3. Conclusion

In general, dark matter is weakly coupled to standard luminous matter (except for gravitational coupling on large scales). However, it is unknown how exactly dark matter interacts with non-standard entities, such as dark energy and the inflaton. We have examined two cases of dark matter coupling.

In the first case, we studied the coupling of dark matter to dark energy without assuming a particular functional form for the conversion rate, and we assumed that dark matter and dark energy were the only components present in the universe. We illustrated a useful way of having interaction between dark matter and dark energy that avoided the need to specify a parametrization for Q, and this is convenient since we do not know what Q should be from first principles. We accomplished our goal by assuming a slowly varying dark energy field and a value of ξ that is very small. We pointed out that, at the very least, there should be coupling between dark matter and dark energy via the ξ term in the Lagrangian necessary for the renormalization of the scalar field for dark energy in a curved background, and we showed in our plots that the magnitude of the coupling Q indeed grew as the coupling constant ξ increased. Of course, one may consider the case of scalar field dark matter, and then another term coupling this dark matter field to R would be present and would indirectly represent another coupling of dark matter and dark energy. Ideally, what is needed is a direct calculation of the cross section between dark energy and dark matter in curved space-time in order to see fundamentally how this non-minimal coupling term affects their interaction. Also, a more accurate treatment would allow for other components of the universe to be present, which would allow for coupling between dark matter and regular luminous matter strictly through curvature via the Ricci scalar, although we would also expect this interaction to be small in general. A more accurate treatment would also allow for back-reaction on the metric and a quantum treatment of gravity itself.

In the second case of dark matter coupling, we showed one way that dark matter may be coupled to the inflaton. We showed an interesting connection between the two fields in the luminogenesis model, which is a unified field theory that consistently combines the Standard Model with other groups that contain dark matter, the inflaton, and other non-standard fields. Using constraints from N-body structure formation simulations, we constrained the mass of self-interacting dark matter, which in turn constrained the DUT scale and the M<sup>1</sup> scale of the luminogenesis model. This constraint on the DUT scale then provided an upper limit on the number of e-folds of inflation allowed in the model.

There are many potential ways in which dark matter couples to other fields, and we simply pointed out interesting facets of two different possible couplings. The true nature of dark matter and how it interacts with other matter is yet to be fully unraveled, but we must pursue every feasible avenue in order to be ready when more precise measurements are available.
