We review two models implementing Newtonian gravity through a continuous measurement and feedback mechanism. These are the Kafri-Taylor-Milburn (KTM) and the Tilloy-Diósi (TD) models. We compare the KTM and the TD models in an appropriate limit and explicitly show that the associated decoherence effects are different. We propose a classification of models which implement gravity through a continuous measurement and feedback mechanism based on two main criteria: the type of observable measured and the type of interaction implemented through the feedback. We argue that within these scenarios, the TD model is the only framework implementing a full Newtonian gravitational interaction physically consistent.
We also study how dynamical collapse models have been implemented within an inflationary context. We
discuss relevant aspects for the generalization of these models within a relativistic context, such as the choice of the collapse operator and its properties. We propose an approach to treat the dynamical collapse model contribution to the evolution of a system as a perturbation to the standard cosmological scenario. We analyse the modifications to the power spectrum associated to scalar cosmological perturbations during inflation and the radiation-dominated era.
