Dark matter, dark energy, and dark radiation coupled with a transversal interaction

LUIS P. CHIMENTO AND MARTIN G. RICHARTE

PHYSICAL REVIEW D

AMER PHYSICAL SOC

Lugar: New York; Año: 2012 vol. 86 p. 1 - 10

1550-7998

We investigate a cosmological scenario with three interacting components that includes dark matter, dark energy, and radiation in the spatially flat Friedmann-Robertson-Walker universe. We introduce a 3-dimensional internal space, the interaction vector $mathbf{Q}=(Q_{x}, Q_{m}, Q_{r})$ satisfying the constraint plane $Q_{x}+ Q_{m}+ Q_{r}=0$, the barotropic index vector $mbox{oldmath ${gamma}$}=(ga_x,ga_m,ga_r)$ and select a transversal interaction vector $mathbf{Q_t}$ in a sense that $mathbf{Q_t}cdotmbox{oldmath ${gamma}$}=0$. We exactly solve the source equation for a linear $mathbf{Q_t}$, that depends on the total energy density and its derivatives up to third order, and find all the component energy densities. We obtain a large set of interactions for which the source equation admits a power law solution and show its asymptotic stability by constructing the Lyapunov function. We apply the $chi^{2}$ method to the observational Hubble data for constraining the cosmic parameters, and analyze the amount of dark energy in the radiation era for the above linear $mathbf{Q_t}$. It turns to be that our model fulfills the severe bound of $Omega_{x}(zsimeq 1100)