What does this equation mean?

If the electroweak vacuum is a local minimum rather than the global one, then in a quantum theory it is not perfectly stable; it can, in principle, decay by quantum tunneling to a lower-energy configuration, a possibility with no analogue in classical statistical mechanics. Coleman’s 1977 paper “Fate of the false vacuum” put the semiclassical machinery for this process on rigorous footing, treating decay as bubble nucleation: a small region of true vacuum appears through tunneling, and if the bubble is large enough that the volume energy released by the lower-energy interior outweighs the surface energy cost of the wall separating it from the surrounding false vacuum, the bubble expands, eventually at close to the speed of light, converting everything it touches [ 7 ] . The decay rate per unit four-volume in this picture takes the schematic form $\frac{\Gamma}{V} = A\,e^{-S_E}$. where $S_E$ is the Euclidean action evaluated on the classical solution that mediates the tunneling — the “bounce” — and A is a prefactor from fluctuations around that solution. The exponential dependence on the bounce action is the entire reason a metastable vacuum can be, for all practical purposes, permanent: a large action makes the exponent enormous and negative, suppressing the decay rate to a number that can be many, many orders of magnitude below one event per observable volume per age of the universe, without the vacuum being absolutely stable in any stronger sense. Coleman and De Luccia extended the calculation to include gravity in 1980, showing that gravitational corrections to the bounce action are not always negligible and can, in some regimes, dominate the outcome, particularly in the late stages of bubble growth and in cases where the vacuum energies involved are comparable to the Planck scale [ 8 ] . For the scales relevant to electroweak vacuum decay, later work established that as long as the bounce’s characteristic scale stays far below the Planck scale, gravitational corrections to the action remain a small, calculable correction rather than a qualitative change to the result, which is part of why modern calculations can treat the calculation in flat spacetime with reasonable confidence [ 12 ] .