As was done with the other categories, here's my initial list of main trunk theories for Growth.
The biggest potential issue now, I think, is the sparsity of farming techs. I wasn't sure what else could be done with farming beside doing it as industrial farming, doing it in space, and eliminating the need for it altogether, and the various genetic-alteration type things that fall under other techs.
There are also a few suggestions that might not be appropriate for Growth, like Nanotech Cybernetics, Symbiotic Biology or Xeni-Hybridization. Presumably these would have some Growth-related benefits though...
Genetic Engineering (create, insert new genes and make transgenic organisms)
Industrial Farming (hydroponics, aeroponics, vehicles, crop rotation)
Planetary Ecology (population capacity, farming, undiscovered species)
Medical Pathology (immunology, epidemiology, pharmacology, surgery)
Orbital Farming (farms in space)
Environmental Encapsulation (building mini-ecologies in domed colonies)
Symbiotic Biology (whole > sum of parts, eg. trills, health benefits)
Genetic Medicine (therapy and modification of already living organisms)
Nanotech Medicine (medical treatment or "vaccination" with nanites)
Xenological Genetics (interplanetary transgenics & new gene creation)
Lifecycle Manipulation (faster growth, longer life & healthy adulthood)
Industrial Cloning (made to order colonists, soldiers, workers, scientists)
Nanotech Cybernetics (augmentation & enhancement, "We are Borg")
Xenological Hybridization (restructuring physiology & genetics, drastic changes)
Pure-Energy Metabolism (eliminate food, absorb radiaton or generate energy)
Edit: And because the pictures get more responses...
Edit again: Removed Population Sociology and rearranged things to look nicer