The connection between the Higgs field and spacetime arises from the framework of the theory known as the Standard Model of particle physics and the broader concept of general relativity.
In the Standard Model, the Higgs field is a fundamental field that permeates all of space. It interacts with elementary particles and gives them mass through a process called spontaneous symmetry breaking. According to this theory, particles acquire mass by interacting with the Higgs field, similar to how an object moving through a medium experiences resistance and therefore "feels" its presence.
On the other hand, general relativity describes the curvature of spacetime in the presence of mass and energy. According to Einstein's theory, massive objects curve the fabric of spacetime around them, causing the effect we perceive as gravity.
The connection between the Higgs field and spacetime lies in the fact that the mass generated by the Higgs field influences the curvature of spacetime. In this sense, the presence of mass (which arises from the interaction with the Higgs field) determines the geometry of the surrounding spacetime, creating the gravitational field associated with that mass.
Therefore, the Higgs field is indirectly connected to the curvature of spacetime through the generation of mass. The presence of mass affects the geometry of spacetime, and this curvature, in turn, governs the behavior of objects under gravity.