Transit Cosmological Models in Non-Coincident Gauge Formulation of \(\boldsymbol{f(Q,C)}\) Gravity Theory with Observational Constraints

The current study investigates dark energy cosmological models using a boundary term and a non-coincident gauge formulation of nonmetricity gravity. To obtain the modified field equations from the action, we considered the function \(f(Q,C)=Q+\lambda C^{m}\), where \(Q\) is the nonmetricity scalar, \(C\) is the boundary term given by \(C=\mathring{R}-Q\), and \(\lambda,m\) are model parameters. The scale factor that we acquired, \(a(t)=[\sinh(k_{0}t)]^{1/n}\), is determined by taking into account the time-dependent deceleration parameter. The constants \(n\) and \(k_{0}\) are used in this calculation. By comparing the Hubble function with \(H(z)\) datasets, we were able to use likelihood analysis to determine the model parameters that best fit the data. We have performed our result analysis and a discussion using the cosmological parameters, including the effective equation-of-state parameter, energy density, energy conditions, deceleration parameter, OM diagnostic analysis, and age of the universe, using these best match values of the model parameters.