Accessing the homogeneity scale with 21 cm intensity mapping surveys

Abstract

The homogeneity scale, $R_{\mathrm{H}}$, offers a fundamental test of the Cosmological Principle, yet it has not yet been measured with 21cm intensity mapping surveys. A key limitation for such a measurement is the telescope beam, which artificially smooths the observed signal. We quantify this effect using the two-point correlation function and the correlation dimension, ${\mathcal{D}}_2(r)$, to model how beam convolution suppresses intrinsic clustering. For any given redshift $z$, we identify a maximum beam width, $\ddot{I}{ƒ}_{\max }(z)$, beyond which the homogeneity scale cannot be recovered. This limit defines an inaccessible region in the $\ddot{I}ƒ\times z$ parameter space, where $R_{\mathrm{H}}$ is erased by beam smoothing. Applying this framework to several current and upcoming radio telescopes, we assess their ability to probe $R_{\mathrm{H}}$. Our results provide the first quantitative forecast of the instrumental requirements for measuring the cosmic homogeneity scale with 21cm IM, and establish a theoretical basis for future observational applications.

6 pages and 4 figures