New initial condition of the new agegraphic dark energy model

Abstract

The initial condition Ωde(zini) = n2 (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 , 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.