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

Cooperative Local Caching under Heterogeneous File Preferences

Local caching is an effective scheme for leveraging the memory of the mobile terminal (MT) and short range communications to save the bandwidth usage and reduce the download delay in the cellular communication system. Specifically, the MTs first cache in their local memories in off-peak hours and then exchange the requested files with each other in the vicinity during peak hours. However, prior works largely overlook MTs' heterogeneity in file preferences and their selfish behaviours. In this paper, we practically categorize the MTs into different interest groups according to the MTs' preferences. Each group of MTs aims to increase the probability of successful file discovery from the neighbouring MTs (from the same or different groups). Hence, we define the groups' utilities as the probability of successfully discovering the file in the neighbouring MTs, which should be maximized by deciding the caching strategies of different groups. By modelling MTs' mobilities as homogeneous Poisson point processes (HPPPs), we analytically characterize MTs' utilities in closed-form. We first consider the fully cooperative case where a centralizer helps all groups to make caching decisions. We formulate the problem as a weighted-sum utility maximization problem, through which the maximum utility trade-offs of different groups are characterized. Next, we study two benchmark cases under selfish caching, namely, partial and no cooperation, with and without inter-group file sharing, respectively. The optimal caching distributions for these two cases are derived. Finally, numerical examples are presented to compare the utilities under different cases and show the effectiveness of the fully cooperative local caching compared to the two benchmark cases