Constraints on the emergent universe from recent temperature and Hubble data

In this paper, the emergent universe model (EU) is explored (as per Mukherjee \({\mathit{et\;al.}}\)) in a flat scenario with equation of state \((EoS)\) \(p=B\rho -A\rho ^{\frac{1}{2}}\) (where \(A\) and \(B\) are constants). Here, the temperature function is evaluated in terms of the EoS parameters and redshift under the conditions of balanced particle creation and annihilation. To examine the thermodynamic evolution and find a viable EU model, constraints on its EoS parameters are determined. First, constraints on \(A_{s}\), and \(B\) (where \(A_{s} = \frac{A}{\rho _{eu0}^{\frac{1}{2}}}\) and \(\rho _{eu0}\) is the present energy density) are obtained from the acceptable transition redshift limit \(z_{tr}\) and decoupling temperature limit \(T_{d}\) as \(A_{s}\) ≈ \((0.84-1.07)\) and \(B\) ≈ \((0.38-0.42)\) for the general EU model. Finally, stricter constraints on \(z_{tr}\) are drawn from recent \(T(z)-z\) and observed Hubble data (OHD). These \(z_{tr}\) and \(T_{d}\) values are then utilized to obtain acceptable limits on \(A_{s}\), and \(B\). On average, the acceptable limits on \(z_{tr}\), \(A_{s}\), and \(B\) are \(0.79\pm 0.03\) (in the 1\(\sigma \) error limit), ≈ \((1.11-1.15)\) and ≈ \((0.41-0.43)\), respectively, for the general EU model. In the \(B=\frac{1}{3}\) model, obtained value \(z_{tr}= 0.71\pm 0.01\) (at the 1\(\sigma \) level). The present values of the EoS parameters are determined, and the viability of the models is examined with plots of the deceleration parameter (\(q\)), equation of state (\(\omega \)) and squared adiabatic sound speed (\(c^{2}_{s}\)) with redshift (\(z\)). The distance modulus (\(\mu \)) of this EU model is compared with the HIIG and Union2.1 data. The models with \(B\) \((= -\frac{1}{3}, 0)\), are not suitable at all according to the present analysis, whereas, the \(B=\frac{1}{3}\) model is quite similar to the observations.