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First, the present work is concerned with generalising constructions andresults in quantum field theory on curved spacetimes from the well-known caseof the Klein-Gordon field to Dirac fields. To this end, the enlarged algebra ofobservables of the Dirac field is constructed in the algebraic framework. Thisalgebra contains normal-ordered Wick polynomials in particular, and an extendedanalysis of one of its elements, the stress-energy tensor, is performed. Basedon detailed calculations of the Hadamard coefficients of the Dirac field, it isfound that a construction of a stress-energy tensor fulfilling necessaryphysical properties is possible. Additionally, the mathematically soundHadamard regularisation prescription of the stress-energy tensor is compared tothe mathematically less rigorous DeWitt-Schwinger regularisation and it isfound that both prescriptions are essentially equivalent in rigorous terms.  While the aforementioned results hold in generic curved spacetimes,particular attention is also devoted to a specific class of Robertson-Walkerspacetimes with a lightlike Big Bang hypersurface. Employing holographicmethods, Hadamard states for the Klein-Gordon and the Dirac field areconstructed. These states are preferred in the sense that they constituteasymptotic equilibrium states in the limit to the Big Bang hypersurface.Finally, solutions of the semiclassical Einstein equation for quantum fields ofarbitrary spin are analysed in the flat Robertson-Walker case. One finds thatthese solutions explain the measured supernova Ia data as good as the $\La$CDMmodel. Hence, one arrives at a natural explanation of dark energy and a simplequantum model of cosmological dark matter.  It is the hope of the author that the present thesis can serve as anaccessible introduction to the field of (algebraic) quantum field theory oncurved spacetimes and its recent developments.

On the Backreaction of Scalar and Spinor Quantum Fields in Curved Spacetimes - From the Basic Foundations to Cosmological Applications