Are there any reasons to assume that organic processes cannot arise in relatively flat spacetime environments? An argument for the existence of a critial value or window.
First, let's assume that the heavier elements already exit but then find themselves in a relatively flat area of space (ie low g). In order for life to begin, and to continue (initially at least), one requires an environment containing a complex mixture of many compounds, in a warm liquid state. To expand on why it would require each of these conditions:
~ complex mixture of compounds would be required as, together, they have the ability to form amino acids, which in turn can form the building blocks of all 'living' things.
~ warm liquid state would be required to ensure that the compounds were close enough to eachother for them to frequently interact (liquid) and moving around eachother enough (warm) to overcome the extremely narrow possibility of their interacts leading to creation of something 'living'.
How exactly these conditions could be met without a planet, for the liquid to be attracted to, and a star (or geothermal energy as in Earth's case,) to provide the required heat is difficult to imagine. Not to mention, as @Georg pointed out, older stars are needed to make the heavier elements (fusion) and distribute them (supernovae,) in the first place.
In summary, and to get back to physics, it seems gravity is essential at every stage. Quantifying this conclusion would involve many assumptions and a great deal of calculation. With regard to star formation however, I believe it has already been done.
~ The steps I have described are (loosely-) based on the first episode of Sir David Attenborough's recent TV series; entitled First Life.
~ To me, his arguments seem plausible and firmly based on scientific research. As such, I am inclined to believe this process as being the most likely 'origin of life'. (Of course, not everyone will agree on either the details or the principle as a hole.)