Previous studies have shown that for the Supernova Legacy Survey three-year （SNLS3） data there is strong evidence for the redshifl- evolution of color-luminosity parameter β of type Ia supernovae （SN Ia）. In this paper, we explore the effects of varying β on the cosmological constraints of holographic dark energy （HDE） model. In addition to the SNLS3 data, we also use Planck distance prior data of cosmic microwave background （CMB）, as well as galaxy clustering （GC） data extracted from Sloan Digital Sky Survey （SDSS） data release 7 and Baryon Oscillation Spectroscopic Survey （BOSS）. We find that, for the both cases of using SN data alone and using SN＋CMB＋GC data, involving an additional parameter of β can reduce χ^2 by - 36; this shows that β deviates from a constant at 6σ- confidence levels. Adopting SN＋CMB＋GC data, we find that compared to the constant β case, varying β yields a larger fractional matter density Ωm0 and a smaller reduced Hubble constant h; moreover, varying β significantly increases the value of HDE model parameter c, leading to c ≈ 0.8, consistent with the constraint results obtained before Planck. These results indicate that the evolution of β should be taken into account seriously in the cosmological fits. In addition, we find that relative to the differences between the constant β and varying β（z） cases, the effects of different light-curve fitters on parameter estimation are very small.
The initial condition Ωde（zini）=n^2（1＋zini）^-2/4 at zini = 2000,widely used to solve the differential equation of the density of the new agegraphic dark energy（NADE） Ωde,makes the NADE model a single-parameter dark-energy cosmological model.However,we find that this initial condition is only applicable in a flat universe with only dark energy and pressureless matter.In fact,in order to obtain more information from current observational data,such as the cosmic microwave background（CMB） and the baryon acoustic oscillations（BAO）,we need to consider the contribution of radiation.For this situation,the initial condition mentioned above becomes invalid.To overcome this shortcoming,we investigate the evolutions of dark energy in matter-dominated and radiation-dominated epochs,and obtain a new initial condition de（zini）=n2（1＋zini）-2（1＋F（zini））2/4 at z ini = 2000,where F（z）≡Ωr0（1＋z）/[Ωm0＋Ωr0（1＋z）] with Ωr0 and Ωm0 being the current density parameters of radiation and pressureless matter,respectively.This revised initial condition is applicable for the differential equation of Ωde obtained in the standard Friedmann-Robertson-Walker（FRW） universe with dark energy,pressureless matter,radiation,and even spatial curvature,and can still keep the NADE model as a single-parameter model.With the revised initial condition and the observational data of type Ia supernova（SNIa）,CMB,and BAO,we finally constrain the NADE model.The results show that the single free parameter n of the NADE model can be constrained tightly.
In this work, we constrain the spectral index nt of the primordial gravitational wave power spectrum in a universe with sterile neutrinos by using the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, and the BICEP2 data. We call this model the ACDM＋r＋vs＋nt model. The additional massive sterile neutrino species can significantly relieve the tension between the Planck and BICEP2 data, and thus can reduce the possible effects of this tension on the fit results of nt. To constrain the parameters of sterile neutrino, we also utilize the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, and the cosmic shear data. We find that due to the fact that the BICEP2 data are most sensitive to the multipole （ - 150 corresponding to k - 0.01 Mpc^-1, there exists a strong anticorrelation between nt and r0.0o2 in the BICEP2 data, and this further results in a strongly blue-tilt spectrum. However, a slightly red-tilt tensor power spectrum is also allowed by the BICEP2 data in the region with larger value of r0.00z. By using the full data sets, we obtain mvisterile ^eff = 0.48 -0.13^＋0.11 eV, Near = 3.73 -0.37^＋0.34, and nt = 0.96 -0.63^ ＋0.48 for the ACDM＋r＋vs＋nt model.
In this paper, a new version of the interacting model of new agegraphic dark energy （INADE） is proposed and analyzed in detail. The interaction between dark energy and dark matter is reconsidered. The interaction term Q = bh0ραdcρ1-α dm is adopted, which abandons the Hubble expansion rate H and involves both Pae and Pare. Moreover, the new initial condition for the agegraphie dark energy is used, which solves the problem of accommodating baryon matter and radiation in the model. The solution of the model can be given using an iterative algorithm. A concrete example for the calculation of the model is given. Furthermore, the model is constrained by using the combined Planck data （Planck＋BAO＋SNIa＋H0） and the combined WMAP-9 data （WMAP＋BAO＋SNIa＋H0）. Three typical cases are considered： （A） Q = bHoPde, （B） Q = bHo√ρdeρdm,and （C） Q = bHopdm, which correspond to α = 1, 1/2, and 0, respectively. The departures of the models from the ACDM model are measured by the ABIC and AAIC values. It is shown that the INADE model is better than the NADE model in the fit, and the 1NADE（A） model is the best in fitting data among the three cases.
