Can Dark Matter be an artifact of extended theories of gravity?

In this article, we propose different background models of extended theories of gravity, which are minimally coupled to the SM fields, to explain the possibility of genesis of dark matter without affecting the SM particle sector. We modify the gravity sector by allowing quantum corrections motivated from (1) local $f(R)$ gravity and (2) non-minimally coupled gravity with SM sector and dilaton field. Next we apply conformal transformation on the metric to transform the action back to the Einstein frame. We also show that an effective theory constructed from these extended theories of gravity and SM sector looks exactly the same. Using the relic constraint observed by Planck 2015, we constrain the scale of the effective field theory ($\Lambda_{UV}$) as well as the dark matter mass ($M$). We consider two cases- (1) light dark matter (LDM) and (2) heavy dark matter (HDM), and deduce upper bounds on thermally averaged cross section of dark matter annihilating to SM particles. Further we show that our model naturally incorporates self interactions of dark matter. Using these self interactions, we derive the constraints on the parameters of the (1) local $f(R)$ gravity and (2) non-minimally coupled gravity from dark matter self interaction. Finally, we propose some different UV complete models from a particle physics point of view, which can give rise to the same effective theory that we have deduced from extended theories of gravity.