Constraining Redshift Parametrization Models with Recentmost Data : Impacts on an Accretion Disc around Finslerian Kiselev Black Hole

Technical Summary: Constraining Redshift Parametrization Models with Recentmost Data: Impacts on an Accretion Disc around Finslerian Kiselev Black Hole

Problem Statement
The paper addresses the evolution of black hole (BH) mass within a cosmological background modeled by a Modified Chaplygin Gas (MCG). While dark energy (DE) is known to drive the accelerated expansion of the universe, its specific equation of state (EoS), denoted as $\omega(z)$, remains a subject of debate. The authors investigate how different redshift-dependent parametrizations of the DE EoS (Linear, Logarithmic, CPL, and JBP models) influence the accretion dynamics and mass evolution of a Finslerian Kiselev Black Hole. The study aims to determine how the time-dependent cosmic pressure landscape and the coupling between local strong gravity and global expansion affect BH mass growth, specifically looking for signatures of repulsive dark energy effects that might suppress or enhance accretion.

Methodology
The research employs a multi-stage theoretical and observational approach:

1. Theoretical Framework:

   • Metric: The study utilizes a Finslerian Kiselev Black Hole (FKBH) solution embedded in an MCG-filled universe. The metric incorporates a deficit solid angle and is derived within the context of Rastall gravity, which allows for non-conservation of the energy-momentum tensor ($G_{\mu\nu} + \kappa\lambda g_{\mu\nu}S = \kappa T_{\mu\nu}$).
   • Accretion Physics: The authors model the accretion of a perfect fluid (DE) onto the BH. By solving the conservation equations for mass flux ($J^\mu$) and energy-momentum ($T^\mu_{\nu;\mu}=0$), they derive the rate of change of the BH mass ($\dot{M}$). The sign of $\dot{M}$ is determined by the term $(\rho + p)$; if $\rho + p < 0$ (phantom regime), the BH loses mass, whereas $\rho + p > 0$ (quintessence) leads to mass gain.
   • Redshift Parametrizations: Four distinct models for the DE EoS parameter $\omega(z)$ are analyzed:
     • Linear Redshift Parametrization (LRP)
     • Chevallier-Polarski-Linder (CPL)
     • Jassal-Bagla-Padmanabhan (JBP)
     • Efstathiou/Logarithmic Parametrization (ERP)

2. Observational Constraints:

   • Data Collection: The study utilizes 85 data points of the Hubble parameter $H(z)$ obtained via the Differential Ages method (using stellar population synthesis of passively evolving galaxies).
   • Statistical Analysis: The free parameters of the DE models are constrained using a $\chi^2$ minimization technique. The analysis incorporates three datasets:
     • Hubble data ($H(z)$)
     • Baryon Acoustic Oscillation (BAO) acoustic parameter measurements.
     • Cosmic Microwave Background (CMB) shift parameter ($R$) from Planck 2018 and WMAP7 data.
   • Parameter Estimation: Joint likelihood analysis is performed to determine the best-fit values and confidence contours for the model parameters ($\omega_0, \omega_1$).

3. Simulation:

   • Using the constrained parameters, the authors calculate the evolution of the BH mass ratio $\log_{10}[M(z)/M_0]$ as a function of redshift for each DE model.

Key Contributions and Results

• Parameter Constraints: The study successfully constrains the free parameters for all four DE models using the combined $H(z)$, BAO, and CMB datasets. The analysis reveals distinct statistical behaviors for the posterior distributions of the parameters:

  • LRP: Shows a right-skewed distribution for $\omega_1$ and a left-skewed distribution for $\omega_0$, suggesting a preference for quintessence-like behavior ($\omega > -1$) but allowing for a phantom regime ($\omega < -1$) within uncertainty bounds.
  • CPL: Exhibits left-skewed distributions, indicating that larger parameter values are more probable, effectively favoring quintessence over phantom regimes.
  • JBP: Shows a bimodal posterior in certain data combinations, suggesting a degeneracy where both the $\Lambda$CDM limit and a phantom regime are comparably probable.
  • ERP: Displays a transition from symmetric constraints (with H(z) and BAO) to an extremely right-skewed distribution when CMB data is added, strongly favoring minimal deviation from the $\Lambda$CDM limit.

• Mass Evolution Dynamics: The most significant finding is the sensitivity of the BH mass evolution to the specific DE parametrization:

  • Gentle Slopes (Linear, Logarithmic, CPL): These models exhibit a smooth, quasi-static evolution of the mass ratio. The slope of $\log_{10}[M(z)/M_0]$ near the present epoch ($z \sim 0$) is gentle. This indicates that the DE EoS evolves slowly, creating a background where the pressure gradients are weak, and accretion proceeds in a steady, adiabatic manner. The mass ratio decreases gradually from high redshift to the present, reflecting a transition from matter-dominated accretion to a DE-dominated suppression.
  • Steep Slopes (JBP): In contrast, the JBP model produces a steep slope near the horizon at low redshift. This corresponds to a rapid variation in $\omega(z)$, inducing strong local pressure anisotropy in the MCG fluid. This results in a sharp change in accretion dynamics, highlighting a transient suppression or enhancement of accretion due to repulsive dark energy effects.

• Physical Interpretation: The study demonstrates that the logarithmic mass ratio acts as a probe of the cosmic pressure landscape. The amplitude offsets and slopes in the mass ratio curves reflect the dynamic interplay between horizon thermodynamics, the evolving pressure of the MCG, and cosmic expansion.

Significance and Claims
The paper claims that black hole accretion serves as a sensitive probe for the time-dependent nature of dark energy. The authors assert that the evolution of BH mass is directly influenced by both the temporal evolution of the DE EoS and the effective gravitational potential of the surrounding cosmic fluid.

Specifically, the results illustrate that:

1. Local vs. Global Coupling: The mass growth of a black hole is not merely a function of local gravity but is inextricably linked to global cosmological expansion and the specific dynamical behavior of the dark energy fluid.
2. Model Discrimination: The shape of the mass ratio curve (specifically the slope near $z=0$) can distinguish between different DE parametrizations. Gentle slopes imply a quasi-static, adiabatic background, while steep slopes indicate rapid late-time variations and active interaction between DE and the BH environment.
3. Thermodynamic Insight: The study provides physical insights into how repulsive dark energy effects can lead to transient suppression of accretion, effectively altering the thermodynamic balance where the horizon may act as an energy emitter rather than an absorber in phantom regimes.

The authors conclude that their comparative study within an MCG background reveals that the non-monotonic features and slopes of the mass ratio carry deep physical meaning regarding the pressure-density interplay of the cosmic fluid and the thermodynamic behavior of black hole horizons in a universe dominated by both dark matter-like and dark energy-like components.