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Technically, I believe Mercury fulfills those requirements.
Otherwise, maybe something like Glucose?
There are a few substance here that meet that density: https://www.engineeringtoolbox.com/liquids-densities-d_743.html
But, as far as resistance to UV and immiscability with UV resin, testing would be required, as I'm assuming you intend to replace the FEP film layer with a dense liquid.
Mercury? Isn't it opaque and fully reflective? Or does UV light pass through it?
For initial testing, the FEP would remain, but as this liquid would theoretically not stick to the resin, the FEP would remain intact, pretty much eliminating risks that have anything to do with it.
I have seen something like this before, but it uses two different lightwaves in order to make the denser liquid remain inert, so it's impossible to try it with consumer printers.
Ah, yes on the first count at least, though that criteria wasn't on your bulleted list, I guess it was in the title.
That being said, UV breakdown might not be as concerning in the short term if the substance is removed fairly often. I wonder if a clear gelatin or glycerin layer would last long enough?
I've also seen resin-infused paper-like substrate layers of material like carbon fiber attempt to bypass the requirement of an FEP. Each print layer was a new sheet and once the print was done the un-cured material was blown away.
Assuming we're talking about refractive index here, metals technically still have a refractive index despite being reflective (light can penetrate a very short distance through metals). In the UV, the refractive index of mercury is <1 and of course it's very dense. But that's probably not going to be useful to you.
For transparent materials, water actually has a lower refractive index than most liquids (around 1.34 in the UV). You can check this website to see if there's anything better (probably an organic), but I doubt it would be by much.
I don't know much about 3D resin printing, but I assume you a focus an image (in the UV) onto a resin layer to selectively cure it. As you suggest, the presence of a liquid would refract the focusing light rays and change the position of the focal plane. This could in principle be accounted for by changing the distance from the focusing optic, though there could be some (perhaps minor) blurring of the image.
Sounds like some sort of oil🤔