Study of metastable vacuum decay with gravity

It is possible for a classical field theory to have two stable equilibrium states with different energy densities. In the quantum field theory the state of higher energy density becomes unstable through barrier penetration. It is a false vacuum, whyle lower state we call true vacuum. The transition happens through a first order phase transition started by nucleation of bubbles of the new vacuum, which increases and takes all the system. The main motivations of my resent work are researches done by Coleman and Coleman de Luccia. In those works authors study decay of metastable vacuum in flat space-time and with gravity. The phase transition probability is expressed by functional integral in Euclidean space-time. Transition amplitude is given by Euclidean action, which is integral along classical solution (instanton). In the absence of gravity, one can prove that tunneling instantons exhibit exactly one negative mode in their spectrum of linear fluctuations. In the presence of gravity the kinetic term of the fluctuations can change sign somewhere along the instanton. Kinetic term negativity produces infinite number of negative modes . That is a catastrophic instability and means creations of infinite number of particles. In Khvedelidze, Lavrelashvili and Tanaka's work is shown existence of infinite number of negative modes in spectrum of small perturbations. The main goal of my thesis is to reaserch if negative mode problem is connected with planck's scale. Study of pre-exponential factor A shows that in quadratic action before the kinetic term appears factor Q, which becomes negative along the instanton. In this thesis I study Q coefficient negativity far from Planck's scale. I have found numerical solutions for field equations far from Planck's scale for which Q coefficient becomes negative.