a Encuesta Fisioterapista
6.3.2. Objetivos Específicos
For completeness, we now list the main cosmological parameters in the concordance ΛCDM model, which govern the global properties of the Universe and the spectrum of the initial density perturbations, together with their current constraints from the latest Planck mission (Planck Collaboration et al. 2013b) (see Table 1.2).
Symbol Definition Constraint
ωb = Ωbh2 Baryon density 0.02214±0.00024
ωcdm = Ωch2 Cold Dark Matter density 0.1187±0.0017
Ωk Spatial curvature -0.0005+0−0..00650066
ΩΛ Dark Energy density 0.692±0.010
ln(1010A
s) Primordial pert. amplitude 3.091±0.025
σ8 RMS matter fluctuations 0.826±0.012
w Constant EoS of Dark Energy -1.13+0−0..2325
τ Reionization optical depth 0.092±0.013
ns Primordial scalar spectral index 0.9608±0.0054
P
mν Sum of the neutrino masses in eV <0.230
Neff Effective number of neutrino-like species 3.30+0−0..5451
H0 Hubble constant 67.80±0.77
t0 Age of the Universe (Gyr) 13.798±0.037
zre Redshift of half-reionization 11.3±1.1
100θ∗ 100 × angular size of sound horizon 1.04162±0.00056 Table 1.2: List of the main cosmological parameters of ΛCDM model, together the con- straints from Planck+WMAP+highL+BAO (Planck Collaboration et al. 2013b) for the following models: six parameter base ΛCDM model and derived parameters (blue, 68% limits) and extensions to the base ΛCDM model (green, 95% limits).
We conclude this Chapter by highlighting the constraining power on cosmolog- ical parameters of clusters of galaxies: in combination with other probes, such as SNIa, BAO and CMB, some parameters degeneracies can be broken and the errors tightened.
Ωm−σ8 constraints
Constraints on Ωm−σ8plane were investigated by Mantz et al. (2010) comparing and
combining three Rosita All Sky Surveys (RASS). Independent clusters studies of op- tical clusters (Rozo et al. 2010) (see left panel of Fig. 1.13), Sunyaev-Zeldovich clus- ters in combination with X-ray measurements (Benson et al. 2013) and X-ray clusters (Vikhlinin et al. 2009) showed consistent results. In the right panel of Fig. 1.13 we show Allen et al. (2008) constraints on the Ωm−ΩΛ plane, from the combination of
Chandra measurements of the X-ray gas mass fraction fgas of galaxy clusters, SNIa
data and CMB measurements.
Neutrinos
As any particle with a non-zero mass transits while cooling from a relativistic state to a non-relativistic state, the mass of neutrinos influences the background evolution and cosmic structure formation. The quantity typically used to describe neutrinos mass is Pmν, which is the species-summed mass. Constraints on this quantity come from clusters combined with CMB data (Burenin & Vikhlinin 2012). Few more considerations on this topic are included in Chapter 6.
Ω m Ω Λ 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 SNIa CMB Cluster fgas
Figure 1.13: Left panel: Joint 68.3% and 95.4% confidence regions in the Ωm −σ8
plane from optical galaxy cluster of the maxBCG catalogue combined with WMAP5 (Dunkley et al. 2009). Right panel: contours for Ωm−ΩΛ from the combination of X-
ray gas mass fraction (pink), CMB (blue) and SNIa (green). The orange contours show the constraint obtained from all three data sets combined. Credit: Rozo et al. (2010); Allen et al. (2008).
1.5 ΛCDM standard model 35 DE equation of state
Allen et al. (2011) analysed the constraints on the DE equation of state together with Ωm (see left panel of Fig. 1.14) or σ8. He combined the abundance and
growth of RASS clusters (Mantz et al. 2010),fgas measurements (Allen et al. 2008),
WMAP5 results (Dunkley et al. 2009), Supernovae Ia data (Kowalski et al. 2008) and BAO measurements (Percival et al. 2010, 2011). Constraints on DE equation of state from data were also performed by Rapetti et al. (2005) with X-ray clus- ters+SNIa+CMB, by Mantz et al. (2010); Benson et al. (2013) with X-ray clusters, while Vikhlinin et al. (2009) constrained w and ΩΛ.
Cosmic growth γ
Rapetti et al. (2013) tested the cosmic growth predicted by GR (γ = 0.55) with three independent measurements: galaxy clusters abundances and fgas from RASS
and Chandra, galaxy clustering from WiggleZ Dark Energy Survey, 6-degree Field Galaxy Survey and CMASS BOSS, and CMB from WMAP. The cosmic growth is modelled by the growth index γ defined in Eq. (1.36) and σ8. We show in the right
panel of Fig. 1.14 the constraints obtained on these parameters.
σ8 γ 0.4 0.6 0.8 1 1.2 1.4 1.6 −0.5 0 0.5 1 1.5 2 2.5 CMB cl gal cl+CMB+gal
Figure 1.14: Left panel: Joint 68.3% and 95.4% confidence regions forw−Ωm, from the
abundance and growth of RASS clusters (violet), X-ray gas mass fraction (pink), WMAP5 (blue), SNIa (green) and BAO (brown). Right panel: joint contours in the σ8−γ plane,
from galaxy growth (green), CMB (blue) and cluster growth (red). The gold contours show the combination of the data sets. Credit: Allen et al. (2011); Rapetti et al. (2013).
Chapter 2
Galaxy Clusters from theory side
In this Chapter the theoretical framework of galaxy clusters one-point (number counts) and two-points statistic (power spectrum) is introduced, in order to un- derstand why they are fundamental probes of the LSS of the Universe. For the study galaxy clusters, in fact, one needs to have first an estimate of their masses, which are not directly accessible. Here, we define the cluster masses and density profiles, with a particular emphasis to the weak lensing mass estimation, as this is the one we use in our analysis. Secondly, to understand how the cluster number counts change with the mass and with the cosmological model assumed, we revise the formulation and calibration of the cluster mass function and its sensitivity to cosmology. In addition to this, the spatial distribution of clusters can give additional information on cosmology. We thus introduce the concept of the model bias and a prescription for the clusters redshift space power spectrum. Finally, some definitions concerning the study of non-Gaussian initial conditions are provided, as clusters can be a good probe in this context.2.1
Cluster masses
As the mass of galaxy clusters is not directly measurable, we describe here how to get an estimate of it. Cosmologists usually define the cluster mass with respect to the critical or the mean density of the Universe and assume a halo density profile. We then focus on the gravitational weak lensing technique to reconstruct the mass distribution, as it is part of the data sets we need for our combined cosmological analysis.