Abstract: Astrophysics faces two critical challenges: the difficulty of observing very distant targets and the difficulty of interpreting science in diverse and often extreme environments that have not been replicated on Earth. In this thesis, we discuss two types of spectra - one from early universe cosmology and one from astrobiology - where improvements in telescope technology are just ushering in a wave of precise observations, addressing the first challenge. This accelerates the need for a solution to the second challenge. Traditional methods for analyzing these two spectra rely heavily on unsettled science, biasing results to match the input assumptions. In this thesis, we present an information entropic spectral method (IESM) that minimizes the necessary input knowledge by using Jensen-Shannon Divergence, a measure sensitive to the most salient features of the spectra.
We apply this method first to the power spectrum of the cosmic microwave background. We develop an IESM-driven Markov Chain Monte Carlo routine to perform cosmological parameter estimation on a restricted parameter space for two popular dark energy models. We find results that generally agree with the Bayesian results, and present an analysis of the differences.
We then apply the method to simulated transmission spectra of the atmospheres of exoplanets. We show that IESM can distinguish between different types of exoplanets, while quantitatively describing the ``Earth-likeness" (in terms of similarity of spectra) of an exoplanet. We also show how the method can be used to determine the Earth-likeness of biosignatures in transmission spectra. Together, these two methods can be used to identify candidates for hosting life and to identify exoplanets that show signs of bioactivity.
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