It looks like the term first appeared in “Quantum Graphity”, a paper by Tomasz Konopka, Fotini Markopoulou, and Lee Smolin. Here, the authors created a model intended as a demonstration of how such a theory could proceed. In the model, degrees of freedom lie on a graph which in a disordered high temperature state can only be described in quantum mechanical terms. The system transitions to an orderly lattice structure at low temperatures.
Markopoulou then added two more (mostly overlapping) papers which step back and survey how theories featuring geometrogenesis fit into the taxonomy of quantum gravity theories and how they differ from other so-called background independent theories like loop quantum gravity.
In the paper “New Directions in Background Independent Quantum Gravity,” Markopoulou describes the “traditional” path to background independent quantum theories of gravity (e.g. LQG) as ones which create microscopic geometric degrees of freedom and then consider quantum superposition or path integrals of these geometries. One challenge for such an approach is that the quest for finding classical dynamical space-time in the low energy limit is made difficult by the fact that the starting point is a timeless, not a dynamical theory. (Note though that Causal Dynamical Triangulations is an approach, discussed in this prior post, which has had some success in getting at least the right large scale dimensionality to emerge from a micro-geometric starting point).
Here is what Markopoulou says in section 1.6.1 of the paper (p.18) about the geometrogenesis picture:
“It is a factor of about twenty orders of magnitude from the physics of the Planck scale described by the microscopic theory to the standard subatomic physics. By analogy with all other physical systems we know, it is reasonable to expect that physics at the two scales decouples to a good approximation. We can expect at least one phase transition interpolating between the microscopic BI phase and the familiar one in which we see dynamical geometry. We shall use the word geometrogenesis for this phase transition.”
She goes on to credit Olaf Dreyer (see this paper, for instance) and quantum computational theorist Seth Lloyd (see here) for advocating this concept of emergence with regard to dynamical space-time.
There are no distances or metrics in the micro-theory; distance is recovered as emerging from the relations among the quantum sub-systems. She also notes that is a feature of this idea that these emergent excitations of the microscopic degrees of freedom define not only geometry but the structure of matter at the same time. Matter and gravity are unified in the pre-geometric phase. The ambition of this approach is highlighted by Markopoulou’s saying that the approach “provides a path towards explaining gravity rather than just quantizing it (emphasis original).”
She discusses some of the challenges the approach faces. One is that the introduction of dynamics in the micro-theory reintroduces time in a theory that is supposed to be background independent (I personally think if local time and causality exist in the micro-theory, that’s OK). Second and more important, can such a theory show that geometry will emerge, or just that it could emerge. In other words will we need to posit a fine-tuning mechanism to have a geometric phase? She thinks some of the early approaches offer the hope that the geometric phase is a generic consequence of the theory.
In the paper, she then goes on to describe a specific approach she’s been working on, which invokes the quantum computing concept of noiseless sub-systems to drive emergence. I have a prior post about this work, so I’ll leave off discussing it here.
I don’t have any right to have an opinion, but I find a lot of intuitive appeal in this approach to quantum gravity. The ground level of reality consists of elementary quantum systems linked in a causal network; it is a natural consequence of this reality that our world emerges at the large scale.