Running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ ρvac without $$\sim m^4$$ ∼m4 terms

Abstract The $$\Lambda $$ Λ -term in Einstein’s equations is a fundamental building block of the ‘concordance’ $$\Lambda $$ Λ CDM model of cosmology. Even though the model is not free of fundamental problems, they have not been circumvented by any alternative dark energy proposal either. Here we sti...

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Main Authors: Cristian Moreno-Pulido, Joan Solà Peracaula
Format: Article
Language:English
Published: SpringerOpen 2020-08-01
Series:European Physical Journal C: Particles and Fields
Online Access:http://link.springer.com/article/10.1140/epjc/s10052-020-8238-6
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spelling doaj-df4b5fadd0b54e4e927e842d688153042020-11-25T03:25:51ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522020-08-0180812310.1140/epjc/s10052-020-8238-6Running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ ρvac without $$\sim m^4$$ ∼m4 termsCristian Moreno-Pulido0Joan Solà Peracaula1Departament de Física Quàntica i Astrofísica, and Institute of Cosmos Sciences, Universitat de BarcelonaDepartament de Física Quàntica i Astrofísica, and Institute of Cosmos Sciences, Universitat de BarcelonaAbstract The $$\Lambda $$ Λ -term in Einstein’s equations is a fundamental building block of the ‘concordance’ $$\Lambda $$ Λ CDM model of cosmology. Even though the model is not free of fundamental problems, they have not been circumvented by any alternative dark energy proposal either. Here we stick to the $$\Lambda $$ Λ -term, but we contend that it can be a ‘running quantity’ in quantum field theory (QFT) in curved space time. A plethora of phenomenological works have shown that this option can be highly competitive with the $$\Lambda $$ Λ CDM with a rigid cosmological term. The, so-called, ‘running vacuum models’ (RVM’s) are characterized by the vacuum energy density, $$\rho _{vac}$$ ρvac , being a series of (even) powers of the Hubble parameter and its time derivatives. Such theoretical form has been motivated by general renormalization group arguments, which look plausible. Here we dwell further upon the origin of the RVM structure within QFT in FLRW spacetime. We compute the renormalized energy-momentum tensor with the help of the adiabatic regularization procedure and find that it leads essentially to the RVM form. This means that $$\rho _{vac}(H)$$ ρvac(H) evolves as a constant term plus dynamical components $${{\mathcal {O}}}(H^2)$$ O(H2) and $$\mathcal{O}(H^4)$$ O(H4) , the latter being relevant for the early universe only. However, the renormalized $$\rho _{vac}(H)$$ ρvac(H) does not carry dangerous terms proportional to the quartic power of the masses ($$\sim m^4$$ ∼m4 ) of the fields, these terms being a well-known source of exceedingly large contributions. At present, $$\rho _{vac}(H)$$ ρvac(H) is dominated by the additive constant term accompanied by a mild dynamical component $$\sim \nu H^2$$ ∼νH2 ($$|\nu |\ll 1$$ |ν|≪1 ), which mimics quintessence.http://link.springer.com/article/10.1140/epjc/s10052-020-8238-6
collection DOAJ
language English
format Article
sources DOAJ
author Cristian Moreno-Pulido
Joan Solà Peracaula
spellingShingle Cristian Moreno-Pulido
Joan Solà Peracaula
Running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ ρvac without $$\sim m^4$$ ∼m4 terms
European Physical Journal C: Particles and Fields
author_facet Cristian Moreno-Pulido
Joan Solà Peracaula
author_sort Cristian Moreno-Pulido
title Running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ ρvac without $$\sim m^4$$ ∼m4 terms
title_short Running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ ρvac without $$\sim m^4$$ ∼m4 terms
title_full Running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ ρvac without $$\sim m^4$$ ∼m4 terms
title_fullStr Running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ ρvac without $$\sim m^4$$ ∼m4 terms
title_full_unstemmed Running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ ρvac without $$\sim m^4$$ ∼m4 terms
title_sort running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ ρvac without $$\sim m^4$$ ∼m4 terms
publisher SpringerOpen
series European Physical Journal C: Particles and Fields
issn 1434-6044
1434-6052
publishDate 2020-08-01
description Abstract The $$\Lambda $$ Λ -term in Einstein’s equations is a fundamental building block of the ‘concordance’ $$\Lambda $$ Λ CDM model of cosmology. Even though the model is not free of fundamental problems, they have not been circumvented by any alternative dark energy proposal either. Here we stick to the $$\Lambda $$ Λ -term, but we contend that it can be a ‘running quantity’ in quantum field theory (QFT) in curved space time. A plethora of phenomenological works have shown that this option can be highly competitive with the $$\Lambda $$ Λ CDM with a rigid cosmological term. The, so-called, ‘running vacuum models’ (RVM’s) are characterized by the vacuum energy density, $$\rho _{vac}$$ ρvac , being a series of (even) powers of the Hubble parameter and its time derivatives. Such theoretical form has been motivated by general renormalization group arguments, which look plausible. Here we dwell further upon the origin of the RVM structure within QFT in FLRW spacetime. We compute the renormalized energy-momentum tensor with the help of the adiabatic regularization procedure and find that it leads essentially to the RVM form. This means that $$\rho _{vac}(H)$$ ρvac(H) evolves as a constant term plus dynamical components $${{\mathcal {O}}}(H^2)$$ O(H2) and $$\mathcal{O}(H^4)$$ O(H4) , the latter being relevant for the early universe only. However, the renormalized $$\rho _{vac}(H)$$ ρvac(H) does not carry dangerous terms proportional to the quartic power of the masses ($$\sim m^4$$ ∼m4 ) of the fields, these terms being a well-known source of exceedingly large contributions. At present, $$\rho _{vac}(H)$$ ρvac(H) is dominated by the additive constant term accompanied by a mild dynamical component $$\sim \nu H^2$$ ∼νH2 ($$|\nu |\ll 1$$ |ν|≪1 ), which mimics quintessence.
url http://link.springer.com/article/10.1140/epjc/s10052-020-8238-6
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