Taming the Runaway Problem of Inflationary Landscapes

TL;DR

The paper addresses the inflation runaway problem in inflationary landscapes where volume weighting exponentially favors vacua with tiny inflaton mass, predicting environments inhospitable to observers. It proposes a general solution: a sharp mapping from fundamental to anthropic parameters combined with a threshold in inflaton decay that makes the reheating temperature $T_R$ highly sensitive to the inflaton mass, creating a mild peak within the anthropic window when paired with an exponential anthropic factor ${\cal A}(\alpha)$. The authors illustrate this mechanism in chaotic inflation scenarios with both thermal and non-thermal leptogenesis, deriving an upper bound on $T_{R}$ and making concrete predictions for neutrino and SUSY sectors (e.g., $M_1<10^{12}$ GeV, a CP phase ${\cal O}(0.1)$, and gravitino DM in the 20–200 MeV range). The work demonstrates that even in an exponentially weighted landscape, observables can be predicted in the middle of the anthropic window, providing a new way to extract particle-cosmology information from anthropic reasoning. Overall, threshold-driven reheating combined with exponential anthropic suppression offers a robust framework to tame runaway behavior and yield testable cosmological implications.

Abstract

A wide variety of vacua, and their cosmological realization, may provide an explanation for the apparently anthropic choices of some parameters of particle physics and cosmology. If the probability on various parameters is weighted by volume, a flat potential for slow-roll inflation is also naturally understood, since the flatter the potential the larger the volume of the sub-universe. However, such inflationary landscapes have a serious problem, predicting an environment that makes it exponentially hard for observers to exist and giving an exponentially small probability for a moderate universe like ours. A general solution to this problem is proposed, and is illustrated in the context of inflaton decay and leptogenesis, leading to an upper bound on the reheating temperature in our sub-universe. In a particular scenario of chaotic inflation and non-thermal leptogenesis, predictions can be made for the size of CP violating phases, the rate of neutrinoless double beta decay and, in the case of theories with gauge-mediated weak scale supersymmetry, for the fundamental scale of supersymmetry breaking.

Figures (3)

• Figure 1: Schematic picture of the inflation runaway problem. From left to right: the anthropic factor ${\cal A}$, the volume factor ${\cal V}$, and the combined probability distribution ${\cal V}{\cal A}$, all on a logarithmic scale. Normalization of each factor is arbitrary, and hence there is no importance in the absolute height in the figure. The region to the right of the vertical axis is the anthropic window, and the peak of the probability distribution lies outside the window.
• Figure 2: A relevant parameter $\alpha(\xi)$ with a sharp dependence on a fundamental parameter $\xi$. This is interpreted as the dependence of the reheating temperature on the inflaton mass, $T_R(m_\phi)$ in section \ref{['ssec:inflatondecay']}, and this figure corresponds to $\lambda' \approx 10^{-3}$.
• Figure 3: Left: various factors of the probability distribution, namely, ${\cal A}, {\cal V}$ and $(d \alpha/d\xi)^{-1}$, on a logarithmic scale. The normalization of each factor is arbitrary, and hence there is no importance to the absolute height. Right: combined probability distribution $d{\cal P}/d\alpha$. Note that the peak of the distribution is inside the anthropic window. [In this figure, the plateau of the volume factor in the threshold region corresponds to $\bar{N}_e \sim 10$. This is why the peak $T_{R,0}$ is close to the upper end of the threshold region.]