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To constrain cosmological parameters, one often makes a joint analysis with different combinations of observational data sets. In this paper we take the figure of merit (FoM) for Dark Energy Task Force fiducial model (CPL model) to estimate goodness of different combinations of data sets, which include 11 widely-used observational data sets (Type Ia Supernovae, Observational Hubble Parameter, Baryon Acoustic Oscillation, Cosmic Microwave Background, X-ray Cluster Baryon Mass Fraction, and Gamma-Ray Bursts). We analyze different combinations and make a comparison for two types of combination based on two types of basic combinations, which are often adopted in the literatures. We find two sets of combinations, which have strong ability to constrain the dark energy parameters, one has the largest FoM, the other contains less observational data with a relative large FoM and a simple fitting procedure.
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Minkowski functionals (MFs) quantify the topological properties of a given field probing its departure from Gaussianity. We investigate their use on lensing convergence maps in order to see whether they can provide further insights on the underlying cosmology with respect to the standard second-order statistics, i.e., cosmic shear tomography. To this end, we first present a method to match theoretical predictions with measured MFs taking care of the shape noise, imperfections in the map reconstruction, and inaccurate description of the nonlinearities in the matter power spectrum and bispectrum. We validate this method against simulated maps reconstructed from shear fields generated by the MICE simulation. We then perform a Fisher matrix analysis to forecast the accuracy on cosmological parameters from a joint MFs and shear tomography analysis. It turns out that MFs are indeed helpful to break the $Omega_{rm m}$--$sigma_8$ degeneracy thus generating a sort of chain reaction leading to an overall increase of the Figure of Merit.
The unprecedented quality, the increased dataset, and the wide area of ongoing and near future weak lensing surveys allows to move beyond the standard two points statistics thus making worthwhile to investigate higher order probes. As an interesting step towards this direction, we expolore the use of higher order moments (HOM) of the convergence field as a way to increase the lensing Figure of Merit (FoM). To this end, we rely on simulated convergence to first show that HOM can be measured and calibrated so that it is indeed possible to predict them for a given cosmological model provided suitable nuisance parameters are introduced and then marginalized over. We then forecast the accuracy on cosmological parameters from the use of HOM alone and in combination with standard shear power spectra tomography. It turns out that HOM allow to break some common degeneracies thus significantly boosting the overall FoM. We also qualitatively discuss possible systematics and how they can be dealt with.
This paper has been withdrawn to allow publication elsewhere.
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.
A non-parametric reconstruction of the deceleration parameter $q$ is carried out. The observational datasets are so chosen that they are model independent as much as possible. The present acceleration and the epoch at which the cosmic acceleration sets in is quite as expected, but beyond a certain redshift ($z sim 2$), a negative value of $q$ appears to be in the allowed region. A survey of existing literature is given and compared with the results obtained in the present work.
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