M-flation: Inflation From Matrix Valued Scalar Fields

TL;DR

M-flation introduces matrix-valued inflatons $\Phi_i$ whose potential is built from commutators $[\Phi_i,\Phi_j]$, enabling a controlled large-field inflation after a consistent SU(2) truncation to $\Phi_i=\hat{\phi}J_i$. The resulting $3N^2$-field system splits into a single adiabatic inflaton $\phi$ and $3N^2-1$ iso-curvature modes $\Psi_i$, with a detailed mass spectrum and decoupled linear perturbations; the paper computes curvature and iso-curvature power spectra for several inflationary realizations (chaotic, symmetry breaking, inflection point) and analyzes particle production and back-reaction that lead to natural preheating. By tying the setup to string theory through D-brane dynamics, the authors show how the parameters scale with $N$ to alleviate fine-tuning and predict observable gravitational waves in some parameter regions. The framework yields distinctive signatures in the CMB, including a calculable iso-curvature component and a natural preheating channel, and offers concrete avenues for testing M-flation with Planck-like observations and future polarization experiments.

Abstract

We propose an inflationary scenario, M-flation, in which inflation is driven by three $N\times N$ hermitian matrices $Φ_i, i=1,2,3$. The inflation potential of our model, which is strongly motivated from string theory, is constructed from $Φ_{i}$ and their commutators. We show that one can consistently restrict the classical dynamics to a sector in which the $Φ_i$ are proportional to the $N\times N$ irreducible representations of SU(2). In this sector our model effectively behaves as an N-flation model with $3 N^2$ number of fields and the effective inflaton field has a super-Planckian field value. Furthermore, the fine-tunings associated with unnaturally small couplings in the chaotic type inflationary scenarios are removed. Due to the matrix nature of the inflaton fields there are $3N^2-1$ extra scalar fields in the dynamics. These have the observational effects such as production of iso-curvature perturbations on cosmic microwave background. Moreover, the existence of these extra scalars provides us with a natural preheating mechanism and exit from inflation. As the effective inflaton field can traverse super-Planckian distances in the field space, the model is capable of producing a considerable amount of gravity waves that can be probed by future CMB polarization experiments such as PLANCK, QUIET and CMBPOL.

Figures (2)

• Figure 1: Left and right graphs respectively show the curvature and isocurvature spectra for chaotic inflation with potential $\frac{m^2}{2}\phi^2$
• Figure 2: Left graph shows the ratio $P_{ {\cal S}_{r,lm} } (N_{e}) /P_{{\cal R}}|_{*}$ vs. $N_e$ for the mode that exit the Hubble radius 60 e-folds before the end of chaotic inflation with $V=\frac{1}{2}m^2 \phi^2$. Right graph shows the evolution of $P_{ {\cal S}_{\beta,3m} } (N_{e}) /P_{{\cal R}}|_{*}$ for $l=1,2$$\beta-$mode in $\lambda_{eff} \, \phi^4/4$ potential. Black and gray curves respectively demonstrate the numerical and analytic results.