Running vacuum in QFT in FLRW spacetime: the dynamics of $$\rho _{\textrm{vac}}(H)$$ ρ vac ( H ) from the quantized matter fields
Abstract Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the $$\Lambda $$ Λ CDM. On the th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-11772-9 |
| _version_ | 1797689096212054016 |
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| author | Cristian Moreno-Pulido Joan Solà Peracaula Samira Cheraghchi |
| author_facet | Cristian Moreno-Pulido Joan Solà Peracaula Samira Cheraghchi |
| author_sort | Cristian Moreno-Pulido |
| collection | DOAJ |
| description | Abstract Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the $$\Lambda $$ Λ CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized $$\rho _{\textrm{vac}}$$ ρ vac in QFT in FLRW spacetime adopts the ‘running vacuum model’ (RVM) form. While in three previous studies by two of us (CMP and JSP) such computations focused solely on scalar fields non-minimally coupled to gravity, in the present work we compute the spin-1/2 fermionic contributions and combine them both. The calculation is performed using a new version of the adiabatic renormalization procedure based on subtracting the UV divergences at an off-shell renormalization point M. The quantum scaling of $$\rho _{\textrm{vac}}$$ ρ vac with M turns into cosmic evolution with the Hubble rate, H. As a result the ‘cosmological constant’ $$\Lambda $$ Λ appears in our framework as the nearly sustained value of $$8\pi G(H)\rho _{\textrm{vac}}(H)$$ 8 π G ( H ) ρ vac ( H ) around (any) given epoch H, where G(H) is the gravitational coupling, which is also running, although very mildly (logarithmically). We find that the VED evolution at present reads $$\delta \rho _\textrm{vac}(H)\sim \nu _{\textrm{eff}}\, m_{\textrm{Pl}}^2 \left( H^2-H_0^2 \right) \ (|\nu _{\textrm{eff}}|\ll 1)$$ δ ρ vac ( H ) ∼ ν eff m Pl 2 H 2 - H 0 2 ( | ν eff | ≪ 1 ) . The coefficient $$\nu _{\textrm{eff}}$$ ν eff receives contributions from all the quantized fields, bosons and fermions, which we compute here for an arbitrary number of matter fields. Remarkably, there also exist higher powers $$\mathcal{O}(H^{6})$$ O ( H 6 ) which can trigger inflation in the early universe. Finally, the equation of state (EoS) of the vacuum receives also quantum corrections from bosons and fermion fields, shifting its value from − 1. The striking consequence is that the EoS of the quantum vacuum may nowadays effectively appears as quintessence. |
| first_indexed | 2024-03-12T01:41:07Z |
| format | Article |
| id | doaj.art-0a37cdab72ff41c4ac9432d27af52396 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-03-12T01:41:07Z |
| publishDate | 2023-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-0a37cdab72ff41c4ac9432d27af523962023-09-10T11:23:08ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-07-0183714810.1140/epjc/s10052-023-11772-9Running vacuum in QFT in FLRW spacetime: the dynamics of $$\rho _{\textrm{vac}}(H)$$ ρ vac ( H ) from the quantized matter fieldsCristian Moreno-Pulido0Joan Solà Peracaula1Samira Cheraghchi2Departament 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 BarcelonaFaculty of Mathematics and Computer Science, Transilvania UniversityAbstract Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the $$\Lambda $$ Λ CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized $$\rho _{\textrm{vac}}$$ ρ vac in QFT in FLRW spacetime adopts the ‘running vacuum model’ (RVM) form. While in three previous studies by two of us (CMP and JSP) such computations focused solely on scalar fields non-minimally coupled to gravity, in the present work we compute the spin-1/2 fermionic contributions and combine them both. The calculation is performed using a new version of the adiabatic renormalization procedure based on subtracting the UV divergences at an off-shell renormalization point M. The quantum scaling of $$\rho _{\textrm{vac}}$$ ρ vac with M turns into cosmic evolution with the Hubble rate, H. As a result the ‘cosmological constant’ $$\Lambda $$ Λ appears in our framework as the nearly sustained value of $$8\pi G(H)\rho _{\textrm{vac}}(H)$$ 8 π G ( H ) ρ vac ( H ) around (any) given epoch H, where G(H) is the gravitational coupling, which is also running, although very mildly (logarithmically). We find that the VED evolution at present reads $$\delta \rho _\textrm{vac}(H)\sim \nu _{\textrm{eff}}\, m_{\textrm{Pl}}^2 \left( H^2-H_0^2 \right) \ (|\nu _{\textrm{eff}}|\ll 1)$$ δ ρ vac ( H ) ∼ ν eff m Pl 2 H 2 - H 0 2 ( | ν eff | ≪ 1 ) . The coefficient $$\nu _{\textrm{eff}}$$ ν eff receives contributions from all the quantized fields, bosons and fermions, which we compute here for an arbitrary number of matter fields. Remarkably, there also exist higher powers $$\mathcal{O}(H^{6})$$ O ( H 6 ) which can trigger inflation in the early universe. Finally, the equation of state (EoS) of the vacuum receives also quantum corrections from bosons and fermion fields, shifting its value from − 1. The striking consequence is that the EoS of the quantum vacuum may nowadays effectively appears as quintessence.https://doi.org/10.1140/epjc/s10052-023-11772-9 |
| spellingShingle | Cristian Moreno-Pulido Joan Solà Peracaula Samira Cheraghchi Running vacuum in QFT in FLRW spacetime: the dynamics of $$\rho _{\textrm{vac}}(H)$$ ρ vac ( H ) from the quantized matter fields European Physical Journal C: Particles and Fields |
| title | Running vacuum in QFT in FLRW spacetime: the dynamics of $$\rho _{\textrm{vac}}(H)$$ ρ vac ( H ) from the quantized matter fields |
| title_full | Running vacuum in QFT in FLRW spacetime: the dynamics of $$\rho _{\textrm{vac}}(H)$$ ρ vac ( H ) from the quantized matter fields |
| title_fullStr | Running vacuum in QFT in FLRW spacetime: the dynamics of $$\rho _{\textrm{vac}}(H)$$ ρ vac ( H ) from the quantized matter fields |
| title_full_unstemmed | Running vacuum in QFT in FLRW spacetime: the dynamics of $$\rho _{\textrm{vac}}(H)$$ ρ vac ( H ) from the quantized matter fields |
| title_short | Running vacuum in QFT in FLRW spacetime: the dynamics of $$\rho _{\textrm{vac}}(H)$$ ρ vac ( H ) from the quantized matter fields |
| title_sort | running vacuum in qft in flrw spacetime the dynamics of rho textrm vac h ρ vac h from the quantized matter fields |
| url | https://doi.org/10.1140/epjc/s10052-023-11772-9 |
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