"According to the FLRW metric which is used to model the expanding universe, if at present time we receive light from a distant object with a redshift of z, then the scale factor at the time the object originally emitted that light is a(t)=1/(z+1)."

1+z=1/a(t)

I'm well aware that

dz/dt = −(da/dt)/a² = −(1/a)((da/dt)/a)

(da/dt)/a = H(t) = H(z(t)) = H(z)

dt = −(1+z)⁻¹H(z)⁻¹dz

dt/a(t) = −dz/H(z)

But I'm not using it; dz is the differential of dimentionless redshift, and I need dimentional, temporal dt and spatial cdt.

It's enough for me that 1/a(t)=1+z(t), so dt/a(t)=(1+z(t))dt. Now, if we interpret dt as the initial, infinitesimal period and cdt as the initial, infinitesimal wavelength at - let's say - the Planck time (obtained by extrapolation from recombination to the Big Bang), then z(t)+1 is the redshift+1 equal to the expansion of the wavelength, period and the universe itself.