Multiple inflation and the WMAP 'glitches'

TL;DR

The work addresses potential oscillations in the primordial curvature spectrum suggested by WMAP glitches, proposing a multiple-inflation mechanism where SUSY-breaking induces a phase transition in a visible flat-direction field that couples to the inflaton. An analytic treatment using a WKB approach to the Mukhanov-Sasaki equation (with turning-point matching) reveals how a sudden inflaton-mass shift generates a localized oscillatory feature and a positive spectral step in $\mathcal{P_R}(k)$, with numerical results validating the qualitative behavior. The findings illuminate how multi-field dynamics during inflation can produce observable imprints on the CMB and large-scale structure, and outline a path for data-driven tests of non-scale-free primordial spectra. The study emphasizes the need for careful treatment beyond slow-roll in multi-field scenarios and motivates further data analysis to gauge the implications for cosmological parameter inference.

Abstract

Observations of anisotropies in the cosmic microwave background by the Wilkinson Microwave Anisotropy Probe suggest the possibility of oscillations in the primordial density perturbation. Such deviations from the usually assumed scale-free spectrum were predicted in the multiple inflation model wherein `flat direction' fields undergo rapid phase transitions due to the breaking of supersymmetry by the large vacuum energy driving inflation. This causes sudden changes in the mass of the (gravitationally coupled) inflaton and interrupts its slow roll. We calculate analytically the resulting modifications to the density perturbation and demonstrate how the oscillations arise.

Figures (8)

• Figure 1: The evolution of the flat direction field $\rho$, corresponding to two different values for the change in the inflaton mass.
• Figure 2: The evolution of $z"/z$ during the phase transition, for two different values of the change in the inflaton mass.
• Figure 3: Comparison of the 1st-order WKB solution (\ref{['will2']}) with $u_k$ calculated numerically for $k = 6.7\times10^{-3}\; \rm {h\; Mpc^{-1}}$. The turning point is at $x_*\simeq8.64$ and $\Delta m_\phi^2=0.1 m_\phi^2$. Note that the solutions $U_{\rm I}$ (\ref{['3']}) and $U_{\rm III}$ (\ref{['UIII1']}) diverge at $x=x_*$ but $U_{\rm II}$ (\ref{['will2']}) is continuous and close to the exact solution.
• Figure 4: Comparison of the 1st-order WKB approximation with the numerically calculated exact spectrum, for two different values of the change in the inflaton mass.
• Figure 5: Comparison of the numerical result for the factor by which $\mathcal{P}_{\mathcal{R}}$ increases due to the phase transition with the 1st-order WKB expression, taking $k = 10\; \rm {h\; Mpc^{-1}}.$