Observational Constraints on EoS parameters of Emergent Universe

We investigate emergent universe model using recent observational data for the background tests as well as for the growth tests. The background test data comprises of Hubble data, Baryon Acoustic Oscillation (BAO) data, cosmic microwave background (CMB) shift data, Union compilation data. The observational growth data are obtained from Wiggle-Z measurements and rms mass fluctuations data from Lyman-$α$ measurements at different red shifts. The flat emergent universe model obtained by Mukherjee {\it et. al.} is permitted with a non-linear equation of state (in short, EoS) ($p=Aρ-Bρ^{\frac{1}{2}}$), where $A$ and $B$ are constants. The observed cosmological data are used here to estimate the range of allowed values of EoS parameters numerically. The best-fit values of the EoS and growth parameters are determined making use of chi-square minimization technique. The analysis is carried out here considering the Wang-Steinhardt ansatz for growth index ($γ$) and growth function ($f$ defined as $f=Ω_{m}^γ (a)$). Subsequently, the best-fit values of the EoS parameters are used to study the evolution of the growth function $f$, growth index $γ$, state parameter $ω$ with red shift parameter $z$. The present value of the parameters, namely, $f$, $γ$, $ω$, $Ω_{m}$ are also estimated. The late accelerating phase of the universe in the model is accommodated satisfactorily.

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