Constraints on inflation revisited: An analysis including the latest local measurement of the Hubble constant

We revisit the constraints on inflation models by using the current cosmological observations involving the latest local measurement of the Hubble constant ($H_{0} = 73.00\pm 1.75$ km s $^{-1}$ Mpc$^{-1}$). We constrain the primordial power spectra of both scalar and tensor perturbations with the observational data including the Planck 2015 CMB full data, the BICEP2 and Keck Array CMB B-mode data, the BAO data, and the direct measurement of $H_0$. In order to relieve the tension between the local determination of the Hubble constant and the other astrophysical observations, we consider the additional parameter $N_{\rm eff}$ in the cosmological model. We find that, for the $\Lambda$CDM+$r$+$N_{\rm eff}$ model, the scale invariance is only excluded at the 3.3$\sigma$ level, and $\Delta N_{\rm eff}>0$ is favored at the 1.6$\sigma$ level. Comparing the obtained 1$\sigma$ and 2$\sigma$ contours of $(n_s,r)$ with the theoretical predictions of selected inflation models, we find that both the convex and concave potentials are favored at 2$\sigma$ level, the natural inflation model is excluded at more than 2$\sigma$ level, the Starobinsky $R^2$ inflation model is only favored at around 2$\sigma$ level, and the spontaneously broken SUSY inflation model is now the most favored model.Comment: 10 pages, 6 figure

Constraining dark energy with Hubble parameter measurements: an analysis including future redshift-drift observations

Dark energy affects the Hubble expansion rate (namely, the expansion history) $H(z)$ by an integral over $w(z)$. However, the usual observables are the luminosity distances or the angular diameter distances, which measure the distance-redshift relation. Actually, dark energy affects the distances (and the growth factor) by a further integration over functions of $H(z)$. Thus, the direct measurements of the Hubble parameter $H(z)$ at different redshifts are of great importance for constraining the properties of dark energy. In this paper, we show how the typical dark energy models, for example, the $\Lambda$CDM, $w$CDM, CPL, and holographic dark energy (HDE) models, can be constrained by the current direct measurements of $H(z)$ (31 data in total, covering the redshift range of $z\in [0.07,2.34]$). In fact, the future redshift-drift observations (also referred to as the Sandage-Loeb test) can also directly measure $H(z)$ at higher redshifts, covering the range of $z\in [2,5]$. We thus discuss what role the redshift-drift observations can play in constraining dark energy with the Hubble parameter measurements. We show that the constraints on dark energy can be improved greatly with the $H(z)$ data from only a 10-year observation of redshift drift.Comment: 20 pages, 5 figures; final version published in EPJ

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

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