Bubble formation in phi^4 theory in the thin-wall limit and beyond
  Scalar field theory with an asymmetric potential is studied at zero temperature and high-temperature for phi^4 theory with both phi and phi^3 symmetry breaking. The equations of motion are solved numerically to obtain O(4) symmetric and O(3) cylindrical symmetric bounce solutions. These solutions control the rates for tunneling from the false vacuum to the true vacuum by bubble formation. The range of validity of the thin-wall approximation (TWA) is investigated. An analytical solution for the bounce is presented, which reproduces the action in the thin-wall as well as the thick-wall limits. 
Hatem Widyan, A. Mukherjee, N. Panchapakesan and R. P. Saxena   (Department of Physics, University of Delhi, India)