Cosmological tests of $$f(R,G,\mathcal {T})$$ dark energy model in FRW universe

Abstract

Abstract The paper is devoted to study the observational signatures of $$f(R,G,\mathcal {T})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> gravity in FRW universe. In this research article, we present a new cosmological model formulated within the $$f(R,G,\mathcal {T})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> framework. To constrain the model parameters, we employ the Markov Chain Monte Carlo (MCMC) technique, which enables us to explore the parameter space effectively, and used the 36 points of cosmic chronometers and 1701 points from Pantheon Plus data. We compare our proposed $$f(R,G,\mathcal {T})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> model with the widely accepted $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM model, considering different cosmological parameters, including deceleration, snap, and jerk. By evaluating these parameters, we gain valuable insights into the dynamics and evolution of the universe within the context of our new model. Moreover, various diagnostic tests have been conducted, such as Statefinder and Om diagnostic, to further investigate the behavior and consistency of our $$f(R,G,\mathcal {T})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> model. These tests offer deeper insights into the properties of our model and its compatibility with observational data. We subject our model to statistical analysis using Information Criteria, which serves as a rigorous quantitative assessment of the model’s goodness of fit to the data. This analysis aids in determining the level of agreement between our $$f(R,G,\mathcal {T})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> model and the observational data, thus establishing the viability and reliability of our proposed cosmological framework. Our findings highlight the potential of the $$f(R,G,\mathcal {T})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> framework in understanding the fundamental aspects of the universe’s evolution and dynamics. The comparative analysis with $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM, as well as the comprehensive diagnostic tests performed, demonstrate the efficacy and validity of our model in explaining the observed cosmological phenomena. These results contribute to the ongoing pursuit of accurate and comprehensive models that can provide a deeper understanding of the nature of our universe.