The $Om3$ diagnostic (Shafieloo et al. 2012) tests the consistency of the cosmological constant as a candidate for dark energy using Baryon Acoustic Oscillation (BAO) data. An important feature of $Om3$ is that it is independent of any parametric assumption for dark energy, neither does it depend upon the dynamics of the Universe during the pre-recombination nor post-recombination eras. In other words, $Om3$ can be estimated using BAO observables and used either to confirm or falsify the cosmological constant independently of the value of the Hubble constant $H_0$ (expansion rate at $z=0$), and the comoving sound horizon at the baryon drag epoch, $r_d$ (which is a function of the physics of the Universe prior to recombination). Consequently, $Om3$ can play a key role in identifying the nature of dark energy (DE) regardless of the existing tensions in the standard model of cosmology and the possible presence of systematics in some of the data sets. We revisit $Om3$ using the most recent BAO observables from the eBOSS survey in order to test the consistency of the cosmological constant with this data. Our results show the consistency of dark energy being the cosmological constant. Moreover, with eBOSS data, we have achieved a precision of $1.5\%$ for this three-point diagnostic. This demonstrates that $Om3$ can be a potent diagnostic of dark energy when used in conjunction with the high precision data expected from forthcoming large scale structure surveys such as the Dark Energy Spectroscopic Instrument (DESI) and Euclid.
We test the mutual consistency between the baryon acoustic oscillation measurements from the eBOSS SDSS final release, as well as the Pantheon supernova compilation in a model independent fashion using Gaussian process regression. We also test their joint consistency with the $Λ$CDM model, also in a model independent fashion. We also use Gaussian process regression to reconstruct the expansion history that is preferred by these two datasets. While this methodology finds no significant preference for model flexibility beyond $Λ$CDM, we are able to generate a number of reconstructed expansion hi…
We analyse the full shape of anisotropic clustering measurements from the extended Baryon Oscillation Spectroscopic survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS). We obtain constraints on the cosmological parameters independent of the Hubble parameter $h$ for the extensions of the $Λ$CDM models, focusing on cosmologies with free dark energy equation of state parameter $w$. We combine the clustering constraints with those from the latest CMB data from Planck to obtain joint constraints for these cosmologies for $w$ …
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 $(Ω_\mathrm{m},γ,σ_8)$ in a model independent manner. Our results show consistency with a spatially flat FLRW Universe with general relativity to go…
We present the effective-field theory (EFT)-based cosmological full-shape analysis of the anisotropic power spectrum of eBOSS quasars at the effective redshift $z_{\rm eff}=1.48$. We perform extensive tests of our pipeline on simulations, paying a particular attention to the modeling of observational systematics, such as redshift smearing, fiber collisions, and the radial integral constraint. Assuming the minimal $Λ$CDM model, and fixing the primordial power spectrum tilt and the physical baryon density, we find the Hubble constant $H_0=(66.7\pm 3.2)~$km~s$^{-1}$Mpc$^{-1}$, the matter density …
The late-time integrated Sachs-Wolfe (ISW) imprint of $R\gtrsim 100~h^{-1}{\rm Mpc}$ super-structures is sourced by evolving large-scale potentials due to a dominant dark energy component in the $Λ$CDM model. The aspect that makes the ISW effect distinctly interesting is the repeated observation of stronger-than-expected imprints from supervoids at $z\lesssim0.9$. Here we analyze the un-probed key redshift range $0.8<z<2.2$ where the ISW signal is expected to fade in $Λ$CDM, due to a weakening dark energy component, and eventually become consistent with zero in the matter dominated epoch. On t…
Using the latest observational data from Planck-CMB and its combination with the pre-reconstructed full-shape (FS) galaxy power spectrum measurements from the BOSS DR12 sample and eBOSS LRG DR16 sample, we report the observational constraints on the cosmic neutrino properties given by the extended $Λ$CDM scenario: $Λ$CDM + $N_{\rm eff}$ + $\sum m_ν$ + $c^2_{\rm eff}$ + $c^2_{\rm vis}$ + $ξ_ν$, and its particular case $Λ$CDM + $c^2_{\rm eff}$ + $c^2_{\rm vis}$ + $ξ_ν$, where $N_{\rm eff}$, $\sum m_ν$, $c^2_{\rm eff}$, $c^2_{\rm vis}$, $ξ_ν$ are the effective number of species, the total neutrin…
