Interesting that you should use the word "aspects", since it is the Aspect Experiment that proves on the macroscopic level that quantum mechanics is correct and relativity is not. This experiment proves that two particles created at the same point by pair production and flying off in opposite directions remain interconnected. Physicists say that the particles are "entangled". But that is just giving a word to something they cannot understand theoretically. Nevertheless, the results of the experiment stand. The particles are proven to be interconnected instantaneously at macro-distances that cannot be explained by the theory of relativity and the speed of light.
Regarding universal expansion, that also has experimental rather than a theoretical basis with the work by Harvard and other teams on distant supernovae.
It is true that quantum gravity and superstring theory are still in the developmental stage. However, even when that development is finished it is unlikely that there will be any experiments with enough energy to prove its validity. The results of the theory will have to be largely taken on faith. So do not ever expect to get theoretical proof of anything based on quantum gravity or superstring theory since the theories themselves cannot be proven completely correct. Science will become a matter of faith and beauty. The most simple, elegant theory will be accepted as true.
That makes science into just another religion. In a sense that is already true as Kurt Godel has proven that no mathematical theory as or more complicated than arithematic can be rigorous. Penrose has used Godel`s proof to suggest that consciousness, at least the higher consciousness that humans possess, is based on sufficient neural complexity to exceed Godel`s threshold of non-rigor.
There is an infamous Japanese publication (which is admittedly in disrepute) of the Hundredth Monkey phenomena. It goes like this. They observed monkey behavior on several Pacific islands. They noted that occasionally a monkey on one island would discover or invent some new way of doing something. The monkey would then proceed to teach other monkeys on that island how to do it. Then when a hundred or so monkeys on this first island learned the new trick, suddenly monkeys on other islands began to use the same trick.
I believe, but of course cannot prove, even in the pre-Godel sense, that what has happened is that the hundred or so monkeys exceeded the Godel threshold of complexity, and the system of group thinking of the monkeys became open. In such systems, according to Godel, there are solutions that cannot be derived from any of the postulates of the system. Beyond being just a mathematical nicety, I think the Godel complexity threshold reveals a mechanism of communication. For example, I think self-awareness is based on such a mechanism. When the human brain became sufficiently complex, we became aware of our own consciousness.
I have talked about all of this in previous posts over the past year and there is no need to repeat it over and over. But the bottom line in answer to your query is that interconnectedness and universal expansion have experimental proof. That is the best proof of all. The fact that physicists cannot yet understand it completely does not take anything away from the experimental fact that they are true, as far as we humans can ascertain.
As an aside, does your name RaVeN have anything to do with raving, or is that just coincidence?