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This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.

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Introduction.- A pedagogical introduction to algebraic quantum field on curved spacetimes.- From classical to quantum.- Outline of the cosmological applications.- Algebraic quantum field on curved spacetimes.- Globally hyperbolic spacetimes.- Linear classical fields on curved spacetimes.- Linear quantum fields on curved spacetimes.- Hadamard states.- Locality and general covariance.- The stress-energy tensor and the semiclassical Einstein equation.- Cosmological applications.- A brief introduction to cosmology.- The cosmological expansion in QFT on curved spacetimes.- A birds-eye view of perturbations in Inflation.

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"The main intent of this short volume is to provide a largely self-contained and broadly accessible exposition of two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime. ... There is a very long reference list at the end of each chapter and the overall impression is that the author transmits a great deal of information about this subject in a brief volume." (Paul F. Bracken, Mathematical Reviews, April, 2016)

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