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

Comparing holographic dark energy models with statefinder

We apply the statefinder diagnostic to the holographic dark energy models, including the original holographic dark energy (HDE) model, the new holographic dark energy model, the new agegraphic dark energy (NADE) model, and the Ricci dark energy model. In the low-redshift region the holographic dark energy models are degenerate with each other and with the $\Lambda$CDM model in the $H(z)$ and $q(z)$ evolutions. In particular, the HDE model is highly degenerate with the $\Lambda$CDM model, and in the HDE model the cases with different parameter values are also in strong degeneracy. Since the observational data are mainly within the low-redshift region, it is very important to break this low-redshift degeneracy in the $H(z)$ and $q(z)$ diagnostics by using some quantities with higher order derivatives of the scale factor. It is shown that the statefinder diagnostic $r(z)$ is very useful in breaking the low-redshift degeneracies. By employing the statefinder diagnostic the holographic dark energy models can be differentiated efficiently in the low-redshift region. The degeneracy between the holographic dark energy models and the $\Lambda$CDM model can also be broken by this method. Especially for the HDE model, all the previous strong degeneracies appearing in the $H(z)$ and $q(z)$ diagnostics are broken effectively. But for the NADE model, the degeneracy between the cases with different parameter values cannot be broken, even though the statefinder diagnostic is used. A direct comparison of the holographic dark energy models in the $r$--$s$ plane is also made, in which the separations between the models (including the $\Lambda$CDM model) can be directly measured in the light of the current values $\{r_0,s_0\}$ of the models.Comment: 8 pages, 8 figures; accepted by European Physical Journal C; matching the publication versio

A search for sterile neutrinos with the latest cosmological observations

We report the result of a search for sterile neutrinos with the latest cosmological observations. Both cases of massless and massive sterile neutrinos are considered in the $\Lambda$CDM cosmology. The cosmological observations used in this work include the Planck 2015 temperature and polarization data, the baryon acoustic oscillation data, the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck lensing data, and the cosmic shear data. We find that the current observational data give a hint of the existence of massless sterile neutrino (as dark radiation) at the 1.44$\sigma$ level, and the consideration of an extra massless sterile neutrino can indeed relieve the tension between observations and improve the cosmological fit. For the case of massive sterile neutrino, the observations give a rather tight upper limit on the mass, which implies that actually a massless sterile neutrino is more favored. Our result is consistent with the recent result of neutrino oscillation experiment done by the Daya Bay and MINOS collaborations, as well as the recent result of cosmic ray experiment done by the IceCube collaboration.Comment: 16 pages, 4 figures; accepted for publication in Eur. Phys. J.

Quantifying the impact of future Sandage-Loeb test data on dark energy constraints

The Sandage-Loeb (SL) test is a unique method to probe dark energy in the "redshift desert" of $2\lesssim z\lesssim 5$, and thus it provides an important supplement to the other dark energy probes. Therefore, it is of great importance to quantify how the future SL test data impact on the dark energy constraints. To avoid the potential inconsistency in data, we use the best-fitting model based on the other geometric measurements as the fiducial model to produce 30 mock SL test data. The 10-yr, 20-yr, and 30-yr observations of SL test are analyzed and compared in detail. We show that compared to the current combined data of type Ia supernovae, baryon acoustic oscillation, cosmic microwave background, and Hubble constant, the 30-yr observation of SL test could improve the constraint on $\Omega_m$ by about $80$ and the constraint on $w$ by about $25$. Furthermore, the SL test can also improve the measurement of the possible direct interaction between dark energy and dark matter. We show that the SL test 30-yr data could improve the constraint on $\gamma$ by about $30$ and $10$ for the $Q=\gamma H\rho_c$ and $Q=\gamma H\rho_{de}$ models, respectively.Comment: 10 pages, 3 figure