Large deviations in the early Universe

Fluctuations play a critical role in cosmology. They are relevant across a range of phenomena from the dynamics of inflation to the formation of structure. In many cases, these fluctuations are coarse grained and follow a Gaussian distribution as a consequence of the central limit theorem. Yet, some classes of observables are dominated by rare fluctuations and are sensitive to the details of the underlying microphysics. In this paper, we argue that the large deviation principle can be used to diagnose when one must appeal to the fundamental description. Concretely, we investigate the regime of validity for the Fokker-Planck equation that governs stochastic inflation. For typical fluctuations, this framework leads to the central limit-type behavior expected of a random walk. However, fluctuations in the regime of the large deviation principle are determined by instantonlike saddle points accompanied by a new energy scale. When this energy scale is above the UV cutoff of the effective field theory, the tail is only calculable in the microscopic description. We explicitly demonstrate this phenomenon in the context of determining the phase transition to eternal inflation, the distribution of scalar field fluctuations in de Sitter, and the production of primordial black holes

Stochastic Inflation at NNLO

Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the probability distribution for a light scalar field as a function of time. Despite its successes, the quantum field theoretic origins and the range of validity for this equation have remained elusive, and establishing a formalism to systematically incorporate higher order effects has been an area of active study. In this paper, we calculate the next-to-next-to-leading order (NNLO) corrections to Stochastic Inflation using Soft de Sitter Effective Theory (SdSET). In this effective description, Stochastic Inflation manifests as the renormalization group evolution of composite operators. The leading impact of non-Gaussian quantum fluctuations appears at NNLO, which is presented here for the first time; we derive the coefficient of this term from a two-loop anomalous dimension calculation within SdSET. We solve the resulting equation to determine the NNLO equilibrium distribution and the low-lying relaxation eigenvalues. In the process, we must match the UV theory onto SdSET at one-loop order, which provides a non-trivial confirmation that the separation into Wilson-coefficient corrections and contributions to initial conditions persists beyond tree level. Furthermore, these results illustrate how the naive factorization of time and momentum integrals in SdSET no longer holds in the presence of logarithmic divergences. It is these effects that ultimately give rise to the renormalization group flow that yields Stochastic Inflation.Comment: 50 pages + appendices; v2: minor changes, journal versio

Invariant Representations through Adversarial Forgetting

We propose a novel approach to achieving invariance for deep neural networks in the form of inducing amnesia to unwanted factors of data through a new adversarial forgetting mechanism. We show that the forgetting mechanism serves as an information-bottleneck, which is manipulated by the adversarial training to learn invariance to unwanted factors. Empirical results show that the proposed framework achieves state-of-the-art performance at learning invariance in both nuisance and bias settings on a diverse collection of datasets and tasks.Comment: To appear in Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI-20

Disparate Central and Peripheral Effects of Circulating IGF-1 Deficiency on Tissue Mitochondrial Function

© 2019, The Author(s). Age-related decline in circulating levels of insulin-like growth factor (IGF)-1 is associated with reduced cognitive function, neuronal aging, and neurodegeneration. Decreased mitochondrial function along with increased reactive oxygen species (ROS) and accumulation of damaged macromolecules are hallmarks of cellular aging. Based on numerous studies indicating pleiotropic effects of IGF-1 during aging, we compared the central and peripheral effects of circulating IGF-1 deficiency on tissue mitochondrial function using an inducible liver IGF-1 knockout (LID). Circulating levels of IGF-1 (~ 75%) were depleted in adult male Igf1f/f mice via AAV-mediated knockdown of hepatic IGF-1 at 5 months of age. Cognitive function was evaluated at 18 months using the radial arm water maze and glucose and insulin tolerance assessed. Mitochondrial function was analyzed in hippocampus, muscle, and visceral fat tissues using high-resolution respirometry O2K as well as redox status and oxidative stress in the cortex. Peripherally, IGF-1 deficiency did not significantly impact muscle mass or mitochondrial function. Aged LID mice were insulin resistant and exhibited ~ 60% less adipose tissue but increased fat mitochondrial respiration (20%). The effects on fat metabolism were attributed to increases in growth hormone. Centrally, IGF-1 deficiency impaired hippocampal-dependent spatial acquisition as well as reversal learning in male mice. Hippocampal mitochondrial OXPHOS coupling efficiency and cortex ATP levels (~ 50%) were decreased and hippocampal oxidative stress (protein carbonylation and F2-isoprostanes) was increased. These data suggest that IGF-1 is critical for regulating mitochondrial function, redox status, and spatial learning in the central nervous system but has limited impact on peripheral (liver and muscle) metabolism with age. Therefore, IGF-1 deficiency with age may increase sensitivity to damage in the brain and propensity for cognitive deficits. Targeting mitochondrial function in the brain may be an avenue for therapy of age-related impairment of cognitive function. Regulation of mitochondrial function and redox status by IGF-1 is essential to maintain brain function and coordinate hippocampal-dependent spatial learning. While a decline in IGF-1 in the periphery may be beneficial to avert cancer progression, diminished central IGF-1 signaling may mediate, in part, age-related cognitive dysfunction and cognitive pathologies potentially by decreasing mitochondrial function