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Register a new userCosmological perturbations for two cold fluids in $Lambda$CDM
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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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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.
The homogeneous, isotropic, and flat $Lambda$CDM universe favored by observations of the cosmic microwave background can be described using only Euclidean geometry, locally correct Newtonian mechanics, and the basic postulates of special and general relativity. We present simple derivations of the most useful equations connecting astronomical observables (redshift, flux density, angular diameter, brightness, local space density,...) with the corresponding intrinsic properties of distant sources (lookback time, distance, spectral luminosity, linear size, specific intensity, source counts,...). We also present an analytic equation for lookback time that is accurate within 0.1% for all redshifts $z$. The exact equation for comoving distance is an elliptic integral that must be evaluated numerically, but we found a simple approximation with errors $< 0.2$% for all redshifts up to $z approx 50$.
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.
In this work we discuss a general approach for the dissipative dark matter considering a nonextensive bulk viscosity and taking into account the role of generalized Friedmann equations. This generalized $Lambda$CDM model encompasses a flat universe with a dissipative nonextensive viscous dark matter component, following the Eckart theory of bulk viscosity. In order to compare models and constrain cosmological parameters, we perform Bayesian analysis using one of the most recent observations of Type Ia Supernova, baryon acoustic oscillations, and cosmic microwave background data.
We analyze Brans-Dicke gravity with a cosmological constant, $Lambda$, and cold dark matter (BD-$Lambda$CDM for short) in the light of the latest cosmological observations on distant supernovae, Hubble rate measurements at different redshifts, baryonic acoustic oscillations, large scale structure formation data, gravitational weak-lensing and the cosmic microwave background under full Planck 2015 CMB likelihood. Our analysis includes both the background and perturbations equations. We find that BD-$Lambda$CDM is observationally favored as compared to the concordance $Lambda$CDM model, which is traditionally defined within General Relativity (GR). In particular, some well-known persisting tensions of the $Lambda$CDM with the data, such as the excess in the mass fluctuation amplitude $sigma_8$ and specially the acute $H_0$-tension with the local measurements, essentially disappear in this context. Furthermore, viewed from the GR standpoint, BD-$Lambda$CDM cosmology mimics quintessence at $gtrsim3sigma$ c.l. near our time.
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