Note on gravity, entropy, and BF topological field theory

In this article I argue that the expression for entropic force, used as a starting point in Verlinde’s derivation of Newton’s law [E. P. Verlinde, arXiv:1001.0785], can be deduced from the first principles if one assumes that the microscopic theory behind his construction is the topological $\mathsf{S}\mathsf{O}(4,1)$ BF theory coupled to particles.