In this work , we study a direction dependent power spectrum in anisotropic Finsler space-time .
We use this direction dependent power spectrum to address the low- l power observed in WMAP and PLANCK data .
The angular power spectrum of the temperature fluctuations has a lower amplitude in comparison to the \Lambda CDM model in the multipole range l = 2 - 40 .
Our theoretical model gives a correction to the isotropic angular power spectrum C ^ { TT } _ { l } due to the breaking of the rotational invariance of the primordial power spectrum .
We estimate best-fit model parameters along with the six \Lambda CDM cosmological parameters using PLANCK likelihood code in CosmoMC software .
We see that this modified angular power spectrum fits the CMB temperature data in the multipole range l = 2 - 10 to a good extent but fails for the whole multipole range l = 2 - 40 .