The Effects of Spontaneous Symmetry Breaking on Gravity

Staff Emeritus
I'm trying to understand inflation (in the cosmic sense). I know that ultimately that's a subject that involves both quantum field theory and General Relativity, but I'm wondering to what extent it can be understood from the point of view of classical (non-quantum) GR.

If you have a classical field like the Higgs that is initially in an unstable equilbrium, then it can make a transition to a stable equilibrium and release energy. What I don't understand is the effect of this transition on gravity (or spacetime curvature). The transition converts a kind of potential energy in the field to active energy in the form of heat. But in GR, potential energy curves spacetime just as other kinds of energy does. So would such a transition have an effect on spacetime curvature at all?

PeterDonis
Mentor
2020 Award
The transition converts a kind of potential energy in the field to active energy in the form of heat. But in GR, potential energy curves spacetime just as other kinds of energy does. So would such a transition have an effect on spacetime curvature at all?

Yes. Before the transition, the Higgs field has an effective stress-energy tensor that is equivalent to a large positive cosmological constant, i.e., ##T_{ab} = \Lambda g_{ab}## with ##\Lambda## large and positive. This is what causes inflation, i.e., exponentially accelerating expansion.

After the transition, the SET is now a highly relativistic fluid with a large energy density. This SET looks something like ##T_{ab} = \left( \rho + p \right) u^a u^b + p g_{ab}##, where ##u^a## is the fluid 4-velocity and ##p \approx \frac{1}{3} \rho## (because the fluid is highly relativistic). This sort of SET does not cause inflation; its dynamics are that of a radiation-dominated universe, with a decelerating expansion.