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Rapid roll Inflation with Conformal Coupling

Lev Kofman, Shinji Mukohyama

TL;DR

The paper shows that a conformally coupled scalar with a flat potential can drive inflation, realized as rapid-roll rather than slow-roll, and provides a phase-portrait demonstration of its attractor behavior. In warped brane inflation, the inflationary scale and the number of e-folds are constrained by the throat geometry, yielding $N_* \lesssim 34$ and $M \lesssim 10^6$ GeV, with possible TeV-scale inflation for suitable throat offsets. Since the conformal inflaton cannot generate primordial fluctuations, the work advocates modulated reheating or curvaton mechanisms, including light moduli or axion fields, to supply cosmological perturbations. The analysis links low-energy inflation to a possible resolution of the hierarchy problem via warp factors and broadens the scope of conformal coupling in inflationary model building.

Abstract

Usual inflation is realized with a slow rolling scalar field minimally coupled to gravity. In contrast, we consider dynamics of a scalar with a flat effective potential, conformally coupled to gravity. Surprisingly, it contains an attractor inflationary solution with the rapidly rolling inflaton field. We discuss models with the conformal inflaton with a flat potential (including hybrid inflation). There is no generation of cosmological fluctuations from the conformally coupled inflaton. We consider realizations of modulated (inhomogeneous reheating) or curvaton cosmological fluctuations in these models. We also implement these unusual features for the popular string-theoretic warped inflationary scenario, based on the interacting D3-anti D3 branes. The original warped brane inflation suffers a large inflaton mass due to conformal coupling to 4-dimensional gravity. Instead of considering this as a problem and trying to cure it with extra engineering, we show that warped inflation with the conformally coupled, rapidly rolling inflaton is yet possible with N=37 efoldings, which requires low energy scales 1-100 TeV of inflation. Coincidentally, the same warping numerology can be responsible for the hierarchy. It is shown that the scalars associated with angular isometries of the warped geometry of compact manifold (e.g. S^3 of KS geometry) have solutions identical to conformally coupled modes and also cannot be responsible for cosmological fluctuations. We discuss other possibilities.

Rapid roll Inflation with Conformal Coupling

TL;DR

The paper shows that a conformally coupled scalar with a flat potential can drive inflation, realized as rapid-roll rather than slow-roll, and provides a phase-portrait demonstration of its attractor behavior. In warped brane inflation, the inflationary scale and the number of e-folds are constrained by the throat geometry, yielding and GeV, with possible TeV-scale inflation for suitable throat offsets. Since the conformal inflaton cannot generate primordial fluctuations, the work advocates modulated reheating or curvaton mechanisms, including light moduli or axion fields, to supply cosmological perturbations. The analysis links low-energy inflation to a possible resolution of the hierarchy problem via warp factors and broadens the scope of conformal coupling in inflationary model building.

Abstract

Usual inflation is realized with a slow rolling scalar field minimally coupled to gravity. In contrast, we consider dynamics of a scalar with a flat effective potential, conformally coupled to gravity. Surprisingly, it contains an attractor inflationary solution with the rapidly rolling inflaton field. We discuss models with the conformal inflaton with a flat potential (including hybrid inflation). There is no generation of cosmological fluctuations from the conformally coupled inflaton. We consider realizations of modulated (inhomogeneous reheating) or curvaton cosmological fluctuations in these models. We also implement these unusual features for the popular string-theoretic warped inflationary scenario, based on the interacting D3-anti D3 branes. The original warped brane inflation suffers a large inflaton mass due to conformal coupling to 4-dimensional gravity. Instead of considering this as a problem and trying to cure it with extra engineering, we show that warped inflation with the conformally coupled, rapidly rolling inflaton is yet possible with N=37 efoldings, which requires low energy scales 1-100 TeV of inflation. Coincidentally, the same warping numerology can be responsible for the hierarchy. It is shown that the scalars associated with angular isometries of the warped geometry of compact manifold (e.g. S^3 of KS geometry) have solutions identical to conformally coupled modes and also cannot be responsible for cosmological fluctuations. We discuss other possibilities.

Paper Structure

This paper contains 8 sections, 69 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Inflation from Conformally-Coupled Scalar with Flat Potential
  3. Condition for the Rapid Roll Inflation
  4. Phase Portrait for Conformal Inflation
  5. Efoldings of inflation and Mass Hierarchy
  6. Other Examples of Conformal Inflation
  7. Cosmological Fluctuations in Conformal Inflation
  8. Summary

Figures (1)

  • Figure 1: Phase portrait for the system of equations (\ref{['eqn:1st-order-eq']}) with $\Delta=1$. The horizontal axis is $q$ and the vertical axis is $p$.