Quasi-matter Bounce Cosmology in Light of Planck

We study quasi-matter bounce cosmology in light of Planck cosmic microwave background (CMB) angular anisotropy measurements along with the BICEP2/Keck Array data. We propose a new primordial scalar power spectrum by considering a linear approximation of the equation of state $w\cong w_0+\kappa(\eta-\eta_0)$ for quasi-matter field in the contracting phase of the universe. Using this new primordial scalar power spectrum, we constrain the zeroth-order approximation of the equation of state $w_0= -\,0.00340\pm 0.00044$ and first-order correction $10^{4} \zeta= -1.67^{+1.50}_{-0.83}$ at the $1\sigma$ confidence level by Planck temperature and polarization in combination with the BICEP2/Keck Array data in which $\zeta = 12\kappa/k_*$ with pivot scale $k_*$. The spectral index of scalar perturbations is determined to be $n_{\rm Bs}=0.9623\pm0.0055$ which lies 7$\sigma$ away from the scale-invariant primordial spectrum. We find scale dependency for $n_{\rm s}$ at the $1\sigma$ confidence level and a tighter constraint on the running of the spectral index compared to $\Lambda$CDM+$\alpha_s$ cosmology. The running of the spectral index in quasi-matter bounce cosmology is $\alpha_{\rm Bs}= \pi \zeta /2 c_{\rm s} = -\hspace{.5mm}0.0021 \pm 0.0016$ which is nonzero at the $1.3\sigma$ level, whereas in $\Lambda$CDM+$\alpha_{\rm s}$ it is nonzero at the $0.8\sigma$ level for Planck temperature and polarization data. The sound speed of density fluctuations of the quasi-matter field at the crossing time is $c_{\rm s} = 0.097^{+0.037}_{-0.023}$, which is not a very small value in the contracting phase.