A mesh-and-balloon toy model of gravity and dark energy: null cosmological results and one short-range prediction

Purpose. To explore one idea: space as a mesh of fixed spacing with a "balloon" (graviton-like object) at each junction, and to work out what it would actually predict. What it tries to resolve. No open problem. The idea was explored as a way to think about why dark energy stays constant and whether space could have a discrete structure. It does not solve the cosmological-constant problem or explain the DESI hint of evolving dark energy. What it predicts. (1) In cosmology, nothing that current data can distinguish from ΛCDM: the finite-capacity version is indistinguishable from it, and the other version is excluded. (2) One specific prediction: if space is an ordered mesh fixed in space, gravity at short distances varies slightly with direction, with a strength set by d²/12 (d is the mesh spacing), giving a signal that varies with the Earth's rotation. Current experiments limit d to about 250 to 280 μm for a typical orientation. At the dark-energy scale (86 μm) the effect is about 16 to 23 times too small to see today, and a planned experiment would improve this by only about ×1.4. The prediction disappears if the mesh is disordered or not fixed in space. This note was produced with the assistance of Claude (Anthropic); see the disclosure at the end of the PDF. The interactive diagram is a companion to the paper.