Kriging Interpolating Cosmic Velocity Field

[abridged] Volume-weighted statistics of large scale peculiar velocity is preferred by peculiar velocity cosmology, since it is free of uncertainties of galaxy density bias entangled in mass-weighted statistics. However, measuring the volume-weighted velocity statistics from galaxy (halo/simulation particle) velocity data is challenging. For the first time, we apply the Kriging interpolation to obtain the volume-weighted velocity field. Kriging is a minimum variance estimator. It predicts the most likely velocity for each place based on the velocity at other places. We test the performance of Kriging quantified by the E-mode velocity power spectrum from simulations. Dependences on the variogram prior used in Kriging, the number $n_k$ of the nearby particles to interpolate and the density $n_P$ of the observed sample are investigated. First, we find that Kriging induces $1\%$ and $3\%$ systematics at $k\sim 0.1h{\rm Mpc}^{-1}$ when $n_P\sim 6\times 10^{-2} ({\rm Mpc}/h)^{-3}$ and $n_P\sim 6\times 10^{-3} ({\rm Mpc}/h)^{-3}$, respectively. The deviation increases for decreasing $n_P$ and increasing $k$. When $n_P\lesssim 6\times 10^{-4} ({\rm Mpc}/h)^{-3}$, a smoothing effect dominates small scales, causing significant underestimation of the velocity power spectrum. Second, increasing $n_k$ helps to recover small scale power. However, for $n_P\lesssim 6\times 10^{-4} ({\rm Mpc}/h)^{-3}$ cases, the recovery is limited. Finally, Kriging is more sensitive to the variogram prior for lower sample density. The most straightforward application of Kriging on the cosmic velocity field does not show obvious advantages over the nearest-particle method (Zheng et al. 2013) and could not be directly applied to cosmology so far. However, whether potential improvements may be achieved by more delicate versions of Kriging is worth further investigation.Comment: 11 pages, 5 figures, published in PR

Statefinder hierarchy exploration of the extended Ricci dark energy

We apply the statefinder hierarchy plus the fractional growth parameter to explore the extended Ricci dark energy (ERDE) model, in which there are two independent coefficients $\alpha$ and $\beta$. By adjusting them, we plot evolution trajectories of some typical parameters, including Hubble expansion rate $E$, deceleration parameter $q$, the third and fourth order hierarchy $S_3^{(1)}$ and $S_4^{(1)}$ and fractional growth parameter $\epsilon$, respectively, as well as several combinations of them. For the case of variable $\alpha$ and constant $\beta$, in the low-redshift region the evolution trajectories of $E$ are in high degeneracy and that of $q$ separate somewhat. However, the $\Lambda$CDM model is confounded with ERDE in both of these two cases. $S_3^{(1)}$ and $S_4^{(1)}$, especially the former, perform much better. They can differentiate well only varieties of cases within ERDE except $\Lambda$CDM in the low-redshift region. For high-redshift region, combinations $\{S_n^{(1)},\epsilon\}$ can break the degeneracy. Both of $\{S_3^{(1)},\epsilon\}$ and $\{S_4^{(1)},\epsilon\}$ have the ability to discriminate ERDE with $\alpha=1$ from $\Lambda$CDM, of which the degeneracy cannot be broken by all the before-mentioned parameters. For the case of variable $\beta$ and constant $\alpha$, $S_3^{(1)}(z)$ and $S_4^{(1)}(z)$ can only discriminate ERDE from $\Lambda$CDM. Nothing but pairs $\{S_3^{(1)},\epsilon\}$ and $\{S_4^{(1)},\epsilon\}$ can discriminate not only within ERDE but also ERDE from $\Lambda$CDM. Finally we find that $S_3^{(1)}$ is surprisingly a better choice to discriminate within ERDE itself, and ERDE from $\Lambda$CDM as well, rather than $S_4^{(1)}$.Comment: 8 pages, 14 figures; published versio

Measurement of the squeezed vacuum state by a bichromatic local oscillator

We present the experimental measurement of a squeezed vacuum state by means of a bichromatic local oscillator (BLO). A pair of local oscillators at $\pm$5 MHz around the central frequency $\omega_{0}$ of the fundamental field with equal power are generated by three acousto-optic modulators and phase-locked, which are used as a BLO. The squeezed vacuum light are detected by a phase-sensitive balanced-homodyne detection with a BLO. The baseband signal around $\omega_{0}$ combined with a broad squeezed field can be detected with the sensitivity below the shot-noise limit, in which the baseband signal is shifted to the vicinity of 5 MHz (the half of the BLO separation). This work has the important applications in quantum state measurement and quantum informatio