1) As I understand it, you have mathematically proven that 'classical gravity --> stochastic gravity.' You also propose experiments to demonstrate that gravity is stochastic. Suppose we experimentally prove that gravity is stochastic, but purely by the rules of logic, this does not imply that gravity is classical. It could instead be some form of quantum stochastic gravity.
2) Are there any cosmological consequences of the fact that gravity is stochastic? Intuitively, over very large distances, light might deviate from a straight trajectory or scatter in some way.
These are great questions. (1) Yes, if we find there is some level of intrinsic noise, then that could be produced by a number of different theories, and then we would try to use this to understand which theories produce the particular type of noise we observed. This should be possible, because most theories produce noise with certain correlations which have observational signatures. On the other hand, if the upper and lower bounds from the two types of experiments match, then I don't know of any other explanation for that. It is not a feature of quantum gravity, but it is what the postquantum theory predicts.
I’m not a physicist, but I have questions.
1) As I understand it, you have mathematically proven that 'classical gravity --> stochastic gravity.' You also propose experiments to demonstrate that gravity is stochastic. Suppose we experimentally prove that gravity is stochastic, but purely by the rules of logic, this does not imply that gravity is classical. It could instead be some form of quantum stochastic gravity.
2) Are there any cosmological consequences of the fact that gravity is stochastic? Intuitively, over very large distances, light might deviate from a straight trajectory or scatter in some way.
These are great questions. (1) Yes, if we find there is some level of intrinsic noise, then that could be produced by a number of different theories, and then we would try to use this to understand which theories produce the particular type of noise we observed. This should be possible, because most theories produce noise with certain correlations which have observational signatures. On the other hand, if the upper and lower bounds from the two types of experiments match, then I don't know of any other explanation for that. It is not a feature of quantum gravity, but it is what the postquantum theory predicts.
Regarding (2), yes there may be, both of the kind you mention, as well as the fact that stochastic fluctuations may be a candidate for dark matter (e.g. https://arxiv.org/abs/2407.13820 and https://arxiv.org/abs/2402.19459)