Dynamic Vacuum Energy in Weyl Integrable Spacetime Part I: Implications for Inflationary Cosmology
Abstract
We explore a dynamic vacuum energy scenario within the Weyl Integrable Spacetime (WIS) framework and provide the Friedmann--Lema\^itre (FL) cosmology equations under a metric endowed with a lapse function. We pay particular attention to the implications of inflationary dynamics. We show that the explicit vacuum decay source cancels in the FL acceleration equation, where the Hubble slow-roll parameter is controlled by the non-vacuum sector alone, while the dynamic vacuum defined in proper time Λ(τ) itself continues to enter the observables through the expansion rate. We identify the warm inflation (WI) dissipation coefficient with one half of the logarithmic decay rate of the vacuum energy, Υ=−1/2 dlnΛ/dτ, hence the phenomenological friction coefficient is tied to the vacuum sector rather than computed from explicit inflaton--bath microphysics. Notably, we show that the dissipation ratio (Q) is not a free parameter: the cosmological constant hierarchy constrains it through Q Ne,I≃46, where Ne,I is the total number of e-folds of expansion during vacuum decay. For a moderate pre-observable transient, this robustly gives Q=𝒪(1). The graceful exit and the observable parameters are obtained and are in line with cosmological observations. These results indicate that our model is viable and provide a well-posed starting point for a subsequent numerical analysis.
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BibTeX
@article{millo2026dynamic,
title = {{Dynamic Vacuum Energy in Weyl Integrable Spacetime Part I: Implications for Inflationary Cosmology}},
author = {Florian Millo},
journal = {The European Physical Journal: C, Particles and fields},
year = {2026},
month = oct,
doi = {10.1140/epjc/s10052-026-16529-8},
url = {https://hal.science/hal-05802739v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Dynamic Vacuum Energy in Weyl Integrable Spacetime Part I: Implications for Inflationary Cosmology
AU - Florian Millo
PY - 2026
DA - 2026/10/19
JO - The European Physical Journal: C, Particles and fields
DO - 10.1140/epjc/s10052-026-16529-8
UR - https://hal.science/hal-05802739v1
AB - We explore a dynamic vacuum energy scenario within the Weyl Integrable Spacetime (WIS) framework and provide the Friedmann--Lema\^itre (FL) cosmology equations under a metric endowed with a lapse function. We pay particular attention to the implications of inflationary dynamics. We show that the explicit vacuum decay source cancels in the FL acceleration equation, where the Hubble slow-roll parameter is controlled by the non-vacuum sector alone, while the dynamic vacuum defined in proper time Λ(τ) itself continues to enter the observables through the expansion rate. We identify the warm inflation (WI) dissipation coefficient with one half of the logarithmic decay rate of the vacuum energy, Υ=−1/2 dlnΛ/dτ, hence the phenomenological friction coefficient is tied to the vacuum sector rather than computed from explicit inflaton--bath microphysics. Notably, we show that the dissipation ratio (Q) is not a free parameter: the cosmological constant hierarchy constrains it through Q N_e,I≃46, where N_e,I is the total number of e-folds of expansion during vacuum decay. For a moderate pre-observable transient, this robustly gives Q=𝒪(1). The graceful exit and the observable parameters are obtained and are in line with cosmological observations. These results indicate that our model is viable and provide a well-posed starting point for a subsequent numerical analysis.
SN - 1434-6052
ER -