"To summarize, in this article we have used the formalism of electrodynamics
in curved spacetime to generalized Sciama’s law of inertial induction to a curved
spacetime represented by the Friedmann models, and obtained covariant expressions
for the inertial force on a accelerating particle in these models. This extends previous
work by Berry and later by Signore on the subject of inertia in Friedmann universes.
As in Berry’s case we have showed that the total inertial force F = −ma on an
accelerating particle cannot be explained only in terms of inertial induction from
the total matter and radiation in the current universe. We have also seen from
(38) that the inertial force is redshift dependent and increases for earlier times
until it reaches the asymptotic value of −(1/3)ma in the matter dominated case or
−(1/2)ma in the radiation dominated case."
now they only do the past particle horizon and neglect the future event horizon.
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It's curious that the past-particle horizon gives 0.23 same as Omega dark matter
F = [Omega(past particle horizon) + Omega(future event horizon) + Omega(real particles)]ma
= [.23 + .73 + .04]ma present epoch
in general this is time independent because
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/kolb1/kolb1new_Page_21_jpg.htm