Vacuum transitions and eternal inflation

In this thesis, we focus on aspects of inflation and eternal inflation arising in scalar field theories coupled to gravity which possess a number of metastable states. Such theories contain instantons that interpolate between the metastable potential minima, corresponding to the nucleation of bubbles containing a new phase in a background of the old phase. In the first part of this thesis, we describe the classical dynamics and quantum nucleation of vacuum bubbles. We classify all possible spherically symmetric, thin-wall solutions with arbitrary interior and exterior cosmological constant, and find that bubbles possessing a turning point are unstable to aspherical perturbations. Next, we turn to the quantum nucleation of bubbles with zero mass. Focusing on instantons interpolating between positive and negative energy minima, we find that there exists a "Great Divide" in the space of potentials, across which the lifetime of metastable states differs drastically. Generalizing a semi-classical Hamiltonian formalism to treat the nucleation of bubbles with nonzero mass, we show that a number of tunneling mechanisms can be unified in the thin-wall limit, and directly compare their probabilities. In the second part of this thesis, we discuss the measure problem in eternal inflation. We give a detailed analysis of the prospects for making predictions in eternal inflation, and describe the existing probability measures and the connections between them. We then show that all existing measures exhibit a number of rather generic phenomena, for example strongly weighting vacua that can undergo rapid transitions between each other. It is argued that making predictions will require a measure that weights histories as opposed to vacua, and we develop a formalism to addresses this. Finally, we assess the prospects for observing collisions between vacuum bubbles in an eternally inflating universe. Contrary to conventional wisdom, we find that under certain assumptions most positions inside a bubble should have access to a large number of collision events. We calculate the expected number and angular size distribution of such collisions on an observer's "sky", finding that for typical observers the distribution is anisotropic and includes many bubbles, each of which will affect the majority of the observer's sky.