Standard full-shape clustering analyses in Fourier space rely on a fixed power spectrum template, defined at the fiducial cosmology used to convert redshifts into distances, and compress the cosmological information into the Alcock-Paczynski parameters and the linear growth rate of structure. In this paper, we propose an analysis method that operates directly in the cosmology parameter space and varies the power spectrum template accordingly at each tested point. Predictions for the power spectrum multipoles from the TNS model are computed at different cosmologies in the framework of $Λ\rm{CDM…
We present the first model-agnostic analysis of the complete set of Sloan Digital Sky Survey III (BOSS) and -IV (eBOSS) catalogues of luminous red galaxy and quasar clustering in the redshift range $0.2\leq z \leq 2.2$ (10 billion years of cosmic evolution), which consistently includes the baryon acoustic oscillations (BAO), redshift space distortions (RSD) and the shape of the transfer function signatures, from pre- and post-reconstructed catalogues in Fourier space. This approach complements the standard analyses techniques which only focus on the BAO and RSD signatures, and the full-modelin…
We present the clustering of voids based on the quasar (QSO) sample of the extended Baryon Oscillation Spectroscopic Survey Data Release 16 in configuration space. We define voids as overlapping empty circumspheres computed by Delaunay tetrahedra spanned by quartets of quasars, allowing for an estimate of the depth of underdense regions. To maximise the BAO signal-to-noise ratio, we consider only voids with radii larger than 36$h^{-1}$Mpc. Our analysis shows a negative BAO peak in the cross-correlation of QSOs and voids. The joint BAO measurement of the QSO auto-correlation and the correspondi…
We perform a measurement of the Hubble constant, $H_0$, using the latest baryonic acoustic oscillations (BAO) measurements from galaxy surveys of 6dFGS, SDSS DR7 Main Galaxy Sample, BOSS DR12 sample, and eBOSS DR14 quasar sample, in the framework of a flat $Λ$CDM model. Based on the Kullback-Leibler (KL) divergence, we examine the consistency of $H_0$ values derived from various data sets. We find that our measurement is consistent with that derived from Planck and with the local measurement of $H_0$ using the Cepheids and type Ia supernovae. We perform forecasts on $H_0$ from future BAO measu…
We present cosmological parameter measurements from the effective field theory-based full-shape analysis of the power spectrum of emission line galaxies (ELGs). First, we perform extensive tests on simulations and determine appropriate scale cuts for the perturbative description of the ELG power spectrum. We study in detail non-linear redshift-space distortions (``fingers-of-God'') for this sample and show that they are somewhat weaker than those of luminous red galaxies. This difference is not significant for current data, but may become important for future surveys like Euclid/DESI. Then we …
We present the analysis of the full shape of anisotropic clustering measurement from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS), re-analysed using an updated recipe for the non-linear matter power spectrum and the non-local bias parameters. We obtain constraints for flat $Λ$CDM cosmologies, focusing on the cosmological parameters that are independent of the Hubble parameter $h$. Our recovered value for the RMS linear perturbation theory variance as measured on the sc…
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 $Λ$CDM model with two-point $Omh^2(z_{2};z_{1})$ diagnostic. In $Λ$CDM model, with equation of state (EoS) $w=-1$, two-point diagnostic relation $Omh^2 \equiv Ω_m h^2$ is tenable, where $Ω_m$ 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 i…
Cosmological inference from the eBOSS QSO full-shape analysis with optimal redshift weights
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与天体物理前沿研究院）
Direct measurements of Hubble parameters $H(z)$ are very useful for cosmological model parameters inference. Based on them, Sahni, Shafieloo and Starobinski introduced a two-point diagnostic $Omh^2(z_i, z_j)$ as an interesting tool for testing the validity of the $Λ$CDM model. Applying this test they found a tension between observations and predictions of the $Λ$CDM model. We use the most comprehensive compilation $H(z)$ data from baryon acoustic oscillations (BAO) and differential ages (DA) of passively evolving galaxies to study cosmological models using the Hubble parameters itself and to d…
We investigate the interacting dark energy models by using the diagnostics of statefinder hierarchy and growth rate of structure. We wish to explore the deviations from $Λ$CDM and to differentiate possible degeneracies in the interacting dark energy models with the geometrical and structure growth diagnostics. We consider two interacting forms for the models, i.e., $Q_1=βHρ_c$ and $Q_2=βHρ_{de}$, with $β$ being the dimensionless coupling parameter. Our focus is the I$Λ$CDM model that is a one-parameter extension to $Λ$CDM by considering a direct coupling between the vacuum energy ($Λ$) and col…
