Cosmological dynamics of matter creation with modified Chaplygin gas and bulk viscosity

Abstract This work presents a comprehensive investigation of a novel cosmological model that includes the Modified Chaplygin Gas (MCG) equation of state with gravitationally induced matter creation and bulk viscous dissipation in a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime. The MCG fluid is characterized by an exotic equation of state $$p = A\rho - C/\rho ^\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mi>A</mml:mi> <mml:mi>ρ</mml:mi> <mml:mo>-</mml:mo> <mml:mi>C</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>ρ</mml:mi> <mml:mi>α</mml:mi> </mml:msup> </mml:mrow> </mml:math> . The matter creation rate is taken as $$\varGamma = 3\beta H$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Γ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mi>β</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> and the bulk viscous pressure as $$\pi = -3H\xi _0 \rho _m^{1/2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>π</mml:mi> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> <mml:mi>H</mml:mi> <mml:msub> <mml:mi>ξ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:msubsup> <mml:mi>ρ</mml:mi> <mml:mi>m</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> . We derive the modified Friedmann equations and obtain an analytical expression for the Hubble parameter H ( z ), which is then used to reconstruct the evolutionary trajectories of key cosmological parameters. The model parameters are constrained using two observational datasets: DS1 (Pantheon+ + Cosmic Chronometers + DESI BAO + $$\sigma _8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:math> ) and DS2 (DS1 + R22). Our results indicate that the proposed hybrid model successfully generates a transition from decelerated to accelerated expansion, consistent with current observations. Notably, when the R22 prior is included the best-fit value of $$H_0$$ <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> shifts towards the local SH0ES determination; the hybrid model is flexible enough to accommodate this higher $$H_0$$ <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> while preserving a good fit to the geometric datasets, thereby reducing the level of tension in joint analyses between local and background probes, although it does not dynamically resolve 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> discrepancy by itself. Furthermore, we perform a rigorous thermodynamic analysis of the model by testing the Generalized Second Law (GSL) of thermodynamics. We use the information cretria, like Akaike and Bayesian to check the model stability. This work establishes a physically motivated, observationally viable, and thermodynamically consistent alternative to the standard $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM paradigm.