A few weeks ago I published a post about Ted Jacobson and his deep understanding of general relativity (see here). Jacobson proved in 1995 that Einstein equations can be derived from thermodynamic arguments as an equation of state. To get the proof, Jacobson used Raychaudhuri equation and the proportionality relation between area and entropy holding for all local acceleration horizons. This result implies that exist some fundamental quantum degrees of freedom from which Einstein equations are obtained by properly managing the corresponding partition function. To estabilish such a connection is presently not at all a trivial matter and there are a lot of people around the World trying to achieve this goal even if we lack any experimental result that could lead the way.
Today in arxiv appeared a nice paper by Ram Brustein and Merav Hadad that generalize Jacobson’s result to a wider class of gravitational theories having Einstein equations as a particular case (see here). This result appears relevant in view of the fact that a theory exploiting quantum gravity could have as a low-energy limit some kind of modified Einstein equations, containing at least coupling with matter. Anyhow, we see how vacuum of quantum field theory seems to become even more important in our understanding of behavior of space-time.