  This research article presents a new cosmological model formulated within the
$f(R,G,\mathcal{T})$ framework, focusing on the observational signatures and
parameter constraints of the model. The Markov Chain Monte Carlo (MCMC)
technique is employed to effectively explore the parameter space using data
from 36 Cosmic Chronometers and 1701 Pantheon Plus data points. A comparative
analysis is conducted between the proposed $f(R,G,\mathcal{T})$ model and the
widely accepted $\Lambda$CDM model, considering various cosmological
parameters, such as Deceleration, Snap, and Jerk. By evaluating these
parameters, valuable insights into the dynamics and evolution of the universe
within the context of the new model are obtained. Diagnostic tests including
Statefinder and Om Diagnostic are performed to further investigate the behavior
and consistency of the $f(R,G,\mathcal{T})$ model. These tests provide deeper
insights into the properties of the model and its compatibility with
observational data. The model is subjected to statistical analysis using
Information Criteria to rigorously assess its goodness of fit to the data. This
analysis helps determine the level of agreement between the
$f(R,G,\mathcal{T})$ model and the observational data, establishing the
viability and reliability of the proposed cosmological framework. The results
highlight the potential of the $f(R,G,\mathcal{T})$ framework in understanding
the fundamental aspects of the universe's evolution and dynamics. The
comparative analysis with the $\Lambda$CDM model, along with the comprehensive
diagnostic tests performed, demonstrates the efficacy and validity of the
$f(R,G,\mathcal{T})$ model in explaining observed cosmological phenomena. These
findings contribute to the ongoing pursuit of accurate and comprehensive models
that provide a deeper understanding of the nature of our universe.
