  We explore constraints on dark energy and modified gravity with forecast 21cm
intensity mapping measurements using the Effective Field Theory approach. We
construct a realistic mock data set forecasting a low redshift 21cm signal
power spectrum $P_{21}(z,k)$ measurement from the MeerKAT radio-telescope. We
compute constraints on cosmological and model parameters through Monte Carlo
Markov chain techniques, testing both the constraining power of $P_{21}(k)$
alone and its effect when combined with the latest Planck 2018 CMB data. We
complement our analysis by testing the effects of tomography from an ideal mock
data set of observations in multiple redshift bins. We conduct our analysis
numerically with the codes EFTCAMB/EFTCosmoMC, which we extend by implementing
a likelihood module fully integrated with original codes. We find that adding
$P_{21}(k)$ to CMB data provides significantly tighter constraints on
$\Omega_ch^2$ and $H_0$, with a reduction of the error with respect to Planck
results at the level of more than $60\%$. For the parameters describing beyond
$\Lambda$CDM theories, we observe a reduction in the error with respect to the
Planck constraints at the level of $\lesssim 10\%$. The improvement increases
up to $\sim 35\%$ when we constrain the parameters using ideal, tomographic
mock observations. We conclude that the power spectrum of the 21cm signal is
sensitive to variations of the parameters describing the examined beyond
$\Lambda$CDM models and, thus, $P_{21}(k)$ observations could help to constrain
dark energy. The constraining power on such theories is improved significantly
by tomography.
