Does the nature of the assortment of virtual particles depend upon the warping of spacetime in a direct manner ?
I will undertake a hand waving answer and maybe since the question will come to the top somebody knowledgeable will give a full answer.
Virtual particles are the province of quantum mechanics and led to the development of quantum field theory with creation and annihilation operators.
This led to the realization that the vacuum, in the QFT description is not "empty" but is like a sea where virtual particles continuously create and annihilate with no loss of energy. The vacuum is a "ground state".
Interestingly enough this field theoretic description with creation and annihilation operators does not correspond one to one with particle physics. Back in 1963 I sat through a field theoretical course for nuclear physics where creation and annihilation operators acted on nuclear levels. But I digress.
Now the curvature of space is a unique proposal of General Relativity. General relativity has not been quantized in an irrefutable manner. String theorists believe that they have managed to do that, but I leave it to them to describe what a sea of virtual particles in a string universe is like.
Trying to naively say: suppose gravity is quantized in the classic QFT manner and gravitons exist in the vacuum sea too,
the answer would be: the higher the curvature the more the distribution of the particle antiparticle sea would be weighted statistically towards heavier pairs, due to energy considerations with respect to flat space.
Unruh effect, coordinate dependence.
Creation and annihilation operators are coordinate-dependent.
A ground state in one is a squeezed state in another.