Constraints of Cosmic Expansion Using an MSF

Abstract: In this paper, we propose a modified scale factor (MSF) that allows us to explore the accelerating expansion of the universe without invoking the traditional dark-energy model, as described in the Lambda cold dark matter ($\Lambda$CDM) model. Instead, the MSF model introduces parameters that encapsulate the effects traditionally attributed to dark energy. To test the viability of this MSF, we constrained the model using the observational Hubble parameter (OHD), distance modulus measurements (SNIa), and their combined datasets (OHD + SNIa). We implement a Monte Carlo Markov Chain (MCMC) simulation to find the best-fit values of the model parameters. The MSF model produced best-fit values for the parameter $p$ associated with the power law of the matter-dominated era and $\beta$, the exponential parameter for the darkenergy-dominated era. For our MSF, these values are $p$ = 0.28 and $\beta$ = 0.52 when using SNIa data, $p$ = 0.63 and $\beta$ = 0.30 for OHD data and $p$ = 0.45 and $\beta$ = 0.53 for a combination of datasets (OHD + SNIa). The numerical results and plots of the deceleration parameter, fractional energy density, Hubble parameter, and luminosity distance are presented which are the key parameters for studying the accelerated expansion of the universe. We compare the results of our model with that of the $\Lambda$CDM model and reconcile them with astronomical observational data. Our results indicate that the MSF model shows promise, demonstrating good compatibility with current astronomical observations and performing comparably to the $\Lambda$CDM model across various datasets, particularly in predicting the accelerating expansion of the universe, while providing a unified framework that incorporates the simultaneous influence of matter and dark energy components.