We investigate the general properties of a class of scalar-field dark energy models (i.e., $ϕ$CDM models) which behave like cosmological trackers at early times. Particularly, we choose three $ϕ$CDM models with typical potentials, i.e., $V(ϕ)\propto ϕ^{-α}$ (inverse power-law (IPL) model), $V(ϕ)\propto \coth^αϕ$ (L-model) and $V(ϕ)\propto \cosh(αϕ)$ (Oscillatory tracker model), where the latter two models are based on the $α$-attractors originated from the study of inflation. These models, which reduce to the $Λ$CDM model with $α\to 0$, are studied and compared with the recent observations, in…
Two-point diagnostics $Om(z_i,z_j)$ and $Omh^2(z_i,z_j)$ have been introduced as an interesting tool for testing the validity of the $Λ$CDM model. Quite recently, Sahni, Shafieloo $\&$ Starobinsky (2014) combined two independent measurements of $H(z)$ from BAO data with the value of the Hubble constant $H_0$, and used the second of these diagnostics to test the $Λ$CDM model. Their result indicated a considerable tension between observations and predictions of the $Λ$CDM model. Since reliable data concerning expansion rates of the Universe at different redshifts $H(z)$ are crucial for the succe…
In this paper, we constrain four time-dependent dark energy (TDDE) models by using the Type Ia supernovae (SNe Ia), baryonic acoustic oscillations (BAO), observational Hubble parameter (OHD) data-sets as well as the single data point from the newest event GW150914. Subsequently, adopting the best fitting values of the model parameters, we apply the original statefinder, statefinder hierarchy, the growth rate of matter perturbations and $Om(z)$ diagnostics to distinguish the TDDE scenarios and the $Λ$CDM scenario from each other. We discover that all the TDDE models and $Λ$CDM model can be dist…
With the increasing precision of recent cosmological surveys and the discovery of important tensions within the $Λ$CDM paradigm, it is becoming more and more important to develop tools to quantify accurately the discordance between different probes. One such tool is the Surprise statistic, a measure based on the Kullback-Leibler divergence. The Surprise, however, has been up to now applied only under its Gaussian approximation, which can fail to properly capture discordance in cases that deviate significantly from Gaussianity. In this paper we developed the \texttt{klsurprise} code which compu…
In this paper, we propose a new parametrization of $Om(z)$ diagnostics and show how the most recent and significantly improved observations concerning the $H(z)$ and SN Ia measurements can be used to probe the consistency or tension between $Λ$CDM model and observations. Our results demonstrates that $H_0$ plays a very important role in the consistency test of $Λ$CDM with the $H(z)$ data. Adopting the Hubble constant priors from \textit{Planck} 2013 and Riess (2016), one finds a considerable tension between the current $H(z)$ data and $Λ$CDM model and confirms the conclusions obtained previous…
We reverse the logic behind the apparent existence of $H_0$-tension, to design diagnostics for cosmological models. The basic idea is that the non-constancy of $H_0$ inferred from observations at different redshifts is a null hypothesis test for models within the FLRW paradigm -- if $H_0$ runs, the model is wrong. Depending on the kind of observational data, the most suitable form of the diagnostic can vary. As examples, we present two $H_0$ diagnostics that are adapted to two different BAO observables. We use these and the corresponding BAO data to Gaussian reconstruct the running of $H_0$ in…
We apply the $Om$ diagnostic to models for dark energy based on scalar fields. In case of the power law potentials, we demonstrate the possibility of slowing down the expansion of the Universe around the present epoch for a specific range in the parameter space. For these models, we also examine the issues concerning the age of Universe. We use the $Om$ diagnostic to distinguish the $Λ$CDM model from non minimally coupled scalar field, phantom field and generic quintessence models. Our study shows that the $Om$ has zero, positive and negative curvatures for $Λ$CDM, phantom and quintessence mod…
The newly released observational $H(z)$ data (OHD) is used to constrain $Λ(t)$CDM models as holographic and agegraphic dark energy. By the use of the length scale and time scale as the IR cut-off including Hubble horizon (HH), future event horizon (FEH), age of the universe (AU), and conformal time (CT), we achieve four different $Λ(t)$CDM models which can describe the present cosmological acceleration respectively. In order to get a comparison between such $Λ(t)$CDM models and standard $Λ$CDM model, we use the information criteria (IC), $Om(z)$ diagnostic, and statefinder diagnostic to measur…
