https://doi.org/10.1140/epjc/s10052-025-14917-0
Regular Article - Theoretical Physics
Running gravitational constant induced dark energy as a solution to 
tension
1
Department of Physics, School of Sciences and Humanities, Nazarbayev University, 010000, Astana, Kazakhstan
2
Energetic Cosmos Laboratory, Nazarbayev University, 010000, Astana, Kazakhstan
3
Department of Intelligent Systems, Astana IT University, 010000, Astana, Kazakhstan
4
Department of Electrical and Computer Engineering, School of Engineering and Digital Sciences, Nazarbayev University, 010000, Astana, Kazakhstan
a
tilek.zhumabek@alumni.nu.edu.kz
Received:
24
June
2025
Accepted:
10
October
2025
Published online:
20
October
2025
We consider a modified gravity model with a running gravitational constant coupled to a varying dark energy fluid and test its imprint on the growth of structure in the universe. Using redshift space distortion (RSD) measurement results, we show a tension at the 
level between the best fit 
CDM and the corresponding parameters obtained from the Planck data. Unlike many modified gravity-based solutions that overlook scale dependence and model-specific background evolution, we study this problem in the broadest possible context by incorporating both factors into our investigation. We performed a full perturbation analysis to demonstrate a scale dependence in the growth equation. Fixing the scale to 
Mpc
and introducing a phenomenological functional form for the varying Newton coupling G with only one free parameter, we conduct a likelihood analysis of the RSD selected data. The analysis reveals that the model can bring the tension level within 
while maintaining the deviation of G from Newton’s gravitational constant at the fifth order.
© The Author(s) 2025
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Funded by SCOAP3.
