Low-scale inflation

TL;DR

The paper investigates the possibility of inflation at a low energy scale, potentially at or below the electroweak scale, by focusing on quadratic-inflaton models where the observable perturbations originate from a predominantly quadratic potential near the origin. It develops both analytical and numerical treatments of generic quadratic potentials with end-of-inflation corrections, derives the COBE normalization constraints, and assesses the spectral index, fine-tuning, and reheating implications. The authors show that lowering the inflation scale can alleviate the moduli problem and that such inflation can naturally arise in supersymmetric theories or in scenarios with large extra dimensions, including D-term inflation and brane-world setups. The work suggests broad viable parameter spaces and concrete, testable predictions for CMB/LSS observables and potential supersymmetric or extra-dimensional signatures.

Abstract

We show that the scale of the inflationary potential may be the electroweak scale or even lower, while still generating an acceptable spectrum of primordial density perturbations. Thermal effects readily lead to the initial conditions necessary for low scale inflation to occur, and even the moduli problem can be evaded if there is such an inflationary period. We discuss how low scale inflationary models may arise in supersymmetric theories or in theories with large new space dimensions.

Figures (6)

• Figure 1: The logarithm of the inflationary scale $\Delta$ as a function of $p$ for various values of $q$. The solid lines are the analytical solution (\ref{['Delta']}) while the symbols indicate the numerical results, obtained assuming $\widetilde{b}$ to be negative and spectral index $n_{\rm H}=0.9$. Interesting scales of inflation correspond in particular to the set of values $(p,q,\kappa)=(4,2,1)$, $(4,3,1)$ and $(5,5,1)$, as shown in the Tables. The number of e-folds $N_{\rm H}$ indicated on the right-hand axis is an approximation.
• Figure 2: The spectral index $n_{\rm H}$ (\ref{['spectralindex']}) as a function of the mass parameter $b$ for the cases $(p,q,\kappa)=(4,2,1),(4,3,1),(5,5,1.8\times10^{-3})$ and $(5,5,1)$, denoted by $c_1,c_2,c_3$ and $c_4$ respectively.
• Figure 3: The logarithm of the inflationary scale $\Delta$ (\ref{['Delta']}) as a function of the mass parameter $b$ for the same cases as in Fig. \ref{['fggs4']}.
• Figure 4: The logarithm of the reheat temperature $T_{\rm reh}$ (\ref{['trh']}) as a function of the mass parameter $b$ for the same cases as in Fig. \ref{['fggs4']}.
• Figure 5: The full supergravity potential (\ref{['V']}) (in units of $V_0/\Delta^4$) as a function of $\phi$ and its phase $\alpha$ for the case $(p,q,\kappa)=(4,2,1)$, corresponding to an inflationary scale of $\Delta\sim5\times10^{11}$ GeV.