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arXiv · 2508.04810

Post-Newtonian expansion of scale-dependent gravity

Nicolas R. Bertini·Marcos H. Novaes
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Abstract

Scale-dependent gravity is an extension of general relativity in which the Newton and cosmological constants may vary slightly with the energy scale due to remnant low-energy quantum effects. A fundamental feature of this approach is the scale-setting procedure. In a previous work, a covariant expression for the scale, consistent with conservation laws, was established. Here, we apply the full Will-Nordtvedt version of the parameterized post-Newtonian (PPN) formalism to this framework, assuming that the constants can be expressed as a power series in the scale. We find that a new potential arises at the first post-Newtonian order, which is absent from the standard PPN formalism. This potential modifies the definitions of pressure and internal energy but does not affect center-of-mass orbits and is, therefore, not constrained by Solar System tests.

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Nicolas R. Bertini, Marcos H. Novaes. 2025-08-06. Post-Newtonian expansion of scale-dependent gravity. https://doi.org/10.1103/s2c1-gndl

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