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This research article presents a new cosmological model formulated within the$f(R,G,\mathcal{T})$ framework, focusing on the observational signatures andparameter constraints of the model. The Markov Chain Monte Carlo (MCMC)technique is employed to effectively explore the parameter space using datafrom 36 Cosmic Chronometers and 1701 Pantheon Plus data points. A comparativeanalysis is conducted between the proposed $f(R,G,\mathcal{T})$ model and thewidely accepted $\Lambda$CDM model, considering various cosmologicalparameters, such as Deceleration, Snap, and Jerk. By evaluating theseparameters, valuable insights into the dynamics and evolution of the universewithin the context of the new model are obtained. Diagnostic tests includingStatefinder and Om Diagnostic are performed to further investigate the behaviorand consistency of the $f(R,G,\mathcal{T})$ model. These tests provide deeperinsights into the properties of the model and its compatibility withobservational data. The model is subjected to statistical analysis usingInformation Criteria to rigorously assess its goodness of fit to the data. Thisanalysis helps determine the level of agreement between the$f(R,G,\mathcal{T})$ model and the observational data, establishing theviability and reliability of the proposed cosmological framework. The resultshighlight the potential of the $f(R,G,\mathcal{T})$ framework in understandingthe fundamental aspects of the universe's evolution and dynamics. Thecomparative analysis with the $\Lambda$CDM model, along with the comprehensivediagnostic tests performed, demonstrates the efficacy and validity of the$f(R,G,\mathcal{T})$ model in explaining observed cosmological phenomena. Thesefindings contribute to the ongoing pursuit of accurate and comprehensive modelsthat provide a deeper understanding of the nature of our universe.

Cosmological Tests of $f(R,G,\mathcal{T})$ Dark Energy Model in FRW Universe