| We find a quantitative description for massive dark matter sources that decouple relativistically from the background and obey a relativistic ideal gas equation. This description allows us to explore the consequences such sources have on two basic cosmological observables, namely the age of the universe and angular-size distance at the surface of last scattering. We also explore the consequences of different, but constant, formulations for the equation of state of dark energy on these observables. One of the results we find is an absolute upper-bound to the age of the universe with given assumptions. It is also found that we can include a large range of hot dark matter sources and still satisfy the most stringent current estimates for angular-size distance at the surface for last scattering and the age of the universe. |
