Unstable KleinGordon Modes in an Accelerating Universe Unstable
Unstable Klein-Gordon Modes in an Accelerating Universe
Unstable Klein-Gordon modes in an accelerating universe Dark Energy -does not behave like particles or radiation Quantised unstable modes -no particle or radiation interpretation Accelerating universe -produces unstable Klein-Gordon modes
Plan Solve K-G coupled to exponentially accelerating space background Canonical quantisation ->Hamiltonian partitioned into stable and unstable components Fundamental units of unstable component have no Fock representation Finite no. of unstable modes + Stone von Neumann theorem -> Theory makes sense
BASICS CM QM QFT -Qm Harmonic Oscillator -Fock Space
Classical Mechanics
Quantum Mechanics
Quantum Harmonic Oscillator
Quantum Field Theory
Fock Space
Klein-Gordon Change to time coordinate K-G becomes
Canonical Quantisation
Hamiltonian Sum of quadratic terms Bogoliubov transformation
Bogoliubov transformation preserves Canonical Commutation Relations
Bogoliubov Transformation
Energy Partitioning
Existence of Preferred Physical Representation Stone-von Neumann Theorem guarantees a preferred representation for HD HL has usual Fock representation There is a preferred representation for the whole system
Cosmological Consequences
Current/Future work This theory is semi-classical Dark energy at really long wavelengths A quantum gravity theory Dark energy at short wavelengths (we hope!)
Horava Gravity (Horava Phys. Rev. D 2009) Candidate for a UV completion General Relativity Higher derivative corrections to the Lagrangian Dispersion relation for scalar fields (Visser Phys. Rev. D 2009)
Development of unstable modes
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