Observational constraints on holography in (2 + 1)-dimensional cosmology with a generalized equation of state

In this study we explore the cosmic holographic principle, as proposed by [W. Fischler and L. Susskind, Holography and cosmology, arXiv:hep-th/9806039], within the framework of [Formula: see text]-dimensional cosmological models. A generalized equation of state is employed, given by [Formula: see text], where [Formula: see text] and [Formula: see text] are treated as two free parameters. The analysis confirms the validity of the holographic principle in all flat and open universes. However, for a [Formula: see text]-dimensional closed universe, we apply the method proposed by [N. Kaloper and A. Linde, Cosmology versus holography, Phys. Rev. D 60 (1999) 103509] and observe that the holographic principle is generally not satisfied. Furthermore, we examine the stability of the proposed model using the Markov Chain Monte Carlo (MCMC) method, and estimate the best-fit values for the model parameters based on observational Hubble datasets.