Does coupling to stress-energy imply coupling to Ricci?

[A/4]

Suppose there is a field that couples to the stress-energy tensor. For simplicity, assume it's a scalar field coupling to $$T=T^\mu_\mu$$. Since contracting Einstein's equations with the metric yield the relation $$R = 8\pi G T$$, is it correct to say that the field also couples to $$R$$?

 

[JustinLevy]

Suppose there is a field that couples to the stress-energy tensor. For simplicity, assume it's a scalar field coupling to $$T=T^\mu_\mu$$. Since contracting Einstein's equations with the metric yield the relation $$R = 8\pi G T$$, is it correct to say that the field also couples to $$R$$?

Hmm, I think this will ultimately just end up being a semantics argument. I see what you are saying, and agree with the statement in that context but it probably is best not to use "couple" in that way.

For example, consider an interaction that I can write a potential for in k-space. We can of course contract the momentum vector to mass, but it would give the wrong impression to claim the interaction was "coupling" to mass. Maybe that was not very clear, but do you understand my point?