Hubble tension is routinely presented as a mismatch between the Hubble constant $H_0$ determined locally and a value inferred from the flat $Λ$CDM cosmology. In essence, the tension boils down to a disagreement between two numbers. Here, assuming the tension is cosmological in origin, we predict that within flat $Λ$CDM there should be other inferred values of $H_0$, and that a "running of $H_0$ with redshift" can be expected. These additional determinations of $H_0$ may be traced to a difference between the effective equation of state (EoS) of the Universe within the Friedmann-Lemaître-Roberts…
Using various latest cosmological datasets including Type-Ia supernovae, cosmic microwave background radiation, baryon acoustic oscillations, and estimations of the Hubble parameter, we test some dark energy models with parameterized equations of state and try to distinguish or select observation-preferred models. We obtain the best fitting results of the six models and calculate their values of the Akaike Information Criteria and Bayes Information Criterion. And we can distinguish these dark energy models from each other by using these two information criterions. However, the $Λ$CDM model rem…
As an extension of $Λ$CDM, the decaying vacuum model (DV) describes the dark energy as a varying vacuum whose energy density decays linearly with the Hubble parameter in the late-times, $ρ_Λ(t) \propto H(t)$, and produces the matter component. We examine the high-$z$ cosmic age problem in the DV model, and compare it with $Λ$CDM and the Yang-Mills condensate (YMC) dark energy model. Without employing a dynamical scalar field for dark energy, these three models share a similar behavior of late-time evolution. It is found that the DV model, like YMC, can accommodate the high-$z$ quasar APM 08279…
We study is some detail the Cosmology of Oscillating Dark Energy described by concrete equations-of-state investigated recently in the literature. In particular, at the background level we compute the statefinder parameters, while at the level of linear cosmological perturbations we compute the growth index $γ$ as well as the combination parameter $A=f σ_8$. The comparison with $Λ$CDM is made as well.
In this work we introduce a new set of parameters $(r_{g}, s_{g})$ involving the linear growth of matter perturbation that can distinguish and constrain different dark energy models very efficiently. Interestingly, for $Λ$CDM model these parameters take exact value $(1,1)$ at all red shifts whereas for models different from $Λ$CDM, they follow different trajectories in the $(r_{g}, s_{g})$ phase plane. By considering the parametrization for the dark energy equation of state ($w$) and for the linear growth rate ($f_{g}$), we show that different dark energy behaviours with similar evolution of t…
We apply the statefinder diagnostic to the holographic dark energy models, including the original holographic dark energy (HDE) model, the new holographic dark energy model, the new agegraphic dark energy (NADE) model, and the Ricci dark energy model. In the low-redshift region the holographic dark energy models are degenerate with each other and with the $Λ$CDM model in the $H(z)$ and $q(z)$ evolutions. In particular, the HDE model is highly degenerate with the $Λ$CDM model, and in the HDE model the cases with different parameter values are also in strong degeneracy. Since the observational d…
The Ly-$α$ forest 1D flux power spectrum is a powerful probe of several cosmological parameters. Assuming a $Λ$CDM cosmology including massive neutrinos, we find that the latest SDSS DR14 BOSS and eBOSS Ly-$α$ forest data is in very good agreement with current weak lensing constraints on $(Ω_m, σ_8)$ and has the same small level of tension with Planck. We did not identify a systematic effect in the data analysis that could explain this small tension, but we show that it can be reduced in extended cosmological models where the spectral index is not the same on the very different times and scale…
In this paper, we propose a new pressure parametric model of the total cosmos energy components in a spatially flat Friedmann-Robertson-Walker (FRW) universe and then reconstruct the model into quintessence and phantom scenarios, respectively. By constraining with the datasets of the type Ia supernova (SNe Ia), the baryon acoustic oscillation (BAO) and the observational Hubble parameter data(OHD), we find that $Ω_{m0}=0.270^{+0.039}_{-0.034}$ at the 1$σ$ level and our universe slightly biases towards quintessence behavior. Then we use two diagnostics including $Om(a)$ diagnostic and statefinde…
A new diagnostic method, $Om$ is applied to generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy. On the basis of the recently observed data: the Union supernovae, the observational Hubble data, the SDSS baryon acoustic peak and the five-year WMAP shift parameter, we show the discriminations between GCG and $Λ$CDM model. Furthermore, it is calculated that the current equation of state of dark energy $w_{0de}=-0.964$ according to GCG model.
