Until recently with MiHsC I had assumed that the Hubble-scale Casimir effect modifies standard inertia, and I hadn't specified a model for standard inertia. Recently I proposed such a model as follows. When you accelerate an object (the white circle in the diagram below) to the right, then beyond a certain distance to its left information can never catch up to it, so a Rindler horizon forms (see the shaded line) which is similar to the Hubble horizon in that it is a boundary to what can be known by the object. MiHsC proposes that the Unruh waves seen by an object as it accelerates have to fit exactly within the Hubble horizon. So this rule should also apply to the Rindler horizon on its left.
I summed up all these forces in the paper below, and made a factor of two error in part of it, but if you correct the error* (in Eq. 4 change the first 4 to an 8) then the predicted inertial mass of a particle with a radius of one Planck length (lp) is (pi^2*h)/(48*c*lp) = 2.75x10^-8 kg which is 26% greater than the Planck mass of 2.176x10^-8 kg.
*=this error was kindly pointed out to me by J. Gine.
McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001.
arXiv preprint: 1302.2775