| Summary: | In this article, we examined the behavior of dark energy (DE) and the cosmic acceleration in the framework of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>κ</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity in the standard spherically symmetric coordinates <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msup><mi>x</mi><mi>i</mi></msup><mo>)</mo></mrow></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>θ</mi><mo>,</mo><mi>ϕ</mi></mrow></semantics></math></inline-formula>, a spatially homogeneous and isotropic FLRW space–time. We discovered some remarkable cosmic characteristics in this investigation that are in line with both observations and the accepted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>CDM model. We made two assumptions in order to determine a deterministic solution of the modified field equations (MFEs): (i) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mi>γ</mi><mi>ρ</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>γ</mi><mo>(</mo><mn>1</mn><mo>≥</mo><mi>γ</mi><mo>≥</mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula> is a constant, (ii) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><msup><mi>H</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> is an arbitrary constant. We solved the MFEs and obtained the expression for the Hubble parameter. The depicted model of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>κ</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity was taken into consideration when discussing the behavior of the accelerating Universe. In <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>κ</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity, the statefinder analysis was utilized to distinguish our model from the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>CDM model. The evolution of the cosmos was studied using an effective equation of state (EoS). We investigated the thermodynamic quantities and the generalized energy conditions in order to test the viability of our model. When dominant and weak energy conditions are satisfied, this validates the model; when the strong energy condition is not satisfied, this accelerates the expansion of the Universe.
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