Reaching small scales with low frequency imaging: applications to the Dark Ages

The initial conditions for the density perturbations in the early Universe, which dictate the large scale structure and distribution of galaxies we see today, are set during inflation. Measurements of primordial non-Gaussianity are crucial for distinguishing between different inflationary models. Current measurements of the matter power spectrum from the CMB only constrain this on scales up to $k\sim 0.1$ Mpc$^{-1}$. Reaching smaller angular scales (higher values of $k$) can provide new constraints on non-Gaussianity. A powerful way to do this is by measuring the $\textrm{H}\textrm{I}$ matter power spectrum at $z\gtrsim30$. In this paper, we investigate what values of $k$ can be reached for the LOw Frequency ARray (LOFAR), which can achieve $\lesssim$1$''$ $\,$resolution at $\sim$50 MHz. Combining this with a technique to isolate the spectrally smooth foregrounds to a wedge in $k_{\parallel}$ - $k_{\perp}$ space, we demonstrate what values of $k$ we can feasibly reach within observational constraints. We find that LOFAR is $\sim$5 orders of magnitude away from the desired sensitivity, for 10 years of integration time.