What is the relationship between the Higgs field and General Relativity?
While it is believed that the Higgs boson (carrier of the Higgs field force) is responsible for particle mass, gravity is such a negligible force on the particle level as to have virtually no effect on individual particles. It’s only when there are enough particles to have an impact in our macroworld that gravity is able to exert any influence. In a way, it’s like asking the effect of individual letters on the stock of a bookstore. It’s only when the letters are combined in enough concentration to create books that their effect on the stock carried in the bookstore matters. Remember that Relativity is concerned mainly with the world of the very large. Gravity in the quantum world is still not well understood (there is no valid theory of quantum gravity, for example).