Sub-gravitational theory and experimental tests*

Anomalous accelerations of free-falling cold atoms were confirmed by time-of-flight experiments (Physical Review D, 105: 102006 (2022)). They are attributed to the forces mediated by a heavy scalar field whose self-interaction potential can just rightly drive the cosmic acceleration.

I show that the origin of the spatial gradient forces of the scalar field is a special relativity effect. Unlike gauge interactions, the new interaction between the scalar field and other energy forms is a conformal one. That is, the ratio of the interaction Lagrangian density to the bare Lagrangian density for any other form of energy does not depend on the nature of the energy form, it is a universal and spontaneous symmetry-breaking function of the scalar field.

By canonically subsuming the scalar filed into general relativity, the problems of Hubble constant tension and the cosmological constant are naturally solved (Physical Review D, 107: 103529 (2023)). Under the constraint that the scalar field is alone responsible for dark energy, the range of the interaction is too short in general to be detected.

Therefore, we experimentally chose microprobes of single cold atoms and constructed the permeable force sources in ultrahigh vacuums so that the maximum force can be sensed.