Properties of Quantum Fields in de Sitter

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We analyse the consequences of euclidean conformal symmetry on correlation functions of theories in spacetimes undergoing accelerated expansion. We consider the spectra of quantum mechanical states in field theories on a fixed de Sitter (dS) background, as well as possible extensions and connections to gravitational fluctuations in asymptotic de Sitter. We elucidate the construction of massive Fermionic fields in dS in any dimension using embedding space methods, with analysis of the Wightman propagator. We then analyse field theoretic models which include states transforming in discrete series representations in their Hilbert space. Led by the observation that these representations are unitary and irreducible in dS. We consider the consequences of constraints to dynamical results for these models, as well as the impact of their contact terms appearing in late time gravitational observables. We work primarily in 2 dimensions and hope to extend our analysis to analogous series of representations in higher dimensional dS. This analysis of the spectra of de Sitter states is hoped to further clarify the properties of models which might exhibit the dS/CFT correspondence.