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

Abstract

First, the present work is concerned with generalising constructions and results in quantum field theory on curved spacetimes from the well-known case of the Klein-Gordon field to Dirac fields. To this end, the enlarged algebra of observables of the Dirac field is constructed in the algebraic framework. This algebra contains normal-ordered Wick polynomials in particular, and an extended analysis of one of its elements, the stress-energy tensor, is performed. Based on detailed calculations of the Hadamard coefficients of the Dirac field, it is found that a construction of a stress-energy tensor fulfilling necessary physical properties is possible. Additionally, the mathematically sound Hadamard regularisation prescription of the stress-energy tensor is compared to the mathematically less rigorous DeWitt-Schwinger regularisation and it is found 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-Walker spacetimes with a lightlike Big Bang hypersurface. Employing holographic methods, Hadamard states for the Klein-Gordon and the Dirac field are constructed. These states are preferred in the sense that they constitute asymptotic equilibrium states in the limit to the Big Bang hypersurface. Finally, solutions of the semiclassical Einstein equation for quantum fields of arbitrary spin are analysed in the flat Robertson-Walker case. One finds that these solutions explain the measured supernova Ia data as good as the $\La$CDM model. Hence, one arrives at a natural explanation of dark energy and a simple quantum model of cosmological dark matter. It is the hope of the author that the present thesis can serve as an accessible introduction to the field of (algebraic) quantum field theory on curved spacetimes and its recent developments.

arXiv commentPh.D. thesis, 262 pages, 5 figures

References in corpus (28)

• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Properties of singularities in (phantom) dark energy universe
• Type Ia Supernova Explosion Models
• On smooth Cauchy hypersurfaces and Geroch's splitting theorem
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• Testing the cosmological principle of isotropy: local power spectrum estimates of the WMAP data
• The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
• A general test of the Copernican Principle
• Einstein Equation with Quantum Corrections Reduced to Second Order
• A Test of the Copernican Principle
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• On the Renormalization Group in Curved Spacetime
• Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime
• The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor
• The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson-Walker Spacetimes
• Quantum out-states holographically induced by asymptotic flatness: Invariance under spacetime symmetries, energy positivity and Hadamard property
• Stable cosmological models driven by a free quantum scalar field
• Uniqueness theorem for BMS-invariant states of scalar QFT on the null boundary of asymptotically flat spacetimes and bulk-boundary observable algebra correspondence
• Cosmological horizons and reconstruction of quantum field theories
• Local Temperature in Curved Spacetime
• Tension in the Recent Type Ia Supernovae Datasets
• How unique is the expected stress-energy tensor of a massive scalar field?
• Local Thermal Equilibrium States and Quantum Energy Inequalities
• One-loop stress-tensor renormalization in curved background: the relation between $\zeta$-function and point-splitting approaches, and an improved point-splitting procedure
• The State Space of Perturbative Quantum Field Theory in Curved Spacetimes
• Aspects of locally covariant quantum field theory
• Elementary particles, holography and the BMS group
• General Covariance in Algebraic Quantum Field Theory

Cited by in corpus (14)

• Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction
• Quantum Field Theory on Curved Backgrounds -- A Primer
• Fermionic fields in the functional approach to classical field theory
• Global Existence of Solutions of the Semiclassical Einstein Equation for Cosmological Spacetimes
• The Fermionic Projector in a Time-Dependent External Potential: Mass Oscillation Property and Hadamard States
• Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
• The Regularized Hadamard Expansion
• A Mechanism of Baryogenesis for Causal Fermion Systems
• The Lambda CDM-model in quantum field theory on curved spacetime and Dark Radiation
• Kinetic theory and classical limit for real scalar quantum field in curved space-time
• A No-Go Theorem for the Consistent Quantization of Spin 3/2 Fields on General Curved Spacetimes
• Characteristics of interaction between Gravitons and Photons
• Dynamical Gravitational Coupling as a Modified Theory of General Relativity
• The Casimir effect from the point of view of algebraic quantum field theory