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<p>In the present article, we employ the geometry of absolute parallelism and parameterized absolute parallelism to develop a new theory, denoted as <i>f(X, Y, E)</i> gravity, where <i>X</i> = <i>X (R, T</i>) represents a parameterized curvature scalar, <i>Y</i> = <i>Y(T)</i> a parameterized torsion scalar, and <i>E</i> refers to the trace of the stress-energy tensor. From this new theory, we derive the modified theories <i>f(R)</i> gravity, <i>f(R, E)</i> gravity and <i>f(T)</i> gravity as special cases, where <i>R</i> represents a curvature scalar, <i>T</i> a torsion scalar. We introduce the <i>f(X, Y, E)</i> = <i>λ X</i> + <i>γ Y</i> + 2<i>η E</i>, where <i>λ, γ</i> and <i>η</i> are constants, and apply a quadratic deceleration parameter to describe the cosmological models of the Big Bang, Big Rip, and Big Crunch. Our study demonstrates that the evolution of the universe exhibits remarkably similar behavior across all proposed modified theories. Additionally, we discuss the energy conditions, revealing that the Dominant Energy Condition, Strong Energy Condition, and Weak Energy Condition are violated for these models.</p>

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f(X, Y, E) gravity and cosmological models

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • M. M. Tantawy,
  • M. A. Bakry,
  • G. M. Moatimid

摘要

In the present article, we employ the geometry of absolute parallelism and parameterized absolute parallelism to develop a new theory, denoted as f(X, Y, E) gravity, where X = X (R, T) represents a parameterized curvature scalar, Y = Y(T) a parameterized torsion scalar, and E refers to the trace of the stress-energy tensor. From this new theory, we derive the modified theories f(R) gravity, f(R, E) gravity and f(T) gravity as special cases, where R represents a curvature scalar, T a torsion scalar. We introduce the f(X, Y, E) = λ X + γ Y + 2η E, where λ, γ and η are constants, and apply a quadratic deceleration parameter to describe the cosmological models of the Big Bang, Big Rip, and Big Crunch. Our study demonstrates that the evolution of the universe exhibits remarkably similar behavior across all proposed modified theories. Additionally, we discuss the energy conditions, revealing that the Dominant Energy Condition, Strong Energy Condition, and Weak Energy Condition are violated for these models.