Usually when one reads about the recombination in the standard model ($\Lambda$-$ CDM$) its written that the recombination occurs at a temperature $T\approx 3000 K$. Since, at this temperature the free electrons of the plasma become bound with the ionized hydrogen.
Let's call the Hubble parameter of the standard model $H(z)$. If for some unknown reason it so happens that the real Hubble parameter is $H_0(z)$ such that $H_0(z)>H(z)$, (that is the Universe expands faster than expected), then the recombination still happens in $T\approx 3000 K$? Or at a different temperature?
If $H_0(z)>>H(z)$, then I think that the Universe may never have recombination era, I'm not completely sure.