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Register a new userCosmological model-independent test of $Lambda$CDM with two-point diagnostic by the observational Hubble parameter data
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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.
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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.
In the paper, we consider two models in which dark energy is coupled with either dust matter or dark matter, and discuss the conditions that allow more time for structure formation to take place at high redshifts. These models are expected to have a larger age of the universe than that of $Lambda$CDM [universe consists of cold dark matter (CDM) and dark energy (a cosmological constant, $Lambda$)], so it can explain the formation of high redshift gravitationally bound systems which the $Lambda$CDM model cannot interpret. We use the observational Hubble parameter data (OHD) and Hubble parameter obtained from cosmic chronometers method ($H(z)$) in combination with baryon acoustic oscillation (BAO) data to constrain these models. With the best-fitting parameters, we discuss how the age, the deceleration parameter, and the energy density parameters evolve in the new universes, and compare them with that of $Lambda$CDM.
Inspired by the recent conjecture that the universe has transitioned from AdS vacua to dS vacua in the late universe made via graduated dark energy, we extend the $Lambda$CDM model by a cosmological `constant ($Lambda_{rm s}$) that switches sign at certain redshift, $z_dagger$, and name it as $Lambda_{rm s}$CDM. We discuss the construction and theoretical features of this model, and find out that, when the consistency of $Lambda_{rm s}$CDM with the CMB data is ensured, (i) $z_daggergtrsim1.1$ is implied by the condition that the universe monotonically expands, (ii) $H_0$ is inversely correlated with $z_dagger$ and reaches $approx74.5~{rm km, s^{-1}, Mpc^{-1}}$ for $z_dagger=1.5$, (iii) $H(z)$ presents an excellent fit to the Ly-$alpha$ measurements provided that $z_daggerlesssim 2.34$. We further investigate the model constraints by using the full Planck CMB data, with and without BAO data. We find that the CMB data alone does not constrain $z_dagger$ but CMB+BAO dataset favors the sign switch of $Lambda_{rm s}$ providing the constraint: $z_dagger=2.44pm0.29$ (68% CL). Our analysis reveals that the lower and upper limits of $z_dagger$ are controlled by the Galaxy and Ly-$alpha$ BAO measurements, respectively, and the larger $z_{dagger}$ values imposed by the Galaxy BAO data prevent the model from achieving the highest local $H_0$ measurements. In general, $Lambda_{rm s}$CDM (i) relaxes the $H_0$ tension while being fully consistent with the TRGB measurement, (ii) removes the discrepancy with the Ly-$alpha$ measurements, (iii) relaxes the $S_8$ tension, and (iv) finds a better agreement with the BBN constraints of physical baryon density. We find no strong statistical evidence to discriminate between the $Lambda_{rm s}$CDM and $Lambda$CDM models. However, interesting and promising features of $Lambda_{rm s}$CDM provide an upper edge over $Lambda$CDM.
We combine model-independent reconstructions of the expansion history from the latest Pantheon supernovae distance modulus compilation and measurements from baryon acoustic oscillation to test some important aspects of the concordance model of cosmology namely the FLRW metric and flatness of spatial curvature. We then use the reconstructed expansion histories to fit growth measurement from redshift-space distortion and obtain strong constraints on $(Omega_mathrm{m},gamma,sigma_8)$ in a model independent manner. Our results show consistency with a spatially flat FLRW Universe with general relativity to govern the perturbation in the structure formation and the cosmological constant as dark energy. However, we can also see some hints of tension among different observations within the context of the concordance model related to high redshift observations ($z > 1$) of the expansion history. This supports earlier findings of Sahni et al. (2014) & Zhao et al. (2017) and highlights the importance of precise measurement of expansion history and growth of structure at high redshifts.
The cosmic large-scale structure of our Universe is comprised of baryons and cold dark matter (CDM). Yet it is customary to treat these two components as a combined single-matter fluid with vanishing pressure, which is justified only for sufficiently large scales and late times. Here we go beyond the single-fluid approximation and develop the perturbation theory for two gravitationally coupled fluids while still assuming vanishing pressure. We mostly focus on perturbative expansions in powers of $D$ (or $D_+$), the linear structure growth of matter in a $Lambda$CDM Universe with cosmological constant $Lambda$. We derive in particular (1) explicit recursion relations for the two fluid densities, (2) complementary all-order results in the Lagrangian-coordinates approach, as well as (3) the associated component wavefunctions in a semi-classical approach to cosmic large-scale structure. In our companion paper (Hahn et al. 2020) we apply these new theoretical results to generate novel higher-order initial conditions for cosmological hydrodynamical simulations.
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