Weak Gravity Conjecture

We investigate whether the eternal chaotic inflation can be achieved when the weak gravity conjecture is taken into account. We show that even the assisted chaotic inflation with potential λφ or mφ can not be eternal. The effective field theory description for the inflaton field breaks down before inflation reaches the eternal regime. We also find that the total number of e-folds is still bounded by the inflationary entropy for the assisted inflation. Inflation [1–3] is the leading theoretical paradigm for understanding the early universe and the origin of the primordial perturbations. In the new version of inflation, inflaton may begin either in the false vacuum, or in an unstable state at the top of the effective potential. Then the inflaton field slowly rolls down to the minimum of its effective potential. This picture relies on an application of low-energy effective field theory to inflation. An interesting phenomenon in inflationary scenario is eternal inflation. There are actually two kinds of eternal inflation. One is driven by the quasi-exponential expansion of the meta-stable vacua themselves. In our paper, we focus on the other version called slowroll eternal inflation [4, 5]. In this scenario, during the period of inflation, the evolution of the inflaton field φ is influenced by quantum fluctuations, which can be pictured as a random walk of the field with a step δφ ∼ H/2π on a horizon scale (Hubble scale H) per Hubble time ∆t ∼ H [6]. During the same epoch, the variation of the classical homogeneous inflaton field rolling down its potential is ∆φ ∼ |φ̇| · H. If the classical evolution is smaller than the quantum fluctuations, the role played by fluctuations becomes significant and the inflaton field climbs up its potential rather than rolls down its potential in some spacetime regions. This leads to an eternal process of self-reproduction of the universe. See the recent reviews in [7, 8]. Since superstring theory lives in ten dimensions, the six spatial dimensions must be compactified in order to understand the four-dimensional physics in the observed universe. Recent development on the flux compactification [9–11] suggests a vast number of at least semi-classically self-consistent meta-stable vacua. However not all of the meta-stable vacua are really self-consistent. The vast series of semi-classically consistent effective field theories which are actually inconsistent are called swampland [12]. The series of really selfconsistent vacua, called landscape, is surrounded by the swampland. Usually the Planck scale Mp is taken as a naturally UV cutoff for the effective field theory. But the effective field theory can break down even in the region with low curvature. In [13], the authors suggest a new criterion which distinguishes parts of the swampland from the landscape. A simple observation is that “gravity is the weakest force” and an intrinsic UV cutoff for the U(1) gauge theory is obtained in four dimensions. Recently the author of [14] proposed to study inflation under a version of the weak gravity conjecture, namely, Λ ≤ λMp (1) for λφ theory. This conjecture offers a stringent constraint on inflation model [14]. Some related works on the weak gravity conjecture are discussed in [15]. Unfortunately we still cannot pick out a unique vacuum in string theory and its seems that a huge number of meta-stable vacua in the string landscape are available. Once