Have there been any scientific studies done on how cats and dogs behave when put into a virtual reality environment?

No

No scientists willing to invest time and resources for something that won’t produce any valuable merit.

There aren’t any. However, it wouldn’t escape my mind that someone who is very rich can custom-order the VR equipment for their pets from the manufacturer. There are many head sizes of dogs and cats of different breed so there is no way to design on size that can be universally used by the species, not to mention that the demand for such thing aren’t very high so producers would less motivated to create such thing.

Would dogs or cats take any interest in something that they can’t smell? I remember, as a kid, trying to get my cat interested in the cat in the mirror, and she didn’t even seem to see it.

@Jeruba
Cats are interested in lasers.

Cats are interested in any moving object that moves side-to-side. A laser point is also that—a point—a point they can focus on, like a bug. They will even try to catch side-to-side objects on a television screen, but not vertical.

Dogs will sometimes pay attention to dogs on television, and sounds from the television. Dogs will show curiosity about dogs in the mirror and other reflections—cats act as if they have been duped, recognizing a reflection for what it is, but will paw a reflection in a mirror on the ground as if to see if it is a reflection in water,

Neither dogs nor cats pay any attention to photographs.

Both dogs and cats react very differently than humans in visual stimuli—- and unless the virtual software is greatly modified, would find a virtual reality setting little more than mass confusion.

There haven’t been any scientific studies on animals in virtual reality, however. There HAS been some research done on how they react to television, even as to how they see a television screen. Digital technology IS better for dogs to recognize images than the old T,V,s And dogs are comforted by having talking voices on T,V, and Radio. Dogs are comforted by calming music but for obvious reasons not birds and nature sounds.