Spin-2 gravity for matter fields on Minkowski spacetime: from Schrödinger-Newton dynamics to free-fall cosmology
Abstract
A classical two-field theory is formulated on a fixed Minkowski background: a massless spin-2 field h µν mediates gravity for a continuous complex scalar field ϕ that is the only matter. The gauge-consistent cubic self-coupling reproduces the weak-field and first post-Newtonian tests and the quadrupole law with no free parameter, coinciding with General Relativity. In the non-relativistic limit ϕ yields the Schrödinger-Newton system. Its quantum potential Q carries no gravitational weight at Newtonian order and enters the first post-Newtonian source with the fixed coefficient C Q = 4, so that the far-field mass of a virialized configuration is its total conserved energy. Because the dispersive force is internal to the envelope, the center of mass of an extended wave packet falls universally by momentum conservation, without a self-force prescription. Rotation curves and lensing are tied to the same mass distribution, with no gravitational slip. On cosmological scales the framework embeds a kinematic expansion of an under-dense domain on flat spacetime, where the Hamilton-Jacobi phase dynamics remains consistent with the expansion law and the ambient density acts as an effective cosmological term without inserting one into the action. At the orders treated, the gravitational sector cannot be distinguished empirically from General Relativity; discrimination rests on the matter model and its cosmological embedding.
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BibTeX
@misc{michel2026spin2,
title = {{Spin-2 gravity for matter fields on Minkowski spacetime: from Schrödinger-Newton dynamics to free-fall cosmology}},
author = {Denis Michel},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05835919v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spin-2 gravity for matter fields on Minkowski spacetime: from Schrödinger-Newton dynamics to free-fall cosmology
AU - Denis Michel
PY - 2026
DA - 2026/10/22
PB - HAL
UR - https://hal.science/hal-05835919v1
AB - A classical two-field theory is formulated on a fixed Minkowski background: a massless spin-2 field h µν mediates gravity for a continuous complex scalar field ϕ that is the only matter. The gauge-consistent cubic self-coupling reproduces the weak-field and first post-Newtonian tests and the quadrupole law with no free parameter, coinciding with General Relativity. In the non-relativistic limit ϕ yields the Schrödinger-Newton system. Its quantum potential Q carries no gravitational weight at Newtonian order and enters the first post-Newtonian source with the fixed coefficient C Q = 4, so that the far-field mass of a virialized configuration is its total conserved energy. Because the dispersive force is internal to the envelope, the center of mass of an extended wave packet falls universally by momentum conservation, without a self-force prescription. Rotation curves and lensing are tied to the same mass distribution, with no gravitational slip. On cosmological scales the framework embeds a kinematic expansion of an under-dense domain on flat spacetime, where the Hamilton-Jacobi phase dynamics remains consistent with the expansion law and the ambient density acts as an effective cosmological term without inserting one into the action. At the orders treated, the gravitational sector cannot be distinguished empirically from General Relativity; discrimination rests on the matter model and its cosmological embedding.
ER -