Modulated fluctuations from hybrid inflation

TL;DR

This work introduces a modulated-fluctuation mechanism in which light moduli fields induce spatial variations of couplings, shifting the end of inflation in hybrid models and generating additional adiabatic curvature perturbations during the transition to radiation domination. By employing general relativistic junction conditions on the time hypersurface where the equation of state jumps, the authors compute how moduli fluctuations imprint themselves onto the post-inflationary metric perturbations without requiring detailed preheating microphysics. They show that the total scalar spectrum becomes a sum of an inflaton-driven component and a modulated component with a distinct spectral index, and that the tensor-to-scalar ratio is modified to $\frac{T}{S}=\frac{\varepsilon}{1+4\pi(1-\varepsilon)\gamma^2}$, where $\gamma^2=\sum_a (d\varphi_c/d\chi_a)^2$. These results imply that modulated fluctuations can elevate the inflationary scale while suppressing gravitational waves, and they open the possibility of observable breaks or running in the scalar spectrum depending on the modulation strength and the moduli dynamics.

Abstract

Inflation universally produces classical almost scale free Gaussian inhomogeneities of any light scalars. Assuming the coupling constants at the time of inflation depend on some light moduli fields, we encounter the generation of modulated cosmological fluctuations from (p)reheating. This is an alternative mechanism to generate observable (almost) scale free adiabatic metric perturbations. We extend this idea to the class of hybrid inflation, where the bifurcation value of the inflaton is modulated by the spatial inhomogeneities of the couplings. As a result, the symmetry breaking after inflation occurs not simultaneously in space but with the time laps in different Hubble patches inherited from the long-wavelength moduli inhomogeneities. To calculate modulated fluctuations we introduce techniques of general relativistic matching conditions for metric perturbations at the time hypersurface where the equation of state after inflation undergoes a jump, without evoking the detailed microscopic physics, as far as it justifies the jump. We apply this theory to the modulated fluctuations from the hybrid and chaotic inflations. We discuss what distinguish the modulated from the inflation-driven fluctuations, in particular, their spectral index, modification of the consistency relation and the issue of weak non-Gaussianity.

Figures (2)

• Figure 1: Inflationary period is matched to a radiation dominated era on a spacelike hypersurface $\Sigma$ defined by $q(\varphi,\chi_a) \equiv\varphi-\varphi\c(\chi_a)=0$.
• Figure 2: The evolution of the gravitational potential $\Phi$ through the transition. Both ${\cal R}$ and $\Phi$ are continuous if the transition is a constant density hypersurface. $\Phi_g$ and $\Phi_d$ refer respectively to the growing and decaying modes.