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Reconstruction of Accelerating Nonlinear $f(T)$ Gravity Models via Hybrid Scale Factor: Cosmological Dynamics and Bayesian Evidence

Suraj Kumar Behera, Pratik P. Ray

Abstract

This study offers a comprehensive reconstruction of $f(T)$ gravity model with three distinct non-linear as well as novel forms employing a hybrid scale factor to depict the expansion history of the universe starting from early decelerated epoch to late-time accelerated evolution. Model parameters are rigorously constrained using the Monte Carlo Markov Chain (MCMC) analysis with the help of Bayesian statistics and incorporating late-time observations from BAO and Patheon+SH0ES. The investigation of dynamical parameters such as the equation of state parameter and cosmological parameters indicates alignment with an accelerated expansion phase in both the present and late time epochs. Validation is conducted by assessing the energy conditions, verifying the feasibility of the model forms with particular emphasis on the violation of the strong energy condition that indicates dark energy dominance in modified gravity scenarios. This investigation has been instrumental in determining models that remain consistent with cosmological observations and theoretical requirements. The reconstructed forms of the model effectively mimic $Λ$CDM at late times, providing significant insights into possible extensions of general relativity and bolstering $f(T)$ gravity theory as a robust explanation for cosmic acceleration.

Reconstruction of Accelerating Nonlinear $f(T)$ Gravity Models via Hybrid Scale Factor: Cosmological Dynamics and Bayesian Evidence

Abstract

This study offers a comprehensive reconstruction of gravity model with three distinct non-linear as well as novel forms employing a hybrid scale factor to depict the expansion history of the universe starting from early decelerated epoch to late-time accelerated evolution. Model parameters are rigorously constrained using the Monte Carlo Markov Chain (MCMC) analysis with the help of Bayesian statistics and incorporating late-time observations from BAO and Patheon+SH0ES. The investigation of dynamical parameters such as the equation of state parameter and cosmological parameters indicates alignment with an accelerated expansion phase in both the present and late time epochs. Validation is conducted by assessing the energy conditions, verifying the feasibility of the model forms with particular emphasis on the violation of the strong energy condition that indicates dark energy dominance in modified gravity scenarios. This investigation has been instrumental in determining models that remain consistent with cosmological observations and theoretical requirements. The reconstructed forms of the model effectively mimic CDM at late times, providing significant insights into possible extensions of general relativity and bolstering gravity theory as a robust explanation for cosmic acceleration.
Paper Structure (14 sections, 36 equations, 9 figures, 2 tables)

This paper contains 14 sections, 36 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Mathematical framework for field equations
  3. Parametrization of the hybrid scale factor
  4. Observational Data-Driven Analysis
  5. $H(z)$ Dataset
  6. BAO Dataset
  7. Pantheon+SH0ES Dataset
  8. Dynamics in reconstructed $f(T)$ gravity models
  9. Model I: $f(T)=T-\frac{a}{(-T/6)^n}+b(\frac{-T}{6})^m$
  10. Model II: $f(T)=T-aT_0 \left[\left(1+\frac{T^2}{T_0^2}\right)^{-n}-1 \right]$
  11. Model III: $f(T)=T+aT_0\frac{(T^2/T_0^2)^n}{1+(T^2/T_0^2)^n}$
  12. Energy Conditions
  13. Conclusion
  14. References

Figures (9)

  • Figure 1: 2D-contour plots generated from the analysis of (i)$H(z)$, (ii) BAO, (iii) Pantheon+SH0ES, and (iv) combined ($H(z)$ + BAO + Pantheon+SH0ES) datasets, illustrating the best-fit values and up to $3\sigma$ confidence intervals for the model parameters $\lambda$ and $\beta$.
  • Figure 2: The left panel illustrates the error bar plot of the Hubble parameter, whereas the right panel depicts the distance modulus function for the $\Lambda$CDM model and hybrid scale factor.
  • Figure 3: Illustrates the plot of the deceleration parameter for $H(z)$, BAO, Pantheon+SH0ES, and combined datasets.
  • Figure 4: The left panel displays energy density, and the right panel displays the EoS parameter plot of Model I for $H(z)$, BAO, Pantheon+SH0ES and combined datasets with the parameter scheme $a=0.665$, $b=0.084$,$m=1.505$, and $n=0.245$.
  • Figure 5: The left panel displays energy density, and the right panel displays the EoS parameter plot of Model II for $H(z)$, BAO, Pantheon+SH0ES and combined datasets with the parameter scheme $a=5.2$ and $n=49.8$.
  • ...and 4 more figures