Noncommutative Geometry in the Motor Theory

In this work,we generalise the motor theory [1] to the case of noncommutative geometry.We show that the motor dimension µ can be interpreted as a noncommutative coordinatesatisfying the relation [µ, xν] = iθµν , where θµν is an antisymmetric tensor of noncommuta-tivity parameters of dimension lengthІ. This leads to a deformation of the mass spectrumMn = |n|/(RµΦ), a modication of the inationary potential, and the emergence of neweects at the Planck scale. We derive the modied mass spectrum, discuss the impact ofnoncommutativity on ination and cosmological perturbations, and consider possible exper-imental manifestations: modication of dispersion relations, new signatures in cosmic raysand gravitational-wave observations. The theory yields testable predictions at the Planckscale and may be related to quantum gravity.