On initial condition of the new agegraphic dark energy model

Details On initial condition of the new agegraphic dark energy model On initial condition of the new agegraphic dark energy model

2012-01-26

arxiv.org/abs/1201.5446v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, 1 figure

Scientific paper

The initial condition $\Omega_{\rm de}(z_{\rm ini})=n^2(1+z_{\rm ini})^{-2}/4$ at $z_{\rm ini}=2000$ widely used to solve the differential equation of $\Omega_{\rm de}$, the density of the new agegraphic dark energy (NADE), makes the NADE model be a single-parameter dark-energy cosmological model. However, this initial condition, we find, 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 cosmic microwave background (CMB) and baryon acoustic oscillations (BAO), it often needs us to consider the contribution of radiation. For this situation, the initial condition mentioned above becomes invalid. To overcome this shortage, we deeply investigate the evolution of NADE in the matter-dominated and radiation-dominated epochs, and obtain a new initial condition $\Omega_{\rm de}(z_{\rm ini}) = \frac{n^2(1+z_{\rm ini})^{-2}}{4} (1+\sqrt{F(z_{\rm ini})})^2$ at $z_{\rm ini}=2000$. Here $F(z)\equiv\frac{\Omega_{r0}(1+z)}{\Omega_{m0}+\Omega_{r0}(1+z)}$ with $\Omega_{r0}$ and $\Omega_{m0}$ the current density parameters of radiation and pressureless matter, respectively. This revised initial condition is applicable for the differential equation of $\Omega_{\rm de}$ obtained in the standard 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.

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