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 gravityand Starobinsky's anomaly-induced inflation are either both present or both absent, depending on the particle content of the theory.
Highlights
We will revise the onset of inflation driven by the trace anomaly of the quantum effective action, in the absence of both, a “bare” action for gravity and an inflaton field, in the sense of a scalar field incorporated in the model
Spectral regularisation was first introduced in a context of chiral, and later scale anomalies in Quantum Chromo Dynamics (QCD) in flat space-time [31, 32]
We generalise the spectral regularisation for all quantised fields, in order to study in a systematic way the influence of quantum vacuum fluctuations on the gravitational dynamics
Summary
We will derive a mathematical description of anomaly using spectral regularisation. We will first compute the anomaly and present the anomaly generating functional. The latter is achieved through the introduction of an auxilary field, that can be considered as a collective degree of freedom of vacuum fluctuations of all fields, dual to conformal anomaly
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