After reading through some of the essays in this contest, it may be helpful for any public readers to again consider the questions within the contest rules:
"What exactly are the basic physical and mathematical postulates in our "fundamental" physical theories or candidate theories?"
-- My answer to this would of course be that gravity is "attractive" and that there is no physical cosmological medium. The mathematical postulate is that flat spacetime cannot occur with a cosmological constant.
"Which of these could be replaced with a weaker or less restrictive postulate or even removed?"
-- I would state that the less restrictive postulate is to use the full modified Einstein field equation with a flat spacetime.
"What would be the potential benefits (or disadvantages) of these changes?"
-- It would account for the accelerating expansion, provide a basic model for understanding of quantum field theory and change cosmology into a coherent physical theory.
"What are the implicit assumptions we tend to forget we have postulated, or that have become so ingrained that they have become unquestioned dogma?"
-- It is ingrained in us to think of gravity as attractive between two massive bodies (action at a distance) while at the same time to now accept that the space in between has many properties. We implicitly assume that we are "particles" with energy density that are separate from the vacuum of nothingness, but have also come to accept at the very same time that this vacuum has an energy density.
"What are the most interesting current "anomalous" experiments, and what assumptions would we be forced to give up if we took them seriously?"
-- The most interesting anomalous experiment is of course the accelerating expansion. If we took this seriously, we might reconsider how the cosmological constant relates to attractive gravity.
"Which assumptions in physics and in cosmology are interdependent or required for self-consistency, and which could be modified?"
-- Energy density of the vacuum and how energy density relates to gravity.
"Where are there "paradoxes", or apparent contradictions stemming from the combination of seemingly reasonable assumptions? How do we reconcile these?"
-- How can vacuum have such a high energy density, be the cosmological constant, but yet have not only such a small effect on gravity, but a repulsive one at that?
"Are there "meta"-assumptions or criteria (e.g. "simplicity", or "beauty", or "utility") that can or should underlie some current "fundamental" assumptions?"
-- Symmetry of Riemannian geometry.
"(Note: Successful and interesting essays will not use this topic as an opportunity to trot out their pet theories simply because those theories reject assumptions of some other or established theory. Rather, the challenge here is to create new and insightful questions or analysis about basic, often tacit, assumptions that can be questioned but often are not.) "
-- If the Einstein field equation is a differential equation with a constant of integration, why have we never examined the consequences of any other combinations of the Einstein tensor and the cosmological constant?
"Foundational: This Contest is limited to works addressing, in one of its many facets, our understanding of the deep or "ultimate" nature of reality."
-- What exactly are we made of?
"Accessible to a diverse, well-educated but non-specialist audience, aiming in the range between the level of Scientific American and a review article in Science or Nature."
-- Hopefully I have kept this basic enough so that others can manipulate the equations and find flaws and strengths in my logic for themselves.