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<p>This study presents a comparative analysis of two modified theories of gravity, <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math> <mi>f</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$f(R,T)$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math> <mi>f</mi> <mo stretchy="false">(</mo> <mi mathvariant="script">T</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$f(\mathcal{T})$</EquationSource> </InlineEquation>, within the framework of a locally rotationally symmetric Bianchi type-I spacetime. The primary objective is to explore the role of curvature-matter coupling and torsional dynamics in explaining the universe’s late-time acceleration without invoking a cosmological constant. To solve the highly nonlinear field equations, a hyperbolic sine scale factor and a shear-expansion proportionality condition are employed. The resulting models are constrained using observational Hubble parameter data via a <InlineEquation ID="IEq7"> <EquationSource Format="MATHML"><math> <msup> <mi>χ</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$\chi ^{2}$</EquationSource> </InlineEquation> minimization technique. Key cosmological quantities, including energy density, pressure, and the equation of state (EoS) parameter, are analyzed alongside geometrical diagnostics such as the <InlineEquation ID="IEq8"> <EquationSource Format="MATHML"><math> <mo>Om</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$\operatorname{Om}(z)$</EquationSource> </InlineEquation> and statefinder parameters. Statistical tools like the Akaike and Bayesian information criteria (AIC/BIC) are used to assess model performance relative to <InlineEquation ID="IEq9"> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> <EquationSource Format="TEX">$\Lambda$</EquationSource> </InlineEquation>CDM. Results show that both models capture the transition from decelerated to accelerated expansion, with the <InlineEquation ID="IEq10"> <EquationSource Format="MATHML"><math> <mi>f</mi> <mo stretchy="false">(</mo> <mi mathvariant="script">T</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$f(\mathcal{T})$</EquationSource> </InlineEquation> model exhibiting a more dynamic dark energy behavior and an earlier onset of acceleration. These findings suggest that torsional-based gravity may provide a geometrically motivated and observationally consistent alternative to standard cosmology.</p>

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Evaluating cosmic expansion \(f(\mathcal{T})\) vs \(f(R,T)\) gravity theories

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Rahul Sharma,
  • R. K. Mishra

摘要

This study presents a comparative analysis of two modified theories of gravity, f ( R , T ) $f(R,T)$ and f ( T ) $f(\mathcal{T})$ , within the framework of a locally rotationally symmetric Bianchi type-I spacetime. The primary objective is to explore the role of curvature-matter coupling and torsional dynamics in explaining the universe’s late-time acceleration without invoking a cosmological constant. To solve the highly nonlinear field equations, a hyperbolic sine scale factor and a shear-expansion proportionality condition are employed. The resulting models are constrained using observational Hubble parameter data via a χ 2 $\chi ^{2}$ minimization technique. Key cosmological quantities, including energy density, pressure, and the equation of state (EoS) parameter, are analyzed alongside geometrical diagnostics such as the Om ( z ) $\operatorname{Om}(z)$ and statefinder parameters. Statistical tools like the Akaike and Bayesian information criteria (AIC/BIC) are used to assess model performance relative to Λ $\Lambda$ CDM. Results show that both models capture the transition from decelerated to accelerated expansion, with the f ( T ) $f(\mathcal{T})$ model exhibiting a more dynamic dark energy behavior and an earlier onset of acceleration. These findings suggest that torsional-based gravity may provide a geometrically motivated and observationally consistent alternative to standard cosmology.