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Tilted Ghost Inflation

Leonardo Senatore

TL;DR

Tilted Ghost Inflation investigates how a small tilt in the ghost condensate potential alters the standard ghost inflation predictions. By analyzing the 2-point and 3-point functions under negative and positive tilts, the work shows that negative tilt pushes the model toward slow-roll-like spectra while modifying the bispectrum shape; positive tilt introduces a kinetic instability that can be tamed by freeze-out, yielding an exponential sensitivity in the observables. The study provides explicit expressions for $P_{\zeta}$ and $\langle\zeta^3\rangle$, derives constraints from COBE/WMAP data, and demonstrates that a significant portion of the parameter space remains within experimental reach, with future non-Gaussianity measurements poised to tighten these bounds. Overall, the tilt offers a concrete bridge between ghost inflation and slow-roll phenomenology, with distinctive signatures in the power spectrum tilt $n_s-1$ and the bispectrum that can be tested by current and upcoming CMB observations.

Abstract

In a ghost inflationary scenario, we study the observational consequences of a tilt in the potential of the ghost condensate. We show how the presence of a tilt tends to make contact between the natural predictions of ghost inflation and the ones of slow roll inflation. In the case of positive tilt, we are able to build an inflationary model in which the Hubble constant H is growing with time. We compute the amplitude and the tilt of the 2-point function, as well as the 3-point function, for both the cases of positive and negative tilt. We find that a good fraction of the parameter space of the model is within experimental reach.

Tilted Ghost Inflation

TL;DR

Tilted Ghost Inflation investigates how a small tilt in the ghost condensate potential alters the standard ghost inflation predictions. By analyzing the 2-point and 3-point functions under negative and positive tilts, the work shows that negative tilt pushes the model toward slow-roll-like spectra while modifying the bispectrum shape; positive tilt introduces a kinetic instability that can be tamed by freeze-out, yielding an exponential sensitivity in the observables. The study provides explicit expressions for and , derives constraints from COBE/WMAP data, and demonstrates that a significant portion of the parameter space remains within experimental reach, with future non-Gaussianity measurements poised to tighten these bounds. Overall, the tilt offers a concrete bridge between ghost inflation and slow-roll phenomenology, with distinctive signatures in the power spectrum tilt and the bispectrum that can be tested by current and upcoming CMB observations.

Abstract

In a ghost inflationary scenario, we study the observational consequences of a tilt in the potential of the ghost condensate. We show how the presence of a tilt tends to make contact between the natural predictions of ghost inflation and the ones of slow roll inflation. In the case of positive tilt, we are able to build an inflationary model in which the Hubble constant H is growing with time. We compute the amplitude and the tilt of the 2-point function, as well as the 3-point function, for both the cases of positive and negative tilt. We find that a good fraction of the parameter space of the model is within experimental reach.

Paper Structure

This paper contains 8 sections, 58 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Density Perturbations
  3. Negative Tilt
  4. 2-Point Function
  5. 3-Point Function
  6. Observational Constraints
  7. Positive Tilt
  8. Conclusions

Figures (2)

  • Figure 1: Plot of the function $F(1,x_2,x_3)x^2_2x^2_3$ for the tilted ghost inflation 3-point function. The function has been normalized to have value 1 for the equilateral configuration $x_2=x_3=1$, and it has been set to zero outside of the region $1-x_2\leq x_3\leq x_2$
  • Figure 2: Plot of the similarly defined function $F(1,x_2,x_3)x^2_2x^2_3$ for the standard ghost inflation 3-point function. The function has been normalized to have value 1 for the equilateral configuration $x_2=x_3=1$, and it has been set to zero outside of the region $1-x_2\leq x_3\leq x_2$cremzalda