Origin of inflation in CFT driven cosmology: $R^2$-gravity and non-minimally coupled inflaton models

Abstract

We present a detailed derivation of the recently suggested new type of hill-top inflation [arXiv:1509.07270] originating from the microcanonical density matrix initial conditions in cosmology driven by conformal field theory (CFT). The cosmological instantons of topology $S^1\times S^3$, which set up these initial conditions, have the shape of a garland with multiple periodic oscillations of the scale factor of the spatial $S^3$-section. They describe underbarrier oscillations of the inflaton and scale factor in the vicinity of the inflaton potential maximum, which gives a sufficient amount of inflation required by the known CMB data. We build the approximation of two coupled harmonic oscillators for these garland instantons and show that they can generate inflation consistent with the parameters of the CMB primordial power spectrum in the non-minimal Higgs inflation model and in $R^2$ gravity. In particular, the instanton solutions provide smallness of inflationary slow-roll parameters $\epsilon$ and $\eta <0$ and their relation $\epsilon \sim {\eta }^2$ characteristic of these two models. We present the mechanism of formation of hill-like inflaton potentials, which is based on logarithmic loop corrections to the asymptotically shift-invariant tree level potentials of these models in the Einstein frame. We also discuss the role of $R^2$-gravity as an indispensable finite renormalization tool in the CFT driven cosmology, which guarantees the non-dynamical (ghost free) nature of its scale factor and special properties of its cosmological garland type instantons. Finally, as a solution to the problem of hierarchy between the Planckian scale and the inflation scale we discuss the concept of a hidden sector of conformal higher spin fields.

final version, to be published in European Physical Journal C. arXiv admin note: text overlap with arXiv:1509.07270

References in corpus (17)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The Standard Model Higgs boson as the inflaton
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Higgs inflation: consistency and generalisations
• Inflation scenario via the Standard Model Higgs boson and LHC
• Inflationary schism after Planck2013
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Cosmological Landscape From Nothing: Some Like It Hot
• Thermodynamics via Creation from Nothing: Limiting the Cosmological Constant Landscape
• Why there is something rather than nothing (out of everything)?
• Anomaly Driven Cosmology: Big Boost Scenario and AdS/CFT Correspondence
• Are $R^2$- and Higgs-inflations really unlikely?
• Replication Regulates Volume Weighting in Quantum Cosmology
• Effect of the Trace Anomaly on the Cosmological Constant
• The Gauss-Bonnet Coupling Constant in Classically Scale-Invariant Gravity
• CFT driven cosmology and conformal higher spin fields
• Spacetime Average Density (SAD) Cosmological Measures

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• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities
• Nonminimal Coleman--Weinberg Inflation with an $R^2$ term
• Darkness without dark matter and energy -- generalized unimodular gravity
• CFT driven cosmology and conformal higher spin fields
• Constraints on non-minimal coupling from quantum cosmology
• Notes on conformal anomaly, nonlocal effective action and the metamorphosis of the running scale
• Weyl Anomaly and Initial Singularity Crossing
• Topological Inflation
• Kinetic dominance and the wavefunction of the universe
• Preferred basis, decoherence and a quantum state of the Universe
• Holographic Cosmology and Phase Transitions of SYM theory
• Tunneling in Quantum Cosmology and Holographic SYM theory