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Register a new userModel independent inference of the expansion history and implications for the growth of structure
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We model the expansion history of the Universe as a Gaussian Process and find constraints on the dark energy density and its low-redshift evolution using distances inferred from the Luminous Red Galaxy (LRG) and Lyman-alpha (Ly$alpha$) datasets of the Baryon Oscillation Spectroscopic Survey, supernova data from the Joint Light-curve Analysis (JLA) sample, Cosmic Microwave Background (CMB) data from the Planck satellite, and local measurement of the Hubble parameter from the Hubble Space Telescope ($mathsf H0$). Our analysis shows that the CMB, LRG, Ly$alpha$, and JLA data are consistent with each other and with a $Lambda$CDM cosmology, but the ${mathsf H0}$ data is inconsistent at moderate significance. Including the presence of dark radiation does not alleviate the ${mathsf H0}$ tension in our analysis. While some of these results have been noted previously, the strength here lies in that we do not assume a particular cosmological model. We calculate the growth of the gravitational potential in General Relativity corresponding to these general expansion histories and show that they are well-approximated by $Omega_{rm m}^{0.55}$ given the current precision. We assess the prospects for upcoming surveys to measure deviations from $Lambda$CDM using this model-independent approach.
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Reconstructing the expansion history of the Universe from type Ia supernovae data, we fit the growth rate measurements and put model-independent constraints on some key cosmological parameters, namely, $Omega_mathrm{m},gamma$, and $sigma_8$. The constraints are consistent with those from the concordance model within the framework of general relativity, but the current quality of the data is not sufficient to rule out modified gravity models. Adding the condition that dark energy density should be positive at all redshifts, independently of its equation of state, further constrains the parameters and interestingly supports the concordance model.
The model of holographic dark energy (HDE) with massive neutrinos and/or dark radiation is investigated in detail. The background and perturbation evolutions in the HDE model are calculated. We employ the PPF approach to overcome the gravity instability difficulty (perturbation divergence of dark energy) led by the equation-of-state parameter $w$ evolving across the phantom divide $w=-1$ in the HDE model with $c<1$. We thus derive the evolutions of density perturbations of various components and metric fluctuations in the HDE model. The impacts of massive neutrino and dark radiation on the CMB anisotropy power spectrum and the matter power spectrum in the HDE scenario are discussed. Furthermore, we constrain the models of HDE with massive neutrinos and/or dark radiation by using the latest measurements of expansion history and growth of structure, including the Planck CMB temperature data, the baryon acoustic oscillation data, the JLA supernova data, the Hubble constant direct measurement, the cosmic shear data of weak lensing, the Planck CMB lensing data, and the redshift space distortions data. We find that $sum m_ u<0.186$ eV (95% CL) and $N_{rm eff}=3.75^{+0.28}_{-0.32}$ in the HDE model from the constraints of these data.
Marginal likelihoods for the cosmic expansion rates are evaluated using the `Constitution data of 397 supernovas, thereby updating the results in some previous works. Even when beginning with a very strong prior probability that favors an accelerated expansion, we obtain a marginal likelihood for the deceleration parameter $q_0$ peaked around zero in the spatially flat case. It is also found that the new data significantly constrains the cosmographic expansion rates, when compared to the previous analyses. These results may strongly depend on the Gaussian prior probability distribution chosen for the Hubble parameter represented by $h$, with $h=0.68pm 0.06$. This and similar priors for other expansion rates were deduced from previous data. Here again we perform the Bayesian model-independent analysis in which the scale factor is expanded into a Taylor series in time about the present epoch. Unlike such Taylor expansions in terms of redshift, this approach has no convergence problem.
We perform a joint determination of the distance-redshift relation and cosmic expansion rate at redshifts z = 0.44, 0.6 and 0.73 by combining measurements of the baryon acoustic peak and Alcock-Paczynski distortion from galaxy clustering in the WiggleZ Dark Energy Survey, using a large ensemble of mock catalogues to calculate the covariance between the measurements. We find that D_A(z) = (1205 +/- 114, 1380 +/- 95, 1534 +/- 107) Mpc and H(z) = (82.6 +/- 7.8, 87.9 +/- 6.1, 97.3 +/- 7.0) km/s/Mpc at these three redshifts. Further combining our results with other baryon acoustic oscillation and distant supernovae datasets, we use a Monte Carlo Markov Chain technique to determine the evolution of the Hubble parameter H(z) as a stepwise function in 9 redshift bins of width dz = 0.1, also marginalizing over the spatial curvature. Our measurements of H(z), which have precision better than 7% in most redshift bins, are consistent with the expansion history predicted by a cosmological-constant dark-energy model, in which the expansion rate accelerates at redshift z < 0.7.
In the current work, we have implemented an extension of the standard Gaussian Process formalism, namely the Multi-Task Gaussian Process with the ability to perform a joint learning of several cosmological data simultaneously. We have utilised the low-redshift expansion rate data from Supernovae Type-Ia (SN), Baryon Acoustic Oscillations (BAO) and Cosmic Chronometers (CC) data in a joint analysis. We have tested several possible models of covariance functions and find very consistent estimates for cosmologically relevant parameters. In the current formalism, we also find provisions for heuristic arguments which allow us to select the best-suited kernel for the reconstruction of expansion rate data. We also utilised our method to account for systematics in CC data and find an estimate of $H_0 = 68.52^{+0.94 + 2.51 (sys)}_{-0.94} $ $textrm{km/s Mpc}^{-1}$ and a corresponding $r_d = 145.61^{+2.82}_{ - 2.82 - 4.3 (sys)} $ Mpc as our primary result. Subsequently, we find constraints on the present deceleration parameter $q_0 = -0.52 pm 0.06$ and the transition redshift $z_T = 0.64^{+0.12}_{-0.09}$. All the estimated cosmological parameters are found to be in good agreement with the standard $Lambda$CDM scenario. Including the local model-independent $H_0$ estimate to the analysis we find $H_0 = 71.40^{ + 0.30 + 1.65 (sys)}_{- 0.30 } $ $textrm{km/s Mpc}^{-1}$ and the corresponding $r_d = 141.29^{ + 1.31 }_{-1.31-2.63 (sys)}$ Mpc. Also, the constraints on $r_d H_0$ remain consistent throughout our analysis and also with the model-dependent CMB estimate. Using the $mathcal{O}m(z)$ diagnostic, we find that the concordance model is very consistent within the redshift range $z lesssim 2$ and mildly discrepant for $z gtrsim 2$.
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