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General Single Field Inflation with Large Positive Non-Gaussianity

Miao Li, Tower Wang, Yi Wang

TL;DR

This work demonstrates that general single-field inflation with non-canonical, higher-order kinetic terms can yield a large positive equilateral non-Gaussianity $f_{NL}^{equil}$, even when the local non-Gaussianity is sizable. It formulates the framework for p(\phi,X) theories, identifies a no-go for pure $p(X)$ models to generate large $f_{NL}^{equil}$, and provides explicit reconstruction strategies in generalized slow-roll and power-law $k$-inflation. Through three concrete power-law models (polynomial and DBI-like forms), the authors show that large $f_{NL}^{equil}$ can be achieved with sensible choices of $\epsilon$, $c_s$ and $r$, while addressing stability and EFT-scale issues via higher-order $X$ terms and a string-scale cutoff $M_s$. The results broaden the landscape of viable single-field inflation models capable of producing observable non-Gaussian signatures, offering concrete avenues for observational tests and model-building.

Abstract

Recent analysis of the WMAP three year data suggests $f_{NL}^{local}\simeq86.8$ in the WMAP convention. It is necessary to make sure whether general single field inflation can produce a large positive $f_{NL}$ before turning to other scenarios. We give some examples to generate a large positive $f_{NL}^{equil}$ in general single field inflation. Our models are different from ghost inflation. Due to the appearance of non-conventional kinetic terms, $f_{NL}^{equil}\gg1$ can be realized in single field inflation.

General Single Field Inflation with Large Positive Non-Gaussianity

TL;DR

This work demonstrates that general single-field inflation with non-canonical, higher-order kinetic terms can yield a large positive equilateral non-Gaussianity , even when the local non-Gaussianity is sizable. It formulates the framework for p(\phi,X) theories, identifies a no-go for pure models to generate large , and provides explicit reconstruction strategies in generalized slow-roll and power-law -inflation. Through three concrete power-law models (polynomial and DBI-like forms), the authors show that large can be achieved with sensible choices of , and , while addressing stability and EFT-scale issues via higher-order terms and a string-scale cutoff . The results broaden the landscape of viable single-field inflation models capable of producing observable non-Gaussian signatures, offering concrete avenues for observational tests and model-building.

Abstract

Recent analysis of the WMAP three year data suggests in the WMAP convention. It is necessary to make sure whether general single field inflation can produce a large positive before turning to other scenarios. We give some examples to generate a large positive in general single field inflation. Our models are different from ghost inflation. Due to the appearance of non-conventional kinetic terms, can be realized in single field inflation.

Paper Structure

This paper contains 10 sections, 91 equations, 1 figure.

Table of Contents

  1. Introduction
  2. A Brief Review of General Single Field Inflation
  3. A No-Go Result for $p(X)$ Model
  4. Reconstruction of the Generalized Slow Roll Inflation
  5. Reconstruction of Power-Law $k$-Inflation
  6. Power-Law Model I: $p=\frac{1}{\phi^2}(c_1X+c_2X^2+c_3X^3+c_4X^4)$
  7. Power-Law Model II: $p=\frac{1}{\phi^2}(-\sqrt{c_0+c_1X+c_2X^2}+c_3)$
  8. Power-Law Model III: $p=-\frac{1}{\phi^2}\sqrt{c_0+c_1X+c_2X^2+c_3X^3}$
  9. Conclusion
  10. Calculation of $R^{equil}(k)$

Figures (1)

  • Figure 1: The (logarithmic) ratio $\log_{10}(\frac{\epsilon}{c_s^2})$ as a function of $r$. The solid blue lines are plotted according to relation (\ref{['ecsratio']}). We have set $n_s\simeq0.97$ in the left plot, and $n_s\simeq0.96$ in the right one. This figure is valid for all of the power-law models considered in section \ref{['pl']}. The dashed red lines are used to highlight the black points corresponding to $c_s=1$, since we have the additional constraint $c_s^2>1$ for power-law model II in subsection \ref{['DBIcpl']}.