https://doi.org/10.1140/epjc/s10052-025-14618-8
Regular Article - Theoretical Physics
Running Einstein constant and a possible vacuum state of the universe
1
Nuclear Department, ENEA, C.R. Frascati, Via E. Fermi 45, 00044, Frascati, Italy
2
Physics Department, Sapienza University of Rome, P.le A. Moro 5, 00185, Rome, Italy
3
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Roma, P.le A. Moro 5, 00185, Rome, Italy
4
Physics Department, Tor Vergata University of Rome, Via della Ricerca Scientifica 1, 00133, Rome, Italy
Received:
29
May
2025
Accepted:
2
August
2025
Published online:
18
August
2025
We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of providing an effective dark energy density expression. Assuming a state close to vacuum, here defined by the vanishing product of the Einstein coupling constant and the Universe’s energy density, we perform a Taylor expansion of the theory and hence extend it to the whole domain. In this framework, the (renormalized) vacuum energy problem is studied, and an additional constant pressure term, which induces a Chaplygin-like contribution to the dark energy sector, arises in the late-time dynamics. The correction to the late-time Hubble parameter is investigated by comparing theoretical predictions with the late Universe observational data. Our findings indicate that the current value of the stated vacuum energy is consistent with zero within 1
. Implications of the modified 
CDM model with respect to the Hubble tension are also discussed.
© The Author(s) 2025
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