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• W4384827356 abstract "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 $$Lambda $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>Λ</mml:mi> </mml:math> CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized $$rho _{textrm{vac}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>vac</mml:mtext> </mml:msub> </mml:math> 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 $$rho _{textrm{vac}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>vac</mml:mtext> </mml:msub> </mml:math> with M turns into cosmic evolution with the Hubble rate, H . As a result the ‘cosmological constant’ $$Lambda $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>Λ</mml:mi> </mml:math> appears in our framework as the nearly sustained value of $$8pi G(H)rho _{textrm{vac}}(H)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mn>8</mml:mn> <mml:mi>π</mml:mi> <mml:mi>G</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>H</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>vac</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>H</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> 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 $$delta rho _textrm{vac}(H)sim nu _{textrm{eff}}, m_{textrm{Pl}}^2 left( H^2-H_0^2 right) (|nu _{textrm{eff}}|ll 1)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>δ</mml:mi> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>vac</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>H</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∼</mml:mo> <mml:msub> <mml:mi>ν</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msub> <mml:mspace /> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mrow> <mml:mtext>Pl</mml:mtext> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mfenced> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>-</mml:mo> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mfenced> <mml:mrow> <mml:mspace /> <mml:mo>(</mml:mo> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>ν</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . The coefficient $$nu _{textrm{eff}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>ν</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msub> </mml:math> 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 $$mathcal{O}(H^{6})$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>6</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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." @default.
• W4384827356 created "2023-07-21" @default.
• W4384827356 creator A5048456456 @default.
• W4384827356 creator A5050756349 @default.
• W4384827356 creator A5076117050 @default.
• W4384827356 date "2023-07-19" @default.
• W4384827356 modified "2023-10-14" @default.
• W4384827356 title "Running vacuum in QFT in FLRW spacetime: the dynamics of $$rho _{textrm{vac}}(H)$$ from the quantized matter fields" @default.
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