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Recently, the Planck 2013 results showed possible evidence for a dipolarpower modulation of the CMB temperature fluctuations at low--(\ell) multipoles.This anomaly might imply certain deviations from statistical isotropy. Toincorporate the Planck's data into standard cosmological model, we propose aninflation model of the very early universe in an anisotropic spacetime. Ageneralized Friedmann-Robertson-Walker (FRW) metric is presented in theRanders-Finsler spacetime. We obtain the primordial power spectrum of thescalar perturbation with direction dependence, such as the dipolar modulation.This is consistent with the dipolar power modulation of the CMB anisotropysignaled by the Planck observation.

Inflation and primordial power spectra at anisotropic spacetime inspired by Planck's constraints on isotropy of CMB