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

Abstract

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 $ \boldmath $γ$=(\ga_x,\ga_m,\ga_r)$ and select a transversal interaction vector ${\mathbf{Q}}_{\mathbf{t}}$ in a sense that $\mathbf{Q_t}\cdot \boldmath $γ$=0$. We exactly solve the source equation for a linear ${\mathbf{Q}}_{\mathbf{t}}$, 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 ${\mathbf{Q}}_{\mathbf{t}}$. It turns to be that our model fulfills the severe bound of ${\Omega }_x(z\simeq 1100)<0.1$ and is consistent with the future constraints achievable by Planck and CMBPol experiments.

9 pages, 4 figures. Accepted for publication in Physical Review D

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• Finite time future singularities in the interacting dark sector
• Gravitational wave signatures from dark sector interactions
• The frozen vanilla model: Exploring dark sector interactions with delta effective theories
• Dissecting the $H_0$ and $S_8$ tensions with Planck + BAO + supernova type Ia in multi-parameter cosmologies