>  , and constraints on  $$\epsilon $$  <math> <mi>ϵ</mi> </math>   are obtained by combining the galaxy cluster gas mass fractions with cosmic chronometers measurements. We find that  $$\epsilon =0$$  <math> <mrow> <mi>ϵ</mi> <mo>=</mo> <mn>0</mn> </mrow> </math>   within 2 $$\sigma $$  <math> <mi>σ</mi> </math>   c.l., in full agreement with other recent analyses.

S. Pereira

A test of the standard dark matter density evolution law using galaxy clusters and cosmic chronometers

We propose a new method to explore a possible departure from the standard time evolution law for the dark matter density. We looked for a violation of this law by using a deformed evolution law, given by  $$\rho _c(z) \propto (1+z)^{3+\epsilon }$$  <math> <mrow> <msub> <mi>ρ</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>∝</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>)</mo> </mrow> <mrow> <mn>3</mn> <mo>+</mo> <mi>ϵ</mi> </mrow> </msup> </mrow> </math>  , and then constrain  $$\epsilon $$  <math> <mi>ϵ</mi> </math>  . The dataset used for this purpose consists of Strong Gravitational Lensing data obtained from SLOAN Lens ACS, BOSS Emission-line Lens Survey, Strong Legacy Survey SL2S, and SLACS; along with galaxy cluster X-ray gas mass fraction measurements obtained using the Chandra Telescope. Our analyses show that  $$\epsilon $$  <math> <mi>ϵ</mi> </math>   is consistent with zero within 1  $$\sigma $$  <math> <mi>σ</mi> </math>   c.l., but the current dataset cannot rule out with high confidence level interacting models of dark matter and dark energy.

Probing the dark matter density evolution law with large scale structures

The gas mass fraction in galaxy clusters has been widely used to determine cosmological parameters. This method assumes that the ratio of the cluster gas mass fraction to the cosmic baryon fraction ( $$\gamma (z)$$  <math> <mrow> <mi>γ</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </math>  ) is constant as a function of redshift. In this work, we look for a time evolution of  $$\gamma (z)$$  <math> <mrow> <mi>γ</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </math>   at  $$R_{500}$$  <math> <msub> <mi>R</mi> <mn>500</mn> </msub> </math>   by using both the SPT-SZ and Planck Early SZ (ESZ) cluster data, in a model-independent fashion without any explicit dependence on the underlying cosmology. For this calculation, we use a non-parametric functional form for the Hubble parameter obtained from Gaussian Process regression using cosmic chronometers. We parameterize  $$\gamma (z)$$  <math> <mrow> <mi>γ</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </math>   as:  $$\gamma (z)= \gamma _0(1+\gamma _1 z)$$  <math> <mrow> <mi>γ</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>γ</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>γ</mi> <mn>1</mn> </msub> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </math>   to constrain the redshift evolution. We find contradictory results between both the samples. For SPT-SZ,  $$\gamma (z)$$  <math> <mrow> <mi>γ</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </math>   decreases as a function of redshift (at more than 5 $$\sigma $$  <math> <mi>σ</mi> </math>  ), whereas a positive trend with redshift is found for Planck ESZ data (at more than 4 $$\sigma $$  <math> <mi>σ</mi> </math>  ). We however find that the  $$\gamma _1$$  <math> <msub> <mi>γ</mi> <mn>1</mn> </msub> </math>   values for a subset of SPT-SZ and Planck ESZ clusters between the same redshift interval agree to within  $$1\sigma $$  <math> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </math>  . When we allow for a dependence on the halo mass in the evolution of the gas depletion factor, the  $$4-5\sigma $$  <math> <mrow> <mn>4</mn> <mo>-</mo> <mn>5</mn> <mi>σ</mi> </mrow> </math>   discrepancy reduces to  $$2\sigma $$  <math> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </math>  .