Vacuum fluctuations and their implications for dark matter, dynamical collapse models and decoherence

Cosmological inflation is widely regarded to be a part of standard cosmology. Not only does it solve several cosmological puzzles, the quantum fluctuations of the inflaton field are also believed to seed the formation of stars, galaxies and the temperature anisotropy of the cosmic microwave background (CMB) radiation. However, there is still no general consensus on the nature of the scalar field driving inflation. Two of the simplest candidates, Starobinsky inflation and nonminimal Higgs inflation, are also among the most successful ones. In the first part of the thesis, a combination of the two models is constructed which is not only consistent with the CMB observations but also offers the possibility to account for the observed cold dark matter content in the universe by triggering the formation of primordial black holes. While the quantum perturbations offer to account for the structure in the universe, they also pose conceptual problems concerning its apparent classicality. Several works have sought a possible resolution by considering the continuous spontaneous localization (CSL) models in which a non-linear and stochastic time evolution of the wavefunction is considered as an alternative to the Schrödinger equation. The non-linearity leads to a continuous localization of the wavefunction within the time intervals which scale inversely with the size (the total mass or the number of particles) of the system so that the quantum-to-classical transition is achieved continuously. In the second part of the thesis, working within the framework of standard cosmological perturbation theory, a possible generalization of the mass proportional CSL model to a cosmological setting is proposed which is found to be compatible with the CMB constraints. The suppression of quantum superpositions does not necessarily require modifications to the Schrödinger equation. It can also be achieved within the framework of standard quantum mechanics due to decoherence. The phenomenon of decoherence or the suppression of the quantum superpositions is inevitable at the level of the system being observed, as soon us one realizes the practical impossibility of completely isolating the system from its environment. Nevertheless, one may still wonder what happens to macroscopic superpositions inside an ideal vacuum? Some works have even argued for the possibility that even the environment of the fundamentally unavoidable vacuum fluctuations can lead to decoherence. In order to address this question, in the third and final part of the thesis, the interaction of a non-relativistic electron with the electromagnetic vacuum is studied within the framework of open quantum systems. It is found that for an electron at rest, the vacuum fluctuations do not behave as an ordinary environment, such as that comprising of thermal photons or air molecules, and that it does not lead to irreversible loss of coherence. In addition, when the same mathematical formalism is applied to study the phenomenon of radiation emission by an accelerated non-relativistic electron, the resulting equation of motion appears to be free of the problems associated with the equation that is derived within classical electrodynamics: the run-away solution of the Abraham-Lorentz formula. While there has been a general expectation that these issues should not persist at a quantum mechanical level, it has not been shown clearly how they can be overcome. The discussion presented in the final part of the thesis offers to do so.