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Vinicius Consolini Busti
Publication date
2011
fields
Physics
and research's language is
English
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In this Comment we discuss a recent analysis by Yu et al. [RAA 11, 125 (2011)] about constraints on the smoothness $alpha$ parameter and dark energy models using observational $H(z)$ data. It is argued here that their procedure is conceptually inconsistent with the basic assumptions underlying the adopted Dyer-Roeder approach. In order to properly quantify the influence of the $H(z)$ data on the smoothness $alpha$ parameter, a $chi^2$-test involving a sample of SNe Ia and $H(z)$ data in the context of a flat $Lambda$CDM model is reanalyzed. This result is confronted with an earlier approach discussed by Santos et al. (2008) without $H(z)$ data. In the ($Omega_m, alpha$) plane, it is found that such parameters are now restricted on the intervals $0.66 leq alpha leq 1.0$ and $0.27 leq Omega_m leq 0.37$ within 95.4% confidence level (2$sigma$), and, therefore, fully compatible with the homogeneous case. The basic conclusion is that a joint analysis involving $H(z)$ data can indirectly improve our knowledge about the influence of the inhomogeneities. However, this happens only because the $H(z)$ data provide tighter constraints on the matter density parameter $Omega_m$.
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The presence of inhomogeneities modifies the cosmic distances through the gravitational lensing effect, and, indirectly, must affect the main cosmological tests. Assuming that the dark energy is a smooth component, the simplest way to account for the influence of clustering is to suppose that the average evolution of the expanding Universe is governed by the total matter-energy density whereas the focusing of light is only affected by a fraction of the total matter density quantified by the $alpha$ Dyer-Roeder parameter. By using two different samples of SNe type Ia data, the $Omega_m$ and $alpha$ parameters are constrained by applying the Zeldovich-Kantowski-Dyer-Roeder (ZKDR) luminosity distance redshift relation for a flat ($Lambda$CDM) model. A $chi^{2}$-analysis using the 115 SNe Ia data of Astier {it et al.} sample (2006) constrains the density parameter to be $Omega_m=0.26_{-0.07}^{+0.17}$($2sigma$) while the $alpha$ parameter is weakly limited (all the values $in [0,1]$ are allowed even at 1$sigma$). However, a similar analysis based the 182 SNe Ia data of Riess {it et al.} (2007) constrains the pair of parameters to be $Omega_m= 0.33^{+0.09}_{-0.07}$ and $alphageq 0.42$ ($2sigma$). Basically, this occurs because the Riess {it et al.} sample extends to appreciably higher redshifts. As a general result, even considering the existence of inhomogeneities as described by the smoothness $alpha$ parameter, the Einstein-de Sitter model is ruled out by the two samples with a high degree of statistical confidence ($11.5sigma$ and $9.9sigma$, respectively). The inhomogeneous Hubble-Sandage diagram discussed here highlight the necessity of the dark energy, and a transition deceleration/accelerating phase at $zsim 0.5$ is also required.
The existence of inhomogeneities in the observed Universe modifies the distance-redshift relations thereby affecting the results of cosmological tests in comparison to the ones derived assuming spatially uniform models. By modeling the inhomogeneities through a Zeldovich-Kantowski-Dyer-Roeder (ZKDR) approach which is phenomenologically characterized by a smoothness parameter $alpha$, we rediscuss the constraints on the cosmic parameters based on Supernovae type Ia and Gamma-Ray Bursts (GRBs) data. The present analysis is restricted to a flat $Lambda$CDM model with the reasonable assumption that $Lambda$ does not clump. A $chi^{2}$-analysis using 557 SNe Ia data from the Union2 Compilation Data (Amanullah {it et al.} 2010) constrains the pair of parameters ($Omega_m, alpha$) to $Omega_m=0.27_{-0.03}^{+0.08}$($2sigma$) and $alpha geq 0.25$. A similar analysis based only on 59 Hymnium GRBs (Wei 2010) constrains the matter density parameter to be $Omega_m= 0.35^{+0.62}_{-0.24}$ ($2sigma$) while all values for the smoothness parameter are allowed. By performing a joint analysis, it is found that $Omega_m = 0.27^{+0.06}_{-0.03}$ and $alpha geq 0.52$. As a general result, although considering that current GRB data alone cannot constrain the smoothness $alpha$ parameter our analysis provides an interesting cosmological probe for dark energy even in the presence of inhomogeneities.
We study the performance of the latest $H(z)$ data in constraining the cosmological parameters of different cosmological models, including that of Chevalier-Polarski-Linder $w_{0}w_{1}$ parametrization. First, we introduce a statistical procedure in which the chi-square estimator is not affected by the value of the Hubble constant. As a result, we find that the $H(z)$ data do not rule out the possibility of either non-flat models or dynamical dark energy cosmological models. However, we verify that the time varying equation of state parameter $w(z)$ is not constrained by the current expansion data. Combining the $H(z)$ and the Type Ia supernova data we find that the $H(z)$/SNIa overall statistical analysis provides a substantial improvement of the cosmological constraints with respect to those of the $H(z)$ analysis. Moreover, the $w_{0}-w_{1}$ parameter space provided by the $H(z)$/SNIa joint analysis is in a very good agreement with that of Planck 2015, which confirms that the present analysis with the $H(z)$ and SNIa probes correctly reveals the expansion of the Universe as found by the team of Planck. Finally, we generate sets of Monte Carlo realizations in order to quantify the ability of the $H(z)$ data to provide strong constraints on the dark energy model parameters. The Monte Carlo approach shows significant improvement of the constraints, when increasing the sample to 100 $H(z)$ measurements. Such a goal can be achieved in the future, especially in the light of the next generation of surveys.
The differential age data of astrophysical objects that have evolved passivelly during the history of the universe (e.g. red galaxies) allows to test theoretical cosmological models through the predicted Hubble function expressed in terms of the redshift $z$, $H(z)$. We use the observational data for $H(z)$ to test unified scenarios for dark matter and dark energy. Specifically, we focus our analysis on the Generalized Chaplygin Gas (GCG) and the viscous fluid (VF) models. For the GCG model, it is shown that the unified scenario for dark energy and dark matter requires some priors. For the VF model we obtain estimations for the free parameters that may be compared with further analysis mainly at perturbative level.
Dynamical dark energy has been recently suggested as a promising and physical way to solve the 3.4 sigma tension on the value of the Hubble constant $H_0$ between the direct measurement of Riess et al. (2016) (R16, hereafter) and the indirect constraint from Cosmic Microwave Anisotropies obtained by the Planck satellite under the assumption of a $Lambda$CDM model. In this paper, by parameterizing dark energy evolution using the $w_0$-$w_a$ approach, and considering a $12$ parameter extended scenario, we find that: a) the tension on the Hubble constant can indeed be solved with dynamical dark energy, b) a cosmological constant is ruled out at more than $95 %$ c.l. by the Planck+R16 dataset, and c) all of the standard quintessence and half of the downward going dark energy model space (characterized by an equation of state that decreases with time) is also excluded at more than $95 %$ c.l. These results are further confirmed when cosmic shear, CMB lensing, or SN~Ia luminosity distance data are also included. However, tension remains with the BAO dataset. A cosmological constant and small portion of the freezing quintessence models are still in agreement with the Planck+R16+BAO dataset at between 68% and 95% c.l. Conversely, for Planck plus a phenomenological $H_0$ prior, both thawing and freezing quintessence models prefer a Hubble constant of less than 70 km/s/Mpc. The general conclusions hold also when considering models with non-zero spatial curvature.
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