  A near-future detection of the 21cm signal from the epoch of reionization
will provide unique opportunities to probe the underlying cosmology, provided
that such cosmological information can be extracted with precision. To this
end, we further develop effective field theory (EFT) inspired techniques for
the 21cm brightness temperature field during the epoch of reionization,
incorporating renormalized bias and a treatment of redshift space distortions.
Notably, we confirm that in redshift space, measures of the 21cm brightness,
e.g the power spectrum, should have irreducible contributions that lack a bias
coefficient and therefore contain direct, astrophysics-free information about
the cosmological density field; in this work, we study this effect beyond
linear order. To validate our theoretical treatment, we fit the predicted EFT
Fourier-space shapes to the THESAN suite of hydrodynamical simulations of
reionization at the field level, where the considerable number of modes
prevents overfitting. We find agreement at the level of a few percent between
the 21cm power spectrum from the EFT fits and simulations over the wavenumber
range $k \lesssim 0.8$ h/Mpc and neutral fraction $x_\mathrm{HI} \gtrsim 0.4$,
which is imminently measurable by the Hydrogen Epoch of Reionization Array
(HERA) and future experiments. The ability of the EFT to describe the 21cm
signal extends to simulations that have different astrophysical prescriptions
for reionization as well as simulations with interacting dark matter.
