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Register a new userBreaking through the high redshift bottleneck of Observational Hubble parameter Data: The Sandage-Loeb signal Scheme
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We propose a valid scheme to measure the Hubble parameter $H(z)$ at high redshifts by detecting the Sandage-Loeb signal (SL signal) which can be realized by the next generation extremely large telescope. It will largely extend the current observational Hubble parameter data (OHD) towards the redshift region of $z in [2.0,5.0]$, the so-called redshift desert, where other dark energy probes are hard to provide useful information of the cosmic expansion. Quantifying the ability of this future measurement by simulating observational data for a CODEX (COsmic Dynamics and EXo-earth experiment)-like survey and constraining various cosmological models, we find that the SL signal scheme brings the redshift upper-limit of OHD from $z_mathrm{max}=2.3$ to $z_mathrm{max}simeq 5.0$, provides more accurate constraints on different dark energy models, and greatly changes the degeneracy direction of the parameters. For the $Lambda$CDM case, the accuracy of $Omega_m$ is improved by $58%$ and the degeneracy between $Omega_m$ and $Omega_ {Lambda}$ is rotated to the vertical direction of $Omega_k = 0$ line strongly; for the $w$CDM case, the accuracy of $w$ is improved by $15%$. The Fisher matrix forecast on different time-dependent $w(z)$ is also performed.
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Two types of interacting dark energy models are investigated using the type Ia supernova (SNIa), observational $H(z)$ data (OHD), cosmic microwave background (CMB) shift parameter and the secular Sandage-Loeb (SL) test. We find that the inclusion of SL test can obviously provide more stringent constraint on the parameters in both models. For the constant coupling model, the interaction term including the SL test is estimated at $delta=-0.01 pm 0.01 (1sigma) pm 0.02 (2sigma)$, which has been improved to be only a half of original scale on corresponding errors. Comparing with the combination of SNIa and OHD, we find that the inclusion of SL test directly reduces the best-fit of interaction from 0.39 to 0.10, which indicates that the higher-redshift observation including the SL test is necessary to track the evolution of interaction. For the varying coupling model, we reconstruct the interaction $delta (z)$, and find that the interaction is also negative similar as the constant coupling model. However, for high redshift, the interaction generally vanishes at infinity. The constraint result also shows that the $Lambda$CDM model still behaves a good fit to the observational data, and the coincidence problem is still quite severe. However, the phantom-like dark energy with $w_X<-1$ is slightly favored over the $Lambda$CDM model.
In order to explore the generic properties of a backreaction model for explaining the accelerated expansion of the Universe, we exploit two metrics to describe the late time Universe. Since the standard FLRW metric cannot precisely describe the late time Universe on small scales, the template metric with an evolving curvature parameter $kappa_{mathcal{D}}(t)$ is employed. However, we doubt the validity of the prescription for $kappa_{mathcal{D}}$, which motivates us apply observational Hubble parameter data (OHD) to constrain parameters in dust cosmology. First, for FLRW metric, by getting best-fit constraints of $Omega^{{mathcal{D}}_0}_m = 0.25^{+0.03}_{-0.03}$, $n = 0.02^{+0.69}_{-0.66}$, and $H_{mathcal{D}_0} = 70.54^{+4.24}_{-3.97} {rm km s^{-1} Mpc^{-1}}$, the evolutions of parameters are explored. Second, in template metric context, by marginalizing over $H_{mathcal{D}_0}$ as a prior of uniform distribution, we obtain the best-fit values of $n=-1.22^{+0.68}_{-0.41}$ and ${{Omega}_{m}^{mathcal{D}_{0}}}=0.12^{+0.04}_{-0.02}$. Moreover, we utilize three different Gaussian priors of $H_{mathcal{D}_0}$, which result in different best-fits of $n$, but almost the same best-fit value of ${{Omega}_{m}^{mathcal{D}_{0}}}sim0.12$. Also, the absolute constraints without marginalization of parameter are obtained: $n=-1.1^{+0.58}_{-0.50}$ and ${{Omega}_{m}^{mathcal{D}_{0}}}=0.13pm0.03$. With these constraints, the evolutions of the effective deceleration parameter $q^{mathcal{D}}$ indicate that the backreaction can account for the accelerated expansion of the Universe without involving extra dark energy component in the scaling solution context. Nevertheless, the results also verify that the prescription of $kappa_{mathcal{D}}$ is insufficient and should be improved.
Redshifts of an astronomical body measured at multiple epochs (e.g., separated by 10 years) are different due to the cosmic expansion. This so-called Sandage-Loeb test offers a direct measurement of the expansion rate of the Universe. However, acceleration in the motion of Solar System with respect to the cosmic microwave background also changes redshifts measured at multiple epochs. If not accounted for, it yields a biased cosmological inference. To address this, we calculate the acceleration of Solar System with respect to the Local Group of galaxies to quantify the change in the measured redshift due to local motion. Our study is motivated by the recent determination of the mass of Large Magellanic Cloud (LMC), which indicates a significant fraction of the Milky Way mass. We find that the acceleration towards the Galactic Center dominates, which gives a redshift change of 7 cm/s in 10 years, while the accelerations due to LMC and M31 cannot be ignored depending on lines of sight. We create all-sky maps of the expected change in redshift and the corresponding uncertainty, which can be used to correct for this effect.
Aiming at exploring the nature of dark energy (DE), we use forty-three observational Hubble parameter data (OHD) in the redshift range $0 < z leqslant 2.36$ to make a cosmological model-independent test of the $Lambda$CDM model with two-point $Omh^2(z_{2};z_{1})$ diagnostic. In $Lambda$CDM model, with equation of state (EoS) $w=-1$, two-point diagnostic relation $Omh^2 equiv Omega_m h^2$ is tenable, where $Omega_m$ is the present matter density parameter, and $h$ is the Hubble parameter divided by 100 $rm km s^{-1} Mpc^{-1}$. We utilize two methods: the weighted mean and median statistics to bin the OHD to increase the signal-to-noise ratio of the measurements. The binning methods turn out to be promising and considered to be robust. By applying the two-point diagnostic to the binned data, we find that although the best-fit values of $Omh^2$ fluctuate as the continuous redshift intervals change, on average, they are continuous with being constant within 1 $sigma$ confidence interval. Therefore, we conclude that the $Lambda$CDM model cannot be ruled out.
We derive an observational constraint on a spherical inhomogeneity of the void centered at our position from the angular power spectrum of the cosmic microwave background(CMB) and local measurements of the Hubble parameter. The late time behaviour of the void is assumed to be well described by the so-called $Lambda$-Lema^itre-Tolman-Bondi~($Lambda$LTB) solution. Then, we restrict the models to the asymptotically homogeneous models each of which is approximated by a flat Friedmann-Lema^itre-Robertson-Walker model. The late time $Lambda$LTB models are parametrized by four parameters including the value of the cosmological constant and the local Hubble parameter. The other two parameters are used to parametrize the observed distance-redshift relation. Then, the $Lambda$LTB models are constructed so that they are compatible with the given distance-redshift relation. Including conventional parameters for the CMB analysis, we characterize our models by seven parameters in total. The local Hubble measurements are reflected in the prior distribution of the local Hubble parameter. As a result of a Markov-Chains-Monte-Carlo analysis for the CMB temperature and polarization anisotropies, we found that the inhomogeneous universe models with vanishing cosmological constant are ruled out as is expected. However, a significant under-density around us is still compatible with the angular power spectrum of CMB and the local Hubble parameter.
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