Spectral Regularisation: Induced Gravity and the Onset of Inflation

Abstract

Using spectral regularisation, we compute the Weyl anomaly and express the anomaly generating functional of the quantum effective action through a collective scalar degree of freedom of all quantum vacuum fluctuations. Such a formulation allows us to describe induced gravity on an equal footing with the anomaly-induced effective action, in a self-consistent way. We then show that requiring stability of the cosmological constant under loop quantum corrections, Sakharov's induced gravity and Starobinsky's anomaly-induced inflation are either both present or both absent, depending on the particle content of the theory.

23 pages, 1 figure Slightly amended file to match published version

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• Inducing Gravity From Connections and Scalar Fields
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Clifford Structures in Noncommutative Geometry and the Extended Scalar Sector
• Gravitational Waves from Preheating in Inflation with Weyl Symmetry
• Unification of Coupling Constants, Dimension six Operators and the Spectral Action
• Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D
• Inflation and cosmic (super)strings: implications of their intimate relation revisited
• Unweaving the Fabric of the Universe: The Interplay between Mathematics and Physics