Exploring the evolution of color-luminosity parameter β\beta and its effects on parameter estimation

It has been found in previous studies that, for the Supernova Legacy Survey three-year (SNLS3) data, there is strong evidence for the redshift-evolution of color-luminosity parameter $\beta$. In this paper, using three simplest dark energy models ($\Lambda$CDM, $w$CDM, and CPL), we further explore the evolution of $\beta$ and its effects on parameter estimation. In addition to the SNLS3 data, we also take into account the Planck distance priors data, as well as the latest galaxy clustering (GC) data extracted from SDSS DR7 and BOSS. We find that, for all the models, adding a parameter of $\beta$ can reduce $\chi^2_{min}$ by $\sim$ 36, indicating that $\beta_1 = 0$ is ruled out at 6$\sigma$ confidence levels. In other words, $\beta$ deviates from a constant at 6$\sigma$ confidence levels. This conclusion is insensitive to the dark energy models considered, showing the importance of considering the evolution of $\beta$ in the cosmology-fits. Furthermore, it is found that varying $\beta$ can significantly change the fitting results of various cosmological parameters: using the SNLS3 data alone, varying $\beta$ yields a larger $\Omega_m$ for the $\Lambda$CDM model; using the SNLS3+CMB+GC data, varying $\beta$ yields a larger $\Omega_m$ and a smaller $h$ for all the models. Moreover, we find that these results are much closer to those given by the CMB+GC data, compared to the cases of treating $\beta$ as a constant. This indicates that considering the evolution of $\beta$ is very helpful for reducing the tension between supernova and other cosmological observations.Comment: 11 pages, 9 figures, 2 tables; accepted for publication in Physical Review D. arXiv admin note: text overlap with arXiv:1306.6423; and with arXiv:1109.3172 by other author

Exploring the full parameter space for an interacting dark energy model with recent observations including redshift-space distortions: Application of the parametrized post-Friedmann approach

Dark energy can modify the dynamics of dark matter if there exists a direct interaction between them. Thus a measurement of the structure growth, e.g., redshift-space distortions (RSD), can provide a powerful tool to constrain the interacting dark energy (IDE) models. For the widely studied $Q=3\beta H\rho_{de}$ model, previous works showed that only a very small coupling ($\beta\sim\mathcal{O}(10^{-3})$) can survive in current RSD data. However, all these analyses had to assume $w>-1$ and $\beta>0$ due to the existence of the large-scale instability in the IDE scenario. In our recent work [Phys. Rev. D 90, 063005 (2014)], we successfully solved this large-scale instability problem by establishing a parametrized post-Friedmann (PPF) framework for the IDE scenario. So we, for the first time, have the ability to explore the full parameter space of the IDE models. In this work, we reexamine the observational constraints on the $Q=3\beta H\rho_{de}$ model within the PPF framework. By using the Planck data, the baryon acoustic oscillation data, the JLA sample of supernovae, and the Hubble constant measurement, we get $\beta=-0.010^{+0.037}_{-0.033}$ ($1\sigma$). The fit result becomes $\beta=-0.0148^{+0.0100}_{-0.0089}$ ($1\sigma$) once we further incorporate the RSD data in the analysis. The error of $\beta$ is substantially reduced with the help of the RSD data. Compared with the previous results, our results show that a negative $\beta$ is favored by current observations, and a relatively larger interaction rate is permitted by current RSD data.Comment: 12 pages, 3 figure

Measuring growth index in a universe with sterile neutrinos

Consistency tests for the general relativity (GR) can be performed by constraining the growth index $\gamma$ using the measurements of redshift-space distortions (RSD) in conjunction with other observations. In previous studies, deviations from the GR expected value of $\gamma\approx 0.55$ at the 2--3$\sigma$ level were found. In this work, we reconsider the measurement of $\gamma$ in a universe with sterile neutrinos. We constrain the sterile neutrino cosmological model using the RSD measurements combined with the cosmic microwave background data (Planck temperature data plus WMAP 9-yr polarization data), the baryon acoustic oscillation data, the Hubble constant direct measurement, the Planck Sunyaev-Zeldovich cluster counts data, and the galaxy shear data. We obtain the constraint result of the growth index, $\gamma=0.584^{+0.047}_{-0.048}$, well consistent with the GR expected value (the consistency is at the 0.6$\sigma$ level). For the parameters of sterile neutrino, we obtain $N_{\rm{eff}}=3.62^{+0.26}_{-0.42}$ and $m_{\nu,{\rm{sterile}}}^{\rm{eff}}=0.48^{+0.11}_{-0.14}$ eV. We also consider the BICEP2 data and perform an analysis on the model with tensor modes. Similar fit results are obtained, showing that once light sterile neutrino is considered in the universe, GR will become well consistent with the current observations.Comment: 5 pages, 3 figures; accepted for publication in Physics Letters

Testing models of vacuum energy interacting with cold dark matter

We test the models of vacuum energy interacting with cold dark matter and try to probe the possible deviation from the $\Lambda$CDM model using current observations. We focus on two specific models, $Q=3\beta H\rho_{\Lambda}$ and $Q=3\beta H\rho_c$. The data combinations come from the Planck 2013 data, the baryon acoustic oscillations measurements, the type-Ia supernovae data, the Hubble constant measurement, the redshift space distortions data and the galaxy weak lensing data. For the $Q=3\beta H\rho_c$ model, we find that it can be tightly constrained by all the data combinations, while for the $Q=3\beta H\rho_{\Lambda}$ model, there still exist significant degeneracies between parameters. The tightest constraints for the coupling constant are $\beta=-0.026^{+0.036}_{-0.053}$ (for $Q=3\beta H\rho_{\Lambda}$) and $\beta=-0.00045\pm0.00069$ (for $Q=3\beta H\rho_c$) at the $1\sigma$ level. For all the fit results, we find that the null interaction $\beta=0$ is always consistent with data. Our work completes the discussion on the interacting dark energy model in the recent Planck 2015 papers. Considering this work together with the Planck 2015 results, it is believed that there is no evidence for the models beyond the standard $\Lambda$CDM model from the point of view of possible interaction.Comment: 7 pages, 2 figures; final version published in Physical Review

Probing f(R)f(R) cosmology with sterile neutrinos via measurements of scale-dependent growth rate of structure

In this paper, we constrain the dimensionless Compton wavelength parameter $B_0$ of $f(R)$ gravity as well as the mass of sterile neutrino by using the cosmic microwave background observations, the baryon acoustic oscillation surveys, and the linear growth rate measurements. Since both the $f(R)$ model and the sterile neutrino generally predict scale-dependent growth rates, we utilize the growth rate data measured in different wavenumber bins with the theoretical growth rate approximatively scale-independent in each bin. The employed growth rate data come from the peculiar velocity measurements at $z=0$ in five wavenumber bins, and the redshift space distortions measurements at $z=0.25$ and $z=0.37$ in one wavenumber bin. By constraining the $f(R)$ model alone, we get a tight 95\% upper limit of $\log_{10}B_0<-4.1$. This result is slightly weakened to $\log_{10}B_0<-3.8$ (at 2$\sigma$ level) once we simultaneously constrain the $f(R)$ model and the sterile neutrino mass, due to the degeneracy between the parameters of the two. For the massive sterile neutrino parameters, we get the effective sterile neutrino mass $m_{\nu,{\rm{sterile}}}^{\rm{eff}}<0.62$ eV (2$\sigma$) and the effective number of relativistic species $N_{\rm eff}<3.90$ (2$\sigma$) in the $f(R)$ model. As a comparison, we also obtain $m_{\nu,{\rm{sterile}}}^{\rm{eff}}<0.56$ eV (2$\sigma$) and $N_{\rm eff}<3.92$ (2$\sigma$) in the standard $\Lambda$CDM model.Comment: 6 pages, 3 figures; revised version accepted for publication in Phys. Lett.