Scalar field theory description of the running vacuum model: the vacuumon

Abstract

We investigate the running vacuum model (RVM) in the framework of scalar field theory. This dynamical vacuum model provides an elegant global explanation of the cosmic history, namely the universe starts from a non-singular initial de Sitter vacuum stage, it passes smoothly from an early inflationary era to a radiation epoch ("graceful exit") and finally it enters the dark matter and dark energy (DE) dominated epochs, where it can explain the large entropy problem and predicts a mild dynamical evolution of the DE. Within this phenomenologically appealing context, we formulate an effective classical scalar field description of the RVM through a field φ, called the vacuumon, which turns out to be very helpful for an understanding and practical implementation of the physical mechanisms of the running vacuum during both the early universe and the late time cosmic acceleration. In the early universe the potential for the vacuumon may be mapped to a potential that behaves similarly to that of the scalaron field of Starobinsky-type inflation at the classical level, whilst in the late universe it provides an effective scalar field description of DE. The two representations, however, are not physically equivalent since the mechanisms of inflation are entirely different. Moreover, unlike the scalaron, vacuumon is treated as a classical background field, and not a fully fledged quantum field, hence cosmological perturbations will be different between the two pictures of inflation.

A Real Scalar Field Unifying the Early Inflation and the Late Accelerating Expansion of the Universe through a Quadratic Equation of State: The Vacuumon

“…They proposed to call the scalar field that accounts for the temporal evolution of the vacuum energy the "vacuumon". As they obtained exactly the same potentials in the early and late universe as the ones obtained previously in our papers (compare Equations (4.18) and (4.42) of [58] with Equations ( 123) and (125) of [42]), we will also call "vacuumon" the scalar field associated with the quadratic equation of state (5) of our model [39][40][41][42][43][44][45][46][47]. 5 Following this terminology, what we referred to as "inflaton" in the early universe (associated with the equation of state (6)) will be called "early vacuumon" and what we referred to as "quintessence" in the late universe (associated with the equation of state (7)) will be called "late vacuumon".…”

“…When combined with radiation and matter, this model produces a phase of early inflation, a phase of decelerated expansion, and a phase of late inflation which are very similar to the ones obtained in our model (see Appendix C for a comparison between the two approaches). Recently, Basilakos et al [58] developed a scalar field representation of the RVM. They proposed to call the scalar field that accounts for the temporal evolution of the vacuum energy the "vacuumon".…”

Gravitational and chiral anomalies in the running vacuum universe and matter-antimatter asymmetry

“…Interestingly enough, the ∼ H 4 behavior can be equivalently mapped to a scalar field behavior. Such a scalar field picture will be called the "vacuumon picture" of the RVM since the field φ is called the vacuumon [57].…”

“…To implement the mapping of the RVM to the vacuumon picture one has the following correspondence with the total density and pressure [8,9,57]:…”

Dynamics in varying vacuum Finsler–Randers cosmology

“…In the framework of General Relativity the Running Vacuum Model (RVM) has been thoroughly studied at the background and perturbation levels respectively (see [70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87] and references therein). Here we want to extend the situation by including in the Finsler Randers geometry the concept of RVM.…”