Cubic Parametrization of the Deceleration Parameter Within <i>f</i>(<i>T</i>) Gravity

Abstract In this study, we used the f ( T ) gravity framework with the energy-momentum tensor for a perfect fluid to derive key cosmological parameters, including the Hubble parameter H , deceleration parameter q and Statefinder diagnostics. Model parameters were optimized using an R 2 test, resulting in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>β</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.31</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.014</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.013</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ξ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.27</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.0071</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.0065</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>72.6</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.49</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.50</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , with an R 2 of 0.9527. Our model aligns closely with the ΛCDM model and shows good performance based on AIC and BIC criteria. Analyzing the q ( z ) curve revealed the transition from deceleration to acceleration in the universe’s expansion. Additionally, we examined pressure, energy density, and equation of state parameter for two models, f ( T ) = λT and f ( T ) = T + βT 2 , both aligning well with observational data. The r – s and r – q diagnostics further confirm our model’s consistency with ΛCDM, making it a strong alternative for explaining cosmic expansion. The evolution of Ω( z ) shows strong consistency with the ΛCDM model, with the Om parameter approaching 0.3 at lower redshifts and parameter uncertainties highlighting the model’s reliability.