Non-commutative geometry at inflation can give arise to parity violating modulations of the primordial power spectrum .
We develop the statistical tools needed for investigating whether these modulations are evident in the Cosmic Microwave Background ( CMB ) .
The free parameters of the models are two directional parameters ( \theta, \phi ) , the signal amplitude { \cal A } _ { * } , and a tilt parameter n _ { * } that modulates correlation power on different scales .
The signature of the model corresponds to a kind of hemispherical power asymmetry .
When analyzing the 7-year WMAP data we find a weak signature for a preferred direction in the Q- , V- , and W bands with direction ( l,b ) = ( -225 ^ { \circ } , -25 ^ { \circ } ) \pm ( 20 ^ { \circ } , 20 ^ { \circ } ) , which is close to another previously discovered hemispherical power asymmetry .
Although these results are intriguing , the significance of the detection in the W- , V- and Q-bands are nonzero at about 2 \sigma , suggesting that the simplest parameterization of the leading correction represents only partially the effects of the space-time non-commutativity possibly responsible for the hemispherical asymmetry .
Our constraints on the presence of a dipole are independent of its physical origin and prefer a blue-tilted spectral index n _ { * } \approx 0 with the amplitude { \cal A } _ { * } \approx 0.18 .