Finsler space-time can explain both parity asymmetry and power deficit seen in CMB temperature anisotropies

We propose a framework of Finsler space-time to explain the observed parity asymmetry and the power deficit in the low-$\mathrm{\ell }$ ($2\leqslant \ell \leqslant 29$) multipole range of cosmic microwave background (CMB) temperature anisotropies. In the $3+1$ dimensional space-time, the three-dimensional space is described by a Randers-Finsler space, which is spatially irreversible, inducing the parity asymmetry in the CMB angular power spectrum. We estimate the constraints on the two parameters introduced by Finsler space-time via analyzing the low-$\mathrm{\ell }$ angular power spectrum in PLANCK 2015 CMB temperature data. We see that the low-$\mathrm{\ell }$ power suppression in the CMB temperature anisotropies can also be resolved in this scenario. Our study shows that the two low-$\mathrm{\ell }$ anomalies, i.e., parity asymmetry and power deficit, may have a common origin.