Polytropic Gas Cosmology and Late-time Acceleration

The accelerated expansion of the Universe has sparked significant interest in the mysterious concept of dark energy within cosmology. Various theories have been proposed to explain dark energy, and many models have been developed to understand its origins and properties. This research explores cosmic expansion using the Polytropic Gas (PG) approach, which combines Dark Matter (DM) and Dark Energy (DE) into a single mysterious fluid. We used the principles of general relativity and built our model within the homogeneous and isotropic framework of Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. We revised the Original Polytropic Gas (OPG) model to expand its applicability beyond the OPG, to the ΛCDM model. Our model's parameters were carefully adjusted to reflect key cosmological features of the variable PG approach. To validate our model, we performed a Markov chain Monte Carlo analysis using recent Supernova data from the Pantheon+ survey, 36 observational data points, 162 Gamma-Ray Bursts, and 24 binned Quasars distance modulus data. The AIC and BIC criteria indicate that our model is slightly preferred over the ΛCDM model based on observational data. We also tested our model with data, Supernova, Gamma-Ray Bursts, and Quasars and found that it exhibits a transition from a quintessential to phantom regime. The Polytropic dark fluid model (PDFM) is a promising candidate that effectively addresses the interplay between cosmic acceleration and dark energy.