Linking Light Scalar Modes with A Small Positive Cosmological Constant in String Theory

Based on the studies in Type IIB string theory phenomenology, we conjecture that a good fraction of the meta-stable de Sitter vacua in the cosmic stringy landscape tend to have a very small cosmological constant $\Lambda$ when compared to either the string scale $M_S$ or the Planck scale $M_P$, i.e., $\Lambda \ll M_S^4 \ll M_P^4$. These low lying de Sitter vacua tend to be accompanied by very light scalar bosons/axions. Here we illustrate this phenomenon with the bosonic mass spectra in a set of Type IIB string theory flux compactification models. We conjecture that small $\Lambda$ with light bosons is generic among de Sitter solutions in string theory; that is, the smallness of $\Lambda$ and the existence of very light bosons (may be even the Higgs boson) are results of the statistical preference for such vacua in the landscape. We also discuss a scalar field $\phi^3/\phi^4$ model to illustrate how this statistical preference for a small $\Lambda$ remains when quantum loop corrections are included, thus bypassing the radiative instability problem.Comment: 35 pages, 7 figures; added subsection: Finite Temperature and Phase Transitio

Early-Time Measure in Eternal Inflation

In a situation like eternal inflation, where our data is replicated at infinitely-many other space-time events, it is necessary to make a prior assumption about our location to extract predictions. The principle of mediocrity entails that we live at asymptotic late times, when the occupational probabilities of vacua has settled to a near-equilibrium distribution. In this paper we further develop the idea that we instead exist during the approach to equilibrium, much earlier than the exponentially-long mixing time. In this case we are most likely to reside in vacua that are easily accessed dynamically. Using first-passage statistics, we prove that vacua that maximize their space-time volume at early times have: 1. maximal ever-hitting probability; 2. minimal mean first-passage time; and 3. minimal decay rate. These requirements are succinctly captured by an early-time measure. The idea that we live at early times is a predictive guiding principle, with many phenomenological implications. First, our vacuum should lie deep in a funneled region, akin to folding energy landscapes of proteins. Second, optimal landscape regions are characterized by relatively short-lived vacua, with lifetime of order the de Sitter Page time. For our vacuum, this lifetime is $\sim 10^{130}$~years, which is consistent with the Standard Model estimate due to Higgs metastability. Third, the measure favors vacua with small, positive vacuum energy. This can address the cosmological constant problem, provided there are sufficiently many vacua in the entire ensemble of funnels. As a concrete example, we study the Bousso-Polchinski lattice of flux vacua, and find that the early-time measure favors lattices with the fewest number of flux dimensions. This favors compactifications with a large hierarchy between the lightest modulus and all other K\"ahler and complex structure moduli.Comment: 34 pages, 3 figure

Bayesian Reasoning in Eternal Inflation: A Solution to the Measure Problem

Probabilities in eternal inflation are traditionally defined as limiting frequency distributions, but a unique and unambiguous probability measure remains elusive. In this paper, we present a different approach, based on Bayesian reasoning. Our starting point is the master equation governing vacuum dynamics, which describes a random walk on the network of vacua. Our probabilities require two pieces of prior information, both pertaining to initial conditions: a prior density $\rho(t)$ for the time of nucleation, and a prior probability $p_\alpha$ for the ancestral vacuum. For ancestral vacua, we advocate the uniform prior as a conservative choice, though our conclusions are fairly insensitive to this choice. For the time of nucleation, we argue that a uniform prior is consistent with the time-translational invariance of the master equation and represents the minimally-informative choice. The resulting predictive probabilities coincide with Bousso's "holographic" prior probabilities and are closely related to Garriga and Vilenkin's "comoving" probabilities. Despite making the least informative priors, these probabilities are surprisingly predictive. They favor vacua whose surrounding landscape topography is that of a deep funnel, akin to the folding funnels of naturally-occurring proteins. They predict that we exist during the approach to near-equilibrium, much earlier than the mixing time for the landscape. We also consider a volume-weighted $\rho(t)$, which amounts to weighing vacua by physical volume. The predictive probabilities in this case coincide with the GSVW measure. The Bayesian framework allows us to compare the plausibility of the uniform-time and volume-weighted hypotheses to explain our data by computing the Bayesian evidence for each. We argue, under general and plausible assumptions, that posterior odds overwhelmingly favor the uniform-time hypothesis.Comment: 34 pages, 1 figur