Its a given that, due to vacuum fluctuations and other forms of quantum nonsense, a virtual particle pair (a particle and its anti-particle) will spontaneously erupt from nothingness and then immediately mutually anihilate, all without interacting with the rest of the universe.
When a VPP form near the event horizon of a black hole, one particle may be drawn in, leaving the other one to become a real particle: this is Hawking radiation.
The question is:
Is the whole of space equally dense in Virtual Particle
Potential, or are there places where the Potential has been
concentrated or depleted?
Well, the first thing we have to clear up is that a virtual particle pair does interact with the rest of the universe. It’s just that they don’t live very long and so can’t interact with all that many things. But you can see the effect in things like the Lamb shift in hydrogen.
As I think about it, while my intuition suggests that you’re more likely to see more VPPs in regions of high energy density, I’m not sure I could prove that.
How about in a Casimir setup, where you have two closely spaced parallel, uncharged, conducting plates. The vacuum energy between the plates only includes those virtual photons whose wavelengths fit a whole number of times into the gap. The measurable vacuum energy must be lower between the plates than outside, where more wavelengths contribute to the total.
The vacuum potential is allowable due to the fitting of wavefunctions to the constraints of the vacuum. It’s a bizarre result of wavemechanics that happens to be the way nature works. The greater the density, the lower the density of virtual particle energy states due to the Casmiri effect. However, this is a broad generalization. As soon as external potentials are applied (with the caveat that gravity doesn’t exactly fit in at this time, ala “Hawking” radiation) there is a noticeable change in the “vacuum” potential. When you have densities, you usually have some other electroweak and strong force potentials thrown into the pot. Mostly, we look at the vacuum potentials in a vacuum, which is where they are the easiest to account for (since they are the only potentials to speak of). Thus the answer to your question is yes, with a but.
Squink has already answered the question, but I just wanted to pop in to say that I love the line “vacuum fluctuations and other forms of quantum nonsense”.