# What quantum effects that involve gravity can be studied without stuff like QFT or string theory?

So there is no a full quantum theory of gravitation. However, there are instances where quantum effects due to gravitation have been studied. Like Gravitational neutron interferometry https://arxiv.org/abs/1701.00259 or maybe gravitational decoherence https://www.nature.com/articles/nphys3366

I would like to know if there are others quantum effects that involve gravity that can be studied (at least in an approximate way) without a full theory of quantized gravity.

If we could prepare a quantum state in which an object having significant mass is in a superposition of two different locations, and if the gravitational effects of that mass could be measured, then we'd be starting to explore quantum gravity experimentally even though such a situation can be described using a Newtonian $$1/r^2$$ model for the gravitational force. This can be studied without using stuff like QFT or string theory.
If we stick with a Newtonian $$1/r^2$$ model of gravity, then describing a non-relativistic quantum system with gravitational interactions between the quantum particles is no problem at all: we can do this in the same way we handle the Coulomb interaction, like we often do in ab initio calculations in quantum chemistry. The obstacle to formulating relativistic quantum gravity is that our current understanding of relativistic quantum theory (namely quantum field theory) relies on having a prescribed spacetime background that, among other things, defines what "timelike separation" and "spacelike separation" mean. Usually when people talk about quantum gravity, they're talking about / hoping for a quantum theory that accounts for the dynamics of spacetime, as general relativity does classically.