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Primordial Non-Gaussianity and Gravitational Waves: Observational Tests of Brane Inflation in String Theory

James E. Lidsey, David Seery

TL;DR

This work links curvature perturbation non-Gaussianity to primordial gravitational waves within a DBI brane-inflation framework in warped throats, deriving a model-independent consistency relation $r+8n_t=-\bigl(\sqrt{1+3f_{NL}}-1\bigr)$ that holds for arbitrary warp factors and potentials. In the KS tip region with near-constant warping, it further yields $1-n_s\simeq -2n_t$ and, for large $f_{NL}$, $1-n_s\simeq 0.4\,r\sqrt{f_{NL}}$, implying a red spectrum and a pronounced anti-correlation between non-Gaussianity and tensor amplitude. The paper assesses detectability with Planck and future CMB polarization experiments, obtaining a model-independent bound on $r$ in the tip regime, $0.001<r<0.01$, and showing that simultaneous observation of sizable $f_{NL}$ and a detectable $r$ would challenge these brane-inflation scenarios. Overall, the results provide robust, testable string-theory predictions that constrain throat geometries and the inflationary dynamics accessible to observation.

Abstract

We study brane inflation scenarios in a warped throat geometry and show that there exists a consistency condition between the non-Gaussianity of the curvature perturbation and the amplitude and scale-dependence of the primordial gravitational waves. This condition is independent of the warping of the throat and the form of the inflaton potential. We find that such a relation could be tested by a future CMB polarization experiment if the Planck satellite is able to detect both a gravitational wave background and a non-Gaussian statistic. In models where the observable stage of inflation occurs when the brane is in the tip region of the throat, we derive a further consistency condition involving the scalar spectral index, the tensor-scalar ratio and the curvature perturbation bispectrum. We show that when such a relation is combined with the WMAP3 results, it leads to a model-independent bound on the gravitational wave amplitude given by 0.001 < r < 0.01. This corresponds to the range of sensitivity of the next generation of CMB polarization experiments.

Primordial Non-Gaussianity and Gravitational Waves: Observational Tests of Brane Inflation in String Theory

TL;DR

This work links curvature perturbation non-Gaussianity to primordial gravitational waves within a DBI brane-inflation framework in warped throats, deriving a model-independent consistency relation that holds for arbitrary warp factors and potentials. In the KS tip region with near-constant warping, it further yields and, for large , , implying a red spectrum and a pronounced anti-correlation between non-Gaussianity and tensor amplitude. The paper assesses detectability with Planck and future CMB polarization experiments, obtaining a model-independent bound on in the tip regime, , and showing that simultaneous observation of sizable and a detectable would challenge these brane-inflation scenarios. Overall, the results provide robust, testable string-theory predictions that constrain throat geometries and the inflationary dynamics accessible to observation.

Abstract

We study brane inflation scenarios in a warped throat geometry and show that there exists a consistency condition between the non-Gaussianity of the curvature perturbation and the amplitude and scale-dependence of the primordial gravitational waves. This condition is independent of the warping of the throat and the form of the inflaton potential. We find that such a relation could be tested by a future CMB polarization experiment if the Planck satellite is able to detect both a gravitational wave background and a non-Gaussian statistic. In models where the observable stage of inflation occurs when the brane is in the tip region of the throat, we derive a further consistency condition involving the scalar spectral index, the tensor-scalar ratio and the curvature perturbation bispectrum. We show that when such a relation is combined with the WMAP3 results, it leads to a model-independent bound on the gravitational wave amplitude given by 0.001 < r < 0.01. This corresponds to the range of sensitivity of the next generation of CMB polarization experiments.

Paper Structure

This paper contains 5 sections, 27 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Brane Inflation in String Theory
  3. An Observational Test of Brane Inflation
  4. Brane Inflation Near the Tip
  5. Discussion

Figures (3)

  • Figure 1: The dashed line illustrates the results of Song and Knox SK anticipating the experimental error, $\sigma$, in $r+8n_t$ as a function of $r$ for a future all-sky CMB polarization experiment with angular resolution $\varphi = 3'$ and noise $\Delta = 3 \mu{\rm K} \cdot {\rm arcmin}$SK. The modulus of the right-hand side of the consistency equation (\ref{['departure']}) is represented by a straight line for a given value of the non-linearity parameter, $f_{NL}$. The point of intersection of the lines yields a lower bound on the tensor-scalar ratio for a detection of the consistency equation (\ref{['departure']}) to be possible.
  • Figure 2: Illustrating the minimal value of the non-linearity parameter $f_{NL}$ deduced from Fig. \ref{['fig1brane']} that will lead in principle to a detection of the consistency equation (\ref{['departure']}). For a given fiducial value of the tensor-to-scalar ratio, $r$, a detection should be possible in the region of parameter space above the solid line. The shaded region is excluded by the WMAP3 data.
  • Figure 3: Illustrating the constraint equation (\ref{['mainresult']}) for the WMAP3 best-fit value $n_s=0.987$ (dot-dashed line) and lower limit $n_s=0.95$ (solid line). The region of parameter space consistent with WMAP3 lies below the solid line. The dashed line represents the curve from Fig. \ref{['fig2brane']}, above which the general consistency condition (\ref{['departure']}) will be detectable.