The CMB modulation from inflation

Erickcek, Kamionkowski and Carroll proposed in 2008 that the dipole modulation of the CMB could be due to a very large scale perturbation of the field ϕ causing the primordial curvature perturbation. We repeat their calculation using weaker assumptions and the current data. If ϕ is the inflaton of any single-field inflation with the attractor behaviour, the asymmetry is almost certainly too small. If instead ϕ is any curvaton-type field (ie. one with the canonical kinetic term and a negligible effect during inflation) the asymmetry can agree with observation if | f NL | in the equilateral configuration is ≃ 10 for k −1 = 1Gpc and ≲3 for k −1 = 1Mpc. An f NL with these properties can apparently be obtained from the curvaton with an axionic potential. Within any specific curvaton-type model, the function f NL ( k 1 , k 2 , k 3 ) required to generate the asymmetry would be determined, and could perhaps already be confirmed or ruled out using existing Planck or WMAP data.