Manu Paranjape, author of The Theory and Applications of Instanton Calculations, discusses the potential end of the universe.

Recently, reports in the media have warned that our universe could be destroyed abruptly in a collision with a bubble of negative energy, and that the process may have already started! Experts theorise that the end of the universe could be caused by a bubble of true vacuum of (relative) negative energy expanding and hitting us out of the blue, meaning we are presently living in a false vacuum. Moreover, the Higgs boson field, sometimes called the god-particle and responsible for giving mass to all known particles, is actually in a meta-stable state.

The decay lifetime of the present value of the Higgs field has been calculated in great detail. In fact, the calculations reported in an article published in the Physical Review are the most complete and detailed to date and, for the first time, thoroughly take into account the scale invariance of the underlying theory. These calculations suggest that the universe should live for another 10^139 years (10 to the 139th power).

Quantum fields in meta-stable false vacuum states decay via quantum tunnelling. The tunnelling rate can be calculated using the methods of Instanton Calculations as covered in my book, The Theory and Applications of Instanton Calculations. Instantons are classical solutions to the Euclidean equations of motion. The amplitudes for the decay of meta-stable states are calculated using bounce type instantons. The instanton solution starts at the false vacuum then reaches a configuration called the bounce, after which it returns to the false vacuum. The tunnelling transition causes the configuration corresponding to the bounce to materialize, and its subsequent evolution occurs in real time. The bubble of true vacuum, which could destroy the universe, would form through a tunnelling transition as first described in “The fate of the false vacuum. 1” by S. R. Coleman and “The fate of the false vacuum. 2” by C. G. Callan, Jr. and S. R. Coleman. Once the bubble of true vacuum forms, the rate of expansion quickly accelerates to the speed of light, meaning that there is little time before catastrophe.

Reportedly, the tunnelling transition to a true vacuum bubble could have already taken place in a remote corner of the universe. The bubble could be expanding at the speed of light, and we don’t even know it. As Coleman explains in his aforementioned articles, there will not even be enough time for a single neuron to fire before the wall hits us. No point in worrying about it, we won’t know what hit us! This aspect specifically, but also the entire calculation is covered in Chapter 6 of my book (free to read until 10th May on Cambridge Core).

In Chapter 4, I cover the analysis of the tunnelling decay of a meta-stable state. Through proper analytic continuation of the functional integral, I show how the imaginary part of the energy is obtained which, of course, gives rise to the width of the meta-stable state. The background calculations mentioned earlier, as well as those corresponding to details of computing fluctuation determinants, changing variables to collective coordinates, determining zero modes and negative modes are covered in my book.