Nonperturbative analysis of the evolution of cosmological perturbations through a nonsingular bounce

In bouncing cosmology, the primordial fluctuations are generated in a cosmic contraction phase before the bounce into the current expansion phase. For a nonsingular bounce, curvature and anisotropy grow rapidly during the bouncing phase, raising questions about the reliability of perturbative analysis. In this paper, we study the evolution of adiabatic perturbations in a nonsingular bounce by nonperturbative methods including numerical simulations of the nonsingular bounce and the covariant formalism for calculating nonlinear perturbations. We show that the bounce is disrupted in regions of the universe with significant inhomogeneity and anisotropy over the background energy density, but is achieved in regions that are relatively homogeneous and isotropic. Sufficiently small perturbations, consistent with observational constraints, can pass through the nonsingular bounce with negligible alteration from nonlinearity. