if you use static coordinates
gtt = 1 - r^2/A
1 + z = [gtt(receiver)/gtt(source)]^1/2
use r ~ A^1/2 - Lp in gtt(source) and r = 0 for gtt(receiver)
for advanced offer wave in the Cramer transaction
result is (first order Taylor series)
1 + z ~ (1/(Lp/A^1/2)^1/2) = (A^1/2/Lp)^1/2
---> infinity as Lp ---> 0
My argument in co-moving Friedmann coordinates below is consistent with the in static coordinates above.
So below ;-)
Indeed Tamara Davis in her PhD says what I say about the change of distance to our past and future horizons It's obvious from her diagram (Fig 1.1)
We recede from our past particle horizon, we approach our future dark energy de Sitter horizon.
1) In a Cramer transaction a retarded offer wave to us from near our past horizon is redshifted.
An advanced confirmation wave from us to near our past particle horizon is blue shifted.
Our relative space is effectively expanding forward in time in this transaction with our past horizon.
2) In a Cramer transaction an advanced offer wave to use from our future horizon is redshifted.
A retarded confirmation wave from us to it is blue shifted.
Our relative space is effectively contracting forward in time in this transaction with our future horizon.
Therefore, it is effectively expanding backwards in time for a back from the future advanced wave to us.
Advanced Wheeler-Feynman Hawking black body radiation of peak energy hc/Lp is then redshifted down to hc/(LpA^1/2)^1/2 at our detectors.
From Stefan-Boltzmann T^4 law this gives energy density hc/Lp^2A, which happens to agree with the actual dark energy density accelerating out causal diamond observable patch of the multiverse.
A = area of our future horizon at intersection with our future light cone.
The co-moving distance from us to our future horizon decreases forward in time.
The co-moving distance from us to our past horizon increases forward in time.
Virtual electron-positron pairs "stuck" on our future horizon are properly accelerating unlike real co-moving charges with zero proper acceleration AWAY from us. Therefore, using Doppler analogy radiation from them to us is redshifted. The virtual pairs are elevated to real pairs by the very hot Unruh radiation they feel locally. This is all in relation to us distant observers according to Susskind's "horizon complementarity".
proper acceleration of the virtual electron positron pairs stuck on the horizon is
g(r) = -(c^2/2)gtt^-1/2dgtt/dr
in static LNIF coordinates ONLY
gtt = 1 - r^2/A
dgtt/dr = -2r/A
g(r) = +c^2(1 - r^2/A)^-1/2r/A
note that we are at r = 0.
IN CONTRAST, for comoving sources in usual FRW coordinates gt't' = 1 so g'(r) = 0.
For details see Wikipedia.