With that headline, I suppose I should begin this article with a definitive and categorical NO!

So then why is this question even being asked? Because Stephen Hawking likes selling books and is mischievous enough to give doomsday scenarios that the media revels in. He knows that making a wild statements about how the world will end will get his new book a lot of publicity, and perhaps if the publicity leads to people learning about modern particle physics and discussing the latest theories, it isn't such a bad thing. I suspect that it is more likely that the masses will read a quick statement like this and assume that it is true, which it isn't.

A fraction of a second after the Big Bang and the birth of the Universe, space was filling up with a Higgs field which caused all matter to acquire an effective mass due to its difficulty in passing through this Higgs sea. This Higgs field is controlled by an as yet unknown potential energy, which has a high energy when the Higgs has zero-density and a lower energy at some non-zero density. The density of the Higgs (represented in the diagram below by a red dot) falls down this potential until it settles at a minimum. The oscillations around the minimum are essentially what was measured at the LHC.

All of this is known and confirmed in experiments. However the part of the potential function on the right of the diagram is as yet unknown. The simplest models simply have it rising and so higher densities of the Higgs field will have higher energies. If energy is added to the Higgs field, it will move up this potential until it runs out of energy, and then will fall back down to the minimum.

However this is not the only possible potential energy for the Higgs field. It could also drop down again so that either there is a minimum at a higher Higgs density, or even no minimum and the Higgs will just increase in density forever. If sufficient energy is added to the Higgs field, it will eventually cross some peak in the potential and not return to its original minium ever again. It is this possibility that worries some people.

This is indeed a possibility, and if it happens then the Universe will be destroyed. However the energy of this peak is so far above the limits of particle accelerators that it will not be measured for centuries, and probably not for millenia. And long before then, other measurements of the Higgs particle will predict whether such a peak exists, and we will then be able to turn back. 

And more important for this discussion, there do exist natural phenomena in nature that can reach very high energies and would have long ago destroyed the Universe if this was possible. Nature also allows for quantum tunneling through this second peak at lower energies, and this too would have happened long ago if it was possible.

In the end, if the Universe can be destroyed by a run-away Higgs field then it is going to happen whether we run experiments or not. Nature will cause this to happen long before humanity will.

So should we waste our lives worrying about a catastrophic end to the Universe which will be sudden and unavoidable, and which we can do nothing to stop? I will let you be the judge of that...