Holographic dark energy models and their behaviors within the framework of f(Q,C) gravity theory

In this study, we have formulated the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model of the universe, selecting the source to be Holographic and Renyi holographic dark energy. Holographic and Renyi holographic dark energy fluids have demonstrated their prevalence over Hubble's and Granda-Oliveros cutoffs in $f(Q,C)$ gravity, where Q is the non-metricity scalar and C represents the boundary term. We assume the scale factor's form, $a\left(t\right)=sin{h}^{\frac{1}{m}}\left(\alpha t\right)$ to illustrate the characteristics of the cosmological parameters. We determine the appropriate values of the parameters by employing the MCMC technique with both the Hubble dataset consisting of 46 data points and 15 BAO dataset. The increasing energy density, coupled with $q=-1$, indicates the Universe's acceleration period, while the EoS parameter $\omega =-1$ corresponds to the ΛCDM model. After investigating the energy conditions, we recognized that our model violates the strong energy constraint. We examine how the statefinder parameters behave in our model. We also investigate the Universe's age.