New initial condition of the new agegraphic dark energy model

The initial condition Ω_de(z_ini)=n²(1+z_ini)^–2/4 at z_ini=2000 widely used to solve the differential equation of the density of the new agegraphic dark energy (NADE) Ω_de, makes the NADE model be 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 shortage, we investigate the evolutions of dark energy in the matter-dominated and the radiation-dominated epochs, and obtain a new initial condition Ω_de(z_ini)=n²(1+z_ini)^–2(1+√F(z_ini)²/4 at z_ini=2000, where F(z)≡Ω_r0(1+z)/[Ω_m0+Ω_r0(1+z)] with Ω_r0 and Ω_m0 being the current density parameters of radiation and pressureless matter, respectively. This revised initial condition is applicable for the differential equation of Ω_de 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 being 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.