Quantum modified inertia: an application to galaxy rotation curves

Abstract

This work explores modified inertia in the context of galactic dynamics by investigating the consequences of introducing quantum-motivated bounds on acceleration. Building on earlier ideas related to maximal acceleration and quantum speed limits, an effective framework is developed in which both upper and lower acceleration bounds are incorporated within special relativity through a correspondence between the proper time of an accelerated object and the quantum speed limit. The resulting modified inertia model is applied to galaxy rotation curves, taking into account the baryonic contributions from stellar disks, gas, and bulges. An analytic expression for the radial acceleration relation is derived within this framework. When confronted with observations, the model provides a good description of several galactic systems, including the Milky Way and the dwarf galaxy DDO 52. It also successfully recovers the Tully-Fisher relation linking the baryonic mass and the terminal speed, with $\mathrm{log}(M) = 4 \, \mathrm{log}(v) + 2.62$. A characteristic minimal acceleration of order $1.8 \times 10^{-11}$ m s$^{-2}$ naturally emerges from the analysis and proves effective in reproducing a wide range of rotation curves. The resulting radial acceleration relation is consistent with Solar System constraints, including the Cassini quadrupole bound, and remains compatible with recent observational results on dwarf spheroidals and ultra-wide binaries. Within this effective description, the presence of a lower acceleration bound significantly reduces the amount of dark matter required to account for galactic rotation curves. Possible implications for the redshift evolution of this minimal acceleration, and for galaxy formation and evolution, are briefly discussed.

Figures (6)

• Figure 1: Synoptic scheme showing the arrangement of the hypothesis used to build the QMI theory. The references grouped in [a] are caianiello_maximal_1984-1feoli_maximal_2003termini_imagination_2006. The references grouped in [b] are frolov_instability_1991gasperini_kinematic_1991. The dashed line separates the quantum and relativistic theories, and the dotted line acts as a symmetric axis between the depicted mechanisms.
• Figure 2: Plot of the two different terms of equation (\ref{['PFD']}) for $m=1$ and $R_u=10^{27}$ m. The black dashed line is the plot of first term associated to the maximal acceleration bound. The blue dotted line is the plot of the second term assigned to minimal acceleration limit. The continuous red line is the equation (\ref{['PFD']}).
• Figure 3: Squares with error bars are the synthetic universal rotation curve of dwarf galaxies modeled by E. V Karukes and P. Salucci karukes_universal_2017. The dashed green curve is a fitting of experimental data with equation (\ref{['veloce4']}).
• Figure 4: Plot of the velocity curve as function of the distance from the Center of the Milky Way. Data from jiao_detection_2023 is represented by circles with error bars. The dashed red, blue and green curves are the contributions to velocity respectively from the bulge, the disk (gas and stars) and the QMI minimal acceleration. The baryonic contents are listed in table \ref{['tab:sofue2025params']}.
• Figure 5: Rotation curve of DDO52. The two dataset are extracted from oh_high-resolution_2015 (black dots) and iorio_little_2017 (blue dots). The plain black line is the modeled rotation curve.The dashed red, blue, yellow and green curves are the contributions to velocity respectively from the bulge, the stellar disk, the gas disk and the QMI minimal acceleration. The baryonic contents are listed in table \ref{['tab:DDO52Oh']}.