Massive graviton dark matter with environment dependent mass: A natural explanation of the dark matter-baryon ratio

We propose a scenario that can naturally explain the observed dark matter-baryon ratio in the context of bimetric theory with a chameleon field. We introduce two additional gravitational degrees of freedom, the massive graviton and the chameleon field, corresponding to dark matter and dark energy, respectively. The chameleon field is assumed to be nonminimally coupled to dark matter, i.e., the massive graviton, through the graviton mass terms. We find that the dark matter-baryon ratio is dynamically adjusted to the observed value due to the energy transfer by the chameleon field. As a result, the model can explain the observed dark matter-baryon ratio independently from the initial abundance of them.

Figure 1

The evolution of the density parameters and the total equation of state parameters in terms of the Jordan frame scale factor $a_J=Aa$ which is normalized to be ${\mathrm{\Omega }}_{\varphi }{|}_{a_J=1}=0.7$. We set $\beta =3$ and $\lambda =2\beta /5=6/5$ in model A (4.1). We assume the initial ratio between dark matter and baryon as ${\rho }_{G,i}/{\rho }_{b,i}={\mathrm{\Omega }}_{G,i}/{\mathrm{\Omega }}_{b,i}=200$ with ${\varphi }_i=0$.

Figure 2

The evolution of the chameleon field $\varphi$ in models A and B with ${\rho }_{G,i}/{\rho }_{b,i}=200$.

Figure 3

The same as Fig. 1 and the evolution of ${\alpha }_A$ and ${\alpha }_f$ in model B. We set $\beta =3$, $\lambda =6/5$ and $M=M_p$. We assume the same initial condition as Fig. 1.

Figure 4

The evolution of the density parameters and the total equation of state parameter. We set $\beta =1$ and $\lambda =2/5$ in model A. We assume the initial ratio between dark matter and baryon as ${\rho }_{G,i}/{\rho }_{b,i}=0.01$ with ${\varphi }_i=0$.

Figure 5

The same as Fig. 3 in the less-produced case. We set $\beta =5$, $\lambda =2$ and $M=M_p$, and assume ${\rho }_{G,i}/{\rho }_{b,i}=0.01$ with ${\varphi }_i=0$.

Figure 6

The evolution of the chameleon field $\varphi$ with ${\rho }_{G,i}/{\rho }_{b,i}=0.01$ and ${\varphi }_i=0$. We set $\beta =1$, $\lambda =2/5$ for model A and $\beta =5$, $\lambda =2$, $M=M_p$ for model B.