Interacting Quantum Fields in Curved Spacetime I was thinking this night that how would the fields interaction or the vacuum expectation value of Higgs field changes when spacetime is not flat? 
e.g., the higgs field interact with the electron field to give mass to the electron, but what would happen to the interaction or to the vacuum expectation value of Higgs field if spacetime is not flat. 
Please explain the possible answer by considering this interacting fields case.
Also, i think for such cases we need a Quantum gravity theory that can accommodate gravity with QFT.
Feel free to answer the question at any level.
 A: How the fields interaction change on those cases is something you'd find in a quantum field theory in curved spacetime. One of the consequences is that what looks like a vacuum to one observer cannot look like a vacuum state to another observer, for example.
A: First, electrons are point particles, elementary particles, with fixed invariant mass. 
In SR, the invariant mass comes from the length of the four vector.
In the standard model, the Higgs mechanism gives mass to the particles at weak symmetry breaking.
All the particles (elementary) are described by the field that exists in all of spacetime. The vacuum expectation value of these fields is all zero. Except the Higgs field. This is a part of the mechanism that gave mass to the elementary particles.
You are saying that the electron gains mass because the electron field interacts with the Higgs field, you write this like it happens all the time, whenever they are interacting. This is a common misconception.
Symmetry breaking happened once, and at that point all the elementary particles gained mass. You write this like this is an interaction, and every time the electron has to gain mass. But it is not right. This happened at some point once, and since all the elementary particles have their (rest) masses.
A: The Higgs field doesn't give mass to the electron. It's responsible for giving mass to the gauge bosons of the electroweak force through spontaneous symmetry breaking.
However, not all of them gain mass. The U(1) gauge boson remains massless as it becomes the photon but the gauge bosons of weak force, the W particles are given mass. 
