Structured Vacuum Theory in Palatini Form: Dynamics from Non-Metricity and Multiscale Consistency

This work develops a metric-affine theory of gravity in which the vacuum possesses intrinsic dynamical structure, modelled by an independent symmetric metric tensor $\Xi_{\mu\nu}$ and affine connection $\Gamma^\lambda{}{\mu\nu}$. Unlike General Relativity, where vacuum dynamics are trivial, this framework employs non-metricity $Q{\alpha\mu\nu}$ as the central dynamical entity, enabling genuine propagating degrees of freedom in the spacetime geometry.A quadratic, parity-even action in non-metricity is constructed and the full field equations are derived. The healthy parameter region, identified via linear analysis, guarantees absence of ghosts and luminal propagation for gravitational waves.A falsifiable principle of multiscale physical consistency is introduced: the same solution must explain galactic rotation curves and gravitational lensing, while remaining consistent with Solar-System and binary pulsar tests—without retuning parameters.This establishes a physically unified framework where dark matter and dark energy phenomena emerge naturally from vacuum dynamics, rather than from unseen components. Full technical details, weak-field limits, and observational tests are included.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-09-26
DOI
https://doi.org/10.5281/zenodo.17211427
Primary Topic
Cosmology and Gravitation Theories
Type
article
Field-Weighted Citation Impact
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article

Structured Vacuum Theory in Palatini Form: Dynamics from Non-Metricity and Multiscale Consistency

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
article

Structured Vacuum Theory in Palatini Form: Dynamics from Non-Metricity and Multiscale Consistency

article en

Abstract

This work develops a metric-affine theory of gravity in which the vacuum possesses intrinsic dynamical structure, modelled by an independent symmetric metric tensor $\Xi_{\mu\nu}$ and affine connection $\Gamma^\lambda{}{\mu\nu}$. Unlike General Relativity, where vacuum dynamics are trivial, this framework employs non-metricity $Q{\alpha\mu\nu}$ as the central dynamical entity, enabling genuine propagating degrees of freedom in the spacetime geometry.A quadratic, parity-even action in non-metricity is constructed and the full field equations are derived. The healthy parameter region, identified via linear analysis, guarantees absence of ghosts and luminal propagation for gravitational waves.A falsifiable principle of multiscale physical consistency is introduced: the same solution must explain galactic rotation curves and gravitational lensing, while remaining consistent with Solar-System and binary pulsar tests—without retuning parameters.This establishes a physically unified framework where dark matter and dark energy phenomena emerge naturally from vacuum dynamics, rather than from unseen components. Full technical details, weak-field limits, and observational tests are included.

Zenodo (CERN European Organization for Nuclear Research)
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Cosmology and Gravitation Theories
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