Bulk viscous matter interacting with decaying vacuum energy density: a model for late-time evolution of the Universe

Abstract The late-time cosmological expansion within a flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime is studied using a model characterized by bulk viscous dark matter (bulk viscosity $$\zeta = \zeta _0 \rho _m H^{-1}+\zeta _1 H $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ζ</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> , $$\zeta _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> &amp; $$\zeta _1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> are constants, and H , the Hubble parameter) interacting with a decaying vacuum density $$\rho _{\Lambda } = \mathcal {C}_0 + 3\nu H^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>Λ</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> <mml:mi>ν</mml:mi> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> , where $$\mathcal {C}_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> and $$\nu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ν</mml:mi> </mml:math> are constants. The bulk viscous pressure is described by Eckart’s theory. The interaction term is defined as $$ Q=3H\alpha (\rho _m+\rho _\Lambda )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mi>H</mml:mi> <mml:mi>α</mml:mi> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>Λ</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , where $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> , the interaction parameter. Analytical solutions for the Hubble parameter and the scale factor have been derived. The validity of the models is evaluated by constraining their free parameters using observational data from Cosmic Chronometer , the Pantheon , and a combination of both datasets. The goodness of fit is assessed by minimizing the $$\chi ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> function utilizing the Markov Chain Monte Carlo (MCMC) method. Selection information criteria, namely AIC and BIC, have been obtained to analyze the models’ stability. Additionally, several essential cosmological parameters characterizing the evolution dynamics are estimated and discussed analytically, and compared with the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model. The proposed model suggests a transition from the deceleration to the acceleration phase, indicating thermodynamic equilibrium in the distant future, aligning with the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model. The model shows a slight deviation from $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model and effectively reduces the $$H_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> tension between local measurements by R 21 and global measurements by Planck 2018. The model is consistent with thermodynamic laws and upholds the second law of thermodynamics. Finally, Phase-space analysis supports the same evolutionary transitional phases.