Towards a unified quantum field theory of dark energy and inflation: unstable de Sitter vacuum and running vacuum
- 1Universitat de Barcelona
- 2Universitat de Girona
Abstract
Inflation is a necessary cosmic mechanism to cure basic inconsistencies of the standard model of cosmology. In its absence, we could not understand the observed spatial flatness, the homogeneity and isotropy of the CMB, and yet the origin of structure formation, nor the large amount of entropy today. These problems are usually ‘fixed’ by postulating the existence of a scalar field (the ‘inflaton’). However, other less ad hoc options are actually possible. In the running vacuum model (RVM) framework, the vacuum energy density (VED) is a function of the Hubble rate H and its time derivatives: ρ vac = ρ vac ( H , H ˙ , H ¨ , … ) . In this context, the VED is dynamical (there is no rigid cosmological term Λ ). In the Friedmann–Lemaître–Robertson–Walker (FLRW) epoch, ρ vac evolves very slowly with expansion, as befits the observed Λ ≃ const. behavior. In contrast, in the very early Universe the vacuum fluctuations of the quantized matter fields induce higher powers H N capable of unleashing fast inflation in a short period in which H ≃ const. We call this mechanism ‘RVM-inflation’. It does not require an inflaton field since inflation is brought about by pure quantum field theory (QFT) effects on the dynamical background. It is different from Starobinsky’s inflation, in which H is never constant. In this work, we study a closely related scenario: the decay of the exact de Sitter vacuum into FLRW spacetime, in its radiation epoch, and its impact on the current Universe, and compare it with the RVM. The two QFT calculations are renormalized using an off-shell adiabatic prescription. We find that in both cases inflation is driven by H 4 powers accompanied by subleading contributions of order H 2 that ease a graceful-exit transition into the radiation-dominated epoch, where the FLRW regime starts and ultimately develops a mildly evolving VED in the late Universe: δ ρ vac ∼ O ( m Pl
Related
- Running into tension: primordial black holes from ultra-slow-roll inflation, spectral running, and the Hubble tension
- Gauss--Bonnet running and the de Sitter saddle of quadratic gravity inflation
- A unified stochastic random walk theory for Kolmogorov spectrum, halo mass functions, and halo density profiles
- Dark Photon Dark Matter from Quantum Fluctuations during Starobinsky Inflation
- Time-reversed stochastic inflation in the quantum well
BibTeX
@article{sola2026towards,
title = {{Towards a unified quantum field theory of dark energy and inflation: unstable de Sitter vacuum and running vacuum}},
author = {Joan Solà and Alex Gonzalez Fuentes and Cristian Moreno-Pulido},
journal = {Classical and Quantum Gravity},
year = {2026},
month = jun,
doi = {10.1088/1361-6382/ae7ba8},
url = {https://doi.org/10.1088/1361-6382/ae7ba8},
note = {CC BY},
}
RIS
TY - JOUR
TI - Towards a unified quantum field theory of dark energy and inflation: unstable de Sitter vacuum and running vacuum
AU - Joan Solà
AU - Alex Gonzalez Fuentes
AU - Cristian Moreno-Pulido
PY - 2026
DA - 2026/06/10
JO - Classical and Quantum Gravity
DO - 10.1088/1361-6382/ae7ba8
UR - https://doi.org/10.1088/1361-6382/ae7ba8
AB - Inflation is a necessary cosmic mechanism to cure basic inconsistencies of the standard model of cosmology. In its absence, we could not understand the observed spatial flatness, the homogeneity and isotropy of the CMB, and yet the origin of structure formation, nor the large amount of entropy today. These problems are usually ‘fixed’ by postulating the existence of a scalar field (the ‘inflaton’). However, other less ad hoc options are actually possible. In the running vacuum model (RVM) framework, the vacuum energy density (VED) is a function of the Hubble rate H and its time derivatives: ρ vac = ρ vac ( H , H ˙ , H ¨ , … ) . In this context, the VED is dynamical (there is no rigid cosmological term Λ ). In the Friedmann–Lemaître–Robertson–Walker (FLRW) epoch, ρ vac evolves very slowly with expansion, as befits the observed Λ ≃ const. behavior. In contrast, in the very early Universe the vacuum fluctuations of the quantized matter fields induce higher powers H N capable of unleashing fast inflation in a short period in which H ≃ const. We call this mechanism ‘RVM-inflation’. It does not require an inflaton field since inflation is brought about by pure quantum field theory (QFT) effects on the dynamical background. It is different from Starobinsky’s inflation, in which H is never constant. In this work, we study a closely related scenario: the decay of the exact de Sitter vacuum into FLRW spacetime, in its radiation epoch, and its impact on the current Universe, and compare it with the RVM. The two QFT calculations are renormalized using an off-shell adiabatic prescription. We find that in both cases inflation is driven by H 4 powers accompanied by subleading contributions of order H 2 that ease a graceful-exit transition into the radiation-dominated epoch, where the FLRW regime starts and ultimately develops a mildly evolving VED in the late Universe: δ ρ vac ∼ O ( m Pl
SN - 0264-9381
SN - 1361-6382
ER -