In the present work, we have adopted a kinematic approach for constraining the extended null diagnostic of concordance cosmology, known as the statefinder hierarchy. A Taylor series expansion of the Hubble parameter has been utilised for the reconstruction. The coefficients of the Taylor series expansion are related to the kinematical parameters like the deceleration parameter, cosmological jerk parameter etc. The present values of the kinematical parameters are constrained from the estimated values of those series coefficients. A Markov chain Monte Carlo analysis has been carried out using th…
Aiming at exploring the nature of dark energy, we use thirty-six observational Hubble parameter data (OHD) in the redshift range $0 \leqslant z \leqslant 2.36$ to make a cosmological model-independent test of the two-point $Omh^2(z_{2};z_{1})$ diagnostic. In $Λ$CDM, we have $Omh^2 \equiv Ω_{m}h^2$, where $Ω_{m}$ is the matter density parameter at present. We bin all the OHD into four data points to mitigate the observational contaminations. By comparing with the value of $Ω_{m}h^2$ which is constrained tightly by the Planck observations, our results show that in all six testing pairs of $Omh^2…
Concordance $Λ$CDM universe is the simplest model that is consistent with a large variety of cosmological observations till date. But few recent observations indicate inconsistencies in $Λ$CDM model. In this paper, we consider the combination of recent SnIa+Bao+Cmb+Growth+$H(z)$+$H_{0}$ measurements to revisit the constraints on the dark energy evolution using the widely studied CPL parametrisation for the dark energy equation of state. Although the reconstructed behaviour for the dark energy equation of state confirms the inconsistency of $Λ$CDM at $95\%$ confidence level, the reconstructed $…
Baryon Acoustic Oscillations (BAO) allow us to determine the expansion history of the Universe, thereby shedding light on the nature of dark energy. Recent observations of BAO's in the SDSS DR9 and DR11 have provided us with statistically independent measurements of $H(z)$ at redshifts of 0.57 and 2.34, respectively. We show that these measurements can be used to test the cosmological constant hypothesis in a model independent manner by means of an improved version of the $Om$ diagnostic. Our results indicate that the SDSS DR11 measurement of $H(z) = 222 \pm 7$ km/sec/Mpc at $z = 2.34$, when t…
A cosmological preferred direction was reported from the type Ia supernovae (SNe Ia) data in recent years. We use the Union2.1 data to give a simple classification of such studies for the first time. Because the maximum anisotropic direction is independent of isotropic dark energy models, we adopt two cosmological models ($Λ$CDM, $w$CDM) for the hemisphere comparison analysis and $Λ$CDM model for dipole fit approach. In hemisphere comparison method, the matter density and the equation of state of dark energy are adopted as the diagnostic qualities in the $Λ$CDM model and $w$CDM model, respecti…
We apply the Statefinder hierarchy and the growth rate of matter perturbations to discriminate modified Chaplygin gas (MCG), generalized Chaplygin gas (GCG), superfluid Chaplygin gas (SCG), purely kinetic k-essence (PKK), and $Λ$CDM model. We plot the evolutional trajectories of these models in the statefinder plane and in the composite diagnostic plane. We find that GCG, MCG, SCG, PKK, and $Λ$CDM can be distinguished well from each other at the present epoch by using the composite diagnostic $\{ε(z), S^{(1)}_{5}\}$. Using other combinations, such as $\{S^{(1)}_{3}, S^{(1)}_4\}$, $\{S^{(1)}_{3…
The Hubble tension and attempts to resolve it by modifying the physics of (or at) recombination motivate finding ways to determine $H_0$ and the sound horizon at the epoch of baryon decoupling $r_{\rm d}$ in ways that neither rely on a recombination model nor on late-time Hubble data. In this work, we investigate what one can learn from the current and future BAO data when treating $r_{\rm d}$ and $H_0$ as independent free parameters. It is well known that BAO gives exquisite constraints on the product $r_{\rm d}H_0$. We show here that imposing a moderate prior on $Ω_{\rm m} h^2$ breaks the de…
In this paper, we place constraints on four alternative cosmological models under the assumption of the spatial flatness of the Universe: CPL, EDE, GCG and MPC. A new compilation of 120 compact radio quasars observed by very-long-baseline interferometry, which represents a type of new cosmological standard rulers, are used to test these cosmological models. Our results show that the fits on CPL obtained from the quasar sample are well consistent with those obtained from BAO. For other cosmological models considered, quasars provide constraints in agreement with those derived with other standar…
We examine the Pantheon supernovae distance data compilation in a model independent analysis to test the validity of cosmic history reconstructions beyond the concordance $Λ$CDM cosmology. Strong deviations are allowed by the data at $z\gtrsim1$ in the reconstructed Hubble parameter, $Om$ diagnostic, and dark energy equation of state. We explore three interpretations: 1) possibility of the true cosmology being far from $Λ$CDM, 2) supernovae property evolution, and 3) survey selection effects. The strong (and theoretically problematic) deviations at $z\gtrsim1$ vanish and good consistency with …
