The redshift staircase: time-domain tests of discrete spatial slices with pulsar timing and redshift drift

In the author's picture, space is a sequence of static slices, and what is seen as expansion is the passage of matter from one slice to the next. If bodies cross between slices by discrete steps of size ℓ in ln R and the redshift is an integer multiple of the step, ln(1+z) = (n_o − n_e)ℓ, redshift surveys can detect the ladder only if the step exceeds the velocity blur, and DESI DR1 excludes ℓ ≳ 0.002. In the time domain, collective crossing makes the redshift of every source change as a staircase whose mean is the standard Sandage–Loeb drift, with step size times mean step rate equal to H₀. For Galactic pulsars it produces fractional frequency steps of ℓ, a common part and pulsar-specific parts delayed by the light-travel time; in synthetic arrays the delayed parts keep the signal detectable after a free clock term is fitted. In public NANOGrav 12.5-yr data for 44 pulsars, periodic steps are excluded at all tested values between 6×10⁻¹² and 3.5×10⁻¹⁰, except for periods near one year and half a year, and random steps are limited by the quietest pulsars to ℓ ≲ 10⁻¹⁸. In the present form of the picture a jump is a quantum transition of matter at one mode, at random times; if the contributions to an observed frequency cross independently, the signal is reduced by their number, and the picture remains consistent with these limits. Its own time-domain prediction is the smooth drift of the exchange-law cosmology, smaller than in ΛCDM by 0.9 cm/s over 20 years at z = 0.3–0.5. Files: the paper (PDF), and the code and converted data (redshift_staircase_code_v4.zip) needed to reproduce all results.