Opening the low frequency window to the high redshift Universe

The epoch of formation of the first luminous structures (stars and galaxies) called the Comic Dawn, is one of the last unexplored periods in the history of the Universe. A new generation of radio telescopes such as LOFAR aim to revolutionize our understanding of structure formation in the early Universe by directly observing the 21-cm line of hydrogen from this epoch. Due to cosmic expansion, this 21-cm signal reaches us at low radio frequencies (50 to 200 MHz). Properly accounting for and correcting the effects of propagation through an atmospheric layer called the ionosphere is an important outstanding challenge in low frequency observations. In this thesis, I develop a mathematical framework to study ionospheric scintillation (akin to stellar twinkling) and compute its effects on radio observations of the early Universe. I find that although formidable, ionospheric corruptions do not pose a fundamental limit to achieve a detection of the 21-cm signal from the early Universe. In addition, I also demonstrate a new observational technique that uses the Moon as a temperature reference to accurately measure the spectrum of the radio sky. While this technique may in future lead to a detection of the sky-averaged 21-cm signal from the cosmic dawn, I touch upon its potential in the near future to determine lunar crustal composition and temperature at unprecedented depths.