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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 $w\cong w_0+κ(η-η_0)$ 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 $10^{4} ζ= -1.67^{+1.50}_{-0.83}$ at the $1σ$ confidence level by Planck temperature and polarization in combination with the BICEP2/Keck Array data in which $ζ= 12κ/k_*$ with pivot scale $k_*$. The spectral index of scalar perturbations is determined to be $n_{\rm Bs}=0.9623\pm0.0055$ which lies 7$σ$ away from the scale-invariant primordial spectrum. We find scale dependency for $n_{\rm s}$ at the $1σ$ confidence level and a tighter constraint on the running of the spectral index compared to $Λ$CDM+$α_s$ cosmology. The running of the spectral index in quasi-matter bounce cosmology is $α_{\rm Bs}= πζ/2 c_{\rm s} = -\hspace{.5mm}0.0021 \pm 0.0016$ which is nonzero at the $1.3σ$ level, whereas in $Λ$CDM+$α_{\rm s}$ it is nonzero at the $0.8σ$ 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.