Cosmological Applications of Algebraic Quantum Field Theory

  • Thomas-Paul Hack
  • Nicola Pinamonti
Part of the Mathematical Physics Studies book series (MPST)


Quantum field theory on curved spacetime is a generalisation of quantum field theory in flat spacetime which is expected to be the proper fundamental description of non–trivial physical phenomena in the presence of a spacetime curvature which is large but below Planck scale. Two prominent physical situations which fall under this characterisation are phenomena both in the vicinity of black holes and in the early universe. Focusing on the latter, we review several applications of algebraic quantum field theory on curved spacetimes to cosmology, as well as foundational results and constructions on which these applications are based. On the foundational side, we collect several proposals to construct Hadamard states on cosmological spacetimes, as this class of states is believed to encompass all physically meaningful states in quantum field theory on curved spacetimes. Afterwards we consider the solution theory of the semiclassical Einstein equation, quote a theorem of existence and uniqueness of solutions to this equation and indicate directions to go beyond the semiclassical Einstein equation. Then we highlight how the observed cosmological expansion may be understood qualitatively and quantitatively in this framework, before we discuss the quantization of perturbations in inflation in the context of algebraic quantum field theory. In the latter subject, the starting point is the assumption that the classical, rather than the semiclassical, Einstein equation is satisfied. We close this chapter briefly discussing how one may generalise the analysis of perturbations in inflation by allowing for spacetimes backgrounds which solve the semiclassical Einstein equations.


Curve Spacetimes Local Observable Cosmological Time Spatial Infinity Hadamard State 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GenovaGenova Italy
  2. 2.INFN—Sezione di GenovaGenovaItaly

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