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Register a new userConstraining the dark energy and smoothness-parameter with supernovae
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Jose Ademir Sales Lima
Publication date
2008
fields
Physics
and research's language is
English
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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.
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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.
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 $Omega_m$.
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.
The Dark Energy Survey (DES) will use a new imaging camera on the Blanco 4-m telescope at CTIO to image 5000 square degrees of sky in the South Galactic Cap in four optical bands, and to carry out repeat imaging over a smaller area to identify and measure lightcurves of Type Ia supernovae. The main imaging area overlaps the planned Sunyaev-Zeldovich survey of the South Pole Telescope. The idea behind DES is to use four distinct and largely independent methods to probe the properties of dark energy: baryon oscillations of the power spectrum, abundance and spatial distribution of clusters, weak gravitational lensing, and Type Ia supernovae. This white paper outlines, in broad terms, some of the theoretical issues associated with the first three of these probes (the issues for supernovae are mostly different in character), and with the general task of characterizing dark energy and distinguishing it from alternative explanations for cosmic acceleration. A companion white paper discusses the kind of numerical simulations and other theoretical tools that will be needed to address the these issues and to create mock catalogs that allow end-to-end tests of analysis procedures. Although we have been thinking about these problems in the specific context of DES, many of them are also relevant to other planned dark energy studies.
We show that peculiar velocities of Type Ia supernovae can be used to derive constraints on the sum of neutrino masses, $Sigma m_{ u}$, and dark energy equation of state, $w = w_0+w_a(1-a)$, from measurements of the magnitude-redshift relation, complementary to galaxy redshift and weak lensing surveys. Light from a supernova propagates through a perturbed Universe so the luminosity distance is modified from its homogeneous prediction. This modification is proportional to the matter density fluctuation and its time derivative due to gravitational lensing and peculiar velocity respectively. At low redshifts, the peculiar velocity signal dominates while at high redshifts lensing does. We show that using lensing and peculiar velocity of supernovae from the upcoming surveys WFIRST and ZTF, without other observations, we can constrain $Sigma m_{ u} lesssim 0.31$ eV, $sigma(w_0) lesssim 0.02$, and ${sigma(w_a)} lesssim 0.18$ ($1-sigma$ CL) in the $Sigma m_{ u}$-$w_0$-$w_a$ parameter space, where all the other cosmological parameters are fixed. We find that adding peculiar velocity information from low redshifts shrinks the volume of the parameter ellipsoid in this space by $sim 33$%. We also allow $Omega_{text{CDM}}$ to vary as well as $Sigma m_{ u}$, $w_0$ and $w_a$, and demonstrate how these constraints degrade as a consequence.
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