Gauged M-flation After BICEP2

TL;DR

Gauged M-flation is revisited in light of the BICEP2 results, showing that the effective inflaton in the SU(2) sector can live in a symmetry-breaking double-well potential that yields a sizable tensor-to-scalar ratio $r$ while keeping the scalar spectral index $n_S$ within Planck constraints. The model naturally incorporates a multi-field spectator sector with a hierarchical mass spectrum, which preserves UV safety and suppresses isocurvature perturbations. Predictions in the $\phi>\mu$ region can place $r$ in the range around the BICEP2 value, whereas hilltop regions $\phi<\mu$ yield smaller $r$; the two regimes share the same $n_S$-$r$ plane trajectories but differ in isocurvature content. Sub-Planckian microscopic displacements coexist with effective Planckian excursions thanks to collective dynamics, and the spectator sector remains sufficiently heavy to keep inflation stable.

Abstract

In view of the recent BICEP2 results [arXiv:1403.3985] which may be attributed to the observation of B-modes polarization of the CMB with tensor-to-scalar ratio $r=0.2_{-0.05}^{+0.07}$, we revisit M-flation model. Gauged M-flation is a string theory motivated inflation model with Matrix valued scalar inflaton fields in the adjoint representation of a $U(N)$ Yang-Mills theory. In continuation of our previous works, we show that in the M-flation model induced from a supersymmetric 10d background probed by a stack of $N$ D3-branes, the "effective inflaton" $φ$ has a double-well Higgs-like potential, with minima at $φ=0,μ$. We focus on the $φ>μ$, symmetry-breaking region. We thoroughly examine predictions of the model for $r$ in the $2σ$ region allowed for $n_S$ by the Planck experiment. As computed in [arXiv:0903.1481], for $N_e=60$ and $n_S=0.96$ we find $r\simeq 0.2$, which sits in the sweet spot of BICEP2 region for $r$. We find that with increasing $μ$ arbitrarily, $n_S$ cannot go beyond $\simeq 0.9670$. As $n_S$ varies in the $2σ$ range which is allowed by Planck and could be reached by the model, $r$ varies in the range $[0.1322,0.2623]$. Future cosmological experiments, like the CMBPOL, that confines $n_S$ with $σ(n_S)=0.0029$ can constrain the model further. Also, in this region of potential, for $n_S=0.9603$, we find that the largest isocurvature mode, which is uncorrelated with curvature perturbations, has a power spectrum with the amplitude of order $10^{-11}$ at the end of inflation. We also discuss the range of predictions of $r$ in the hilltop region, $φ< μ$.

Figures (5)

• Figure 1: The double-well potential which is derived in the context of M-flation. Confining to the $\phi\geq 0$ region, there are three regions one can use to inflate upon. Due to the symmetry of the potential the predictions of the model in region (b) and (c) are the same in the $(n_S,r)$ plane. This degeneracy breaks down at the level of isocurvature perturbations.
• Figure 2: Left and right plots respectively demonstrate $\mu$ vs. $n_S$ in the inflationary region where $\phi>\mu$. Blue and red curves are respectively for $N_e=50$ and $N_e=60$. As $\mu\rightarrow 0$, the predictions of the model approaches the $\lambda\phi^4$ model. As $\mu\rightarrow\infty$$n_S$ reaches its maximal value. For $N_e=50$ and $N_e=50$, the maximum $n_S'$s are respectively $n_S^{50}\lesssim 0.9604$ and $n_S^{60}\lesssim 0.9670$.
• Figure 3: Tensor-to-scalar ratio $r$ and field roaming $\Delta\phi$ vs $n_S$ as $n_S$ changes within the allowed ranges for $N_e=50$ and $N_e=60$ when inflation happens in the $\phi>\mu$ region
• Figure 4: $\mu$ and $\lambda_{\rm eff}$ vs. $n_S$ in the region $\phi<\mu$
• Figure 5: $r$ and $\Delta\phi$ vs. $n_S$ in the region $\phi<\mu$.