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arXiv · 2606.08213

Non conservative conformal Killing gravity: coupling the dark sector with curvature and matter

Salvatore Capozziello·Carlo Alberto Mantica·Luca Guido Molinari
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Abstract

The so called Harada gravity with non conserved energy-momentum tensor is here taken into account. It includes Rastall gravity as a special case. The field equations are written as Einstein equations where the source is supplemented by a divergence-free conformal Killing tensor and a tensor proportional to the metric, linear in the scalar curvature and the trace of the energy-momentum tensor. These terms can be natural candidates for dark sector and give rise to a coupling of the dark sector with the matter content. The field equations are the conformal Killing extension of Rastall gravity, and include Unimodular gravity. In a Friedmann-Robertson-Walker background, the Cosmic Microwave Background restricts parameters so that the dark sector only couples with the trace of the energy-momentum tensor. The explicit form of the tensor for the dark sector is found, and the Friedmann and continuity equations are presented, with a standard cosmological analysis. The sum of energy-momentum tensors of dust matter and of dark fluid is conserved, and the dust energy density evolves with the scale function with exponent -3/(1+tau), modified by the coupling tau with the dark fluid.

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Salvatore Capozziello, Carlo Alberto Mantica, Luca Guido Molinari. 2026-06-06. Non conservative conformal Killing gravity: coupling the dark sector with curvature and matter. https://arxiv.org/abs/2606.08213

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