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In this article, we propose different background models of extended theoriesof gravity, which are minimally coupled to the SM fields, to explain thepossibility 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 anddilaton field. Next we apply conformal transformation on the metric totransform the action back to the Einstein frame. We also show that an effectivetheory constructed from these extended theories of gravity and SM sector looksexactly the same. Using the relic constraint observed by Planck 2015, weconstrain the scale of the effective field theory ($\Lambda_{UV}$) as well asthe 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 averagedcross section of dark matter annihilating to SM particles. Further we show thatour model naturally incorporates self interactions of dark matter. Using theseself interactions, we derive the constraints on the parameters of the (1) local$f(R)$ gravity and (2) non-minimally coupled gravity from dark matter selfinteraction. Finally, we propose some different UV complete models from aparticle physics point of view, which can give rise to the same effectivetheory that we have deduced from extended theories of gravity.

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