Bouncing scenario with causal cosmology

Abstract

We present the cosmological model of a bouncing universe with causal fluid in the universe. The dissipative effects of the causal cosmic fluid is probed with both truncated Israel–Stewart theory and full Israel–Stewart theory. The following classes of non-vanishing scale factors of bouncing cosmology are considered with a viscous fluid: (i) the power-law bouncing model, (ii) the exponential bouncing model and (iii) the matter bouncing model in the Einstein gravity. The cosmological parameters of the Hubble parameter, deceleration parameter, jerk parameter, energy density and bulk viscous pressure of the universe are determined in the theories to obtain realistic cosmologies. The observational constraints of the parameters of bouncing cosmological models are estimated making use of the observed cosmological data. The physical and geometrical aspects of the cosmological models based on the imposed constraints are also discussed.

Appendix A: Appendix material

The expressions corresponding to the parameters $C_{1}$, $C_{2}$ and $C_{3}$ used in Eq. (8), (13) and (24) are given as follows:

$$\begin{aligned} C_{1} = &\epsilon \left [\beta _{1}(s-1)-r\beta - \frac{\omega }{\omega +1} \right ], \end{aligned}$$

(A.1)

$$\begin{aligned} C_{2}=& 3\bigg[ 1+\omega +\frac{H^{1-2s}}{3^{s} \beta _{1}} \\ & + \frac{\epsilon }{2}(1+\omega )\left (\beta _{1}(s-1)-r\beta - \frac{\omega }{\omega +1}\right ) +\frac{\epsilon }{2} \bigg], \end{aligned}$$

(A.2)

and

$$ C_{3} = \frac{9}{2}\left [ \frac{(1+\omega )}{3^{s} \beta _{1}}H^{1-2s}- \frac{\beta 3^{r-s}}{2\beta _{1}} H^{2r-2s} + \frac{\epsilon (1+\omega )}{2}\right ]. $$

(A.3)