Cosmological kinetic mixing

In this paper we generalize the kinetic mixing idea to time reparametrization invariant theories, namely, relativistic point particles and cosmology in order to obtain new insights for dark matter and energy. In the first example, two relativistic particles interact through an appropriately chosen coupling term. It is shown that the system can be diagonalized by means of a nonlocal field redefinition, and, as a result of this procedure, the mass of one the particles gets rescaled. In the second case, inspired by the previous example, two cosmological models (each with its own scale factor) are made to interact in a similar fashion. The equations of motion are solved numerically in different scenarios (dust, radiation or a cosmological constant coupled to each sector of the system). When a cosmological constant term is present, kinetic mixing rescales it to a lower value which may be more amenable to observations.

Figure 1

Numerical solution of the field equations when pressureless matter is coupled to both sectors, for different values of the coupling constant ($\gamma =\{-0.95,-0.65,-0.35,0.25,0.55,0.85\}$). Upper curves correspond to increasing values of $\gamma$. The dotted lines represent the standard GR solution. (a) Evolution of the scale parameter $a(t)$. (b) Evolution of the Hubble parameter $H_a(t)$. (c) A comparison between the evolution of the scale parameter $a(t)$ with kinetic mixing and the standard GR evolution $a_{GR}(t)$ (coupled to dust).

Figure 2

Numerical solution of the field equations when radiation is coupled to both sectors, for different values of the coupling constant ($\gamma =\{-0.95,-0.65,-0.35,0.25,0.55,0.85\}$). Upper curves correspond to increasing values of $\gamma$. The dotted lines represent the standard GR solution. (a) Evolution of the scale parameter $a(t)$. (b) Evolution of the Hubble parameter $H_a(t)$. (c) A comparison between the evolution of the scale parameter $a(t)$ with kinetic mixing and the standard GR evolution $a_{GR}(t)$ (coupled to radiation).

Figure 3

Numerical solution of the field equation when dust is coupled the $a$-sector, while radiation couples to the $b$-sector, for different values of the coupling constant ($\gamma =\{-0.65,-0.35,-0.15,0.3,0.6,0.9\}$). Upper curves correspond to increasing values of $\gamma$. The dotted lines represent the standard GR solutions. (a) Evolution of the scale parameter $a(t)$. (b) Evolution of the scale parameter $b(t)$. (c) Evolution of the Hubble parameter $H_a(t)$. (d) Evolution of the Hubble parameter $H_b(t)$. (e) A comparison between the evolution of the scale parameter $a(t)$ with kinetic mixing and the standard GR evolution $a_{GR}(t)$ (coupled to dust). (f) A comparison between the evolution of the scale parameter $b(t)$ with kinetic mixing and the standard GR evolution $b_{GR}(t)$ (coupled to radiation).

Figure 4

Numerical solution of the field equation when a cosmological constant couples to the $a$-sector, while dust couples to the $b$-sector, for different values of the coupling constant ($\gamma =\{0.15,0.3,0.75\}$). The closest curves to the dotted line correspond to smaller values of $\gamma$. The dotted lines represent the standard GR solution. (a) Evolution of the scale parameter $a(t)$. (b) Evolution of the scale parameter $b(t)$. (c) Evolution of the Hubble parameter $H_a(t)$. (d) Evolution of the Hubble parameter $H_b(t)$. (e) Evolution of the energy density $\rho (t)$ in the $a$-sector. (f) Evolution of the energy density $\stackrel{\sim }{\rho }(t)$ in the $b$-sector.