A flat FLRW dark energy model in f(Q,C)-gravity theory with observational constraints

Abstract: In the recently suggested modified non-metricity gravity theory with boundary terms in a flat FLRWspacetime universe, dark energy scenarios of cosmological models are examined in this study. An arbitrary function, $f(Q, C)=Q+{\alpha}C^{2}$, has been taken into consideration, where Q is the non-metricity scalar, C is the boundary term denoted by $C = R-Q$, and ${\alpha}$ is the model parameter, for the action that is quadratic in C. The Hubble function $H(z) = H0[c_{1} (1+z)^{n}+c_{2}]^{1/2}$, where H0 is the current value of the Hubble constant and n c, and $c_{2}$ are arbitrary parameters with $c_{1}+c_{2}= 1$, has been used to examine the dark energy characteristics of the model. We discovered a transit phase expanding universe model that is both decelerated in the past and accelerated in the present, and we discovered that the dark energy equation of state (EoS) $(\omega^{de})$ behaves as $(-1\leq \omega^{de}<2)$. The $O_{m}$ diagnostic analysis reveals the quintessence behavior in the present and the cosmological constant scenario in the late-time universe. Finally, we calculated the universe's current age, which was found to be quite similar to recent data.