That's just the thing. There is a total incompatibility between general relativity and quantum mechanics, but it's currently a theoretical problem. AFAIK there's no current experiment (coming from an accelerator or an astro. survey) that fundamentally requires it to explain its results (ducks). The latest and greatest was WMAP, and inflation seems to explain that data. (This doesn't mean that a potential theory of QG could not make predictions that one could test tomorrow.) Most papers are speculatory ("We think ... Future surverys will confirm (or deny) our theory...").
The interesting thing is that there is stuff that is (indirectly) observed and actually part of the modern framework of cosmology: dark matter and dark energy. Modern cosmology says that for every pound of regular stuff there is 5x dark matter and 14x dark energy, so it'd be important to figure out what it actually is. As one of my elderly professors put it, "I hope to live long enough to learn what this stuff actually is; my friends always ask me what it is, and I my answer at the end is always 'I don't know'." There are current experiments that try to detect dark matter particles (in cosmic radiation I think), but they don't seem to get a lot of attention, maybe if they find something.
The interesting thing is that there is stuff that is (indirectly) observed and actually part of the modern framework of cosmology: dark matter and dark energy. Modern cosmology says that for every pound of regular stuff there is 5x dark matter and 14x dark energy, so it'd be important to figure out what it actually is. As one of my elderly professors put it, "I hope to live long enough to learn what this stuff actually is; my friends always ask me what it is, and I my answer at the end is always 'I don't know'." There are current experiments that try to detect dark matter particles (in cosmic radiation I think), but they don't seem to get a lot of attention, maybe if they find something.