Lorentz effects on observed distance and lookback as a function of cosmic redshift

Under Albert Einstein’s postulated constant speed of light c, photon travel distance d_λ and time t_λ from source to receptor are unaffected by their recession rate βc:

(1) t_λ = d_λ/c for all 0 ≤ β < 1.

Neither d_λ nor t_λ change after photon emission. Any later increase in the source’s proper distance d, i.e. the ‘expansion of space’, has no effect on t_λ. Under such constraint, d and d_λ become identical.

The presenter proposes that observed source distances d_obs, by all methods of calculation, are in fact contracted, by the Lorentz factor γ:

(2) d_λ = d = d_obsγ

Source lookback (t₀ – t) is twice affected by γ:

(3) (t₀ – t) = t_λγ = d_obsγ²/c

Both d and (t₀ – t) are found as instant products from d_obs and γ(β). To a first approximation, line integration along redshift z is not required to get d and (t₀ – t). General relativistic perturbations in the light path, i.e. mass density variance, may require line integration to resolve. This will not be addressed, nor will dust effects in the light path. Presenter will combine Eqs. (2) and (3) with ΛCDM parameters to show that the Universe at the time of last scattering was at least 170 billion years (Gyr) older than it is today. If we use H₀ = 73 km s^-1 Mpc^-1, then d_λ = d reached a maximum value of 6 Gl-yr at z = 1.6, with (t₀ – t) = 9 Gyr. At z = 10, d = 3.6 Gl-yr and (t₀ – t) = 20 Gyr. Presenter will conclude by proposing that within our frame of reference, general relativistic effects at singularity can be numerically shown to result in an inflationary period. He will also suggest that there may be a singular upper boundary of both redshift z, and energy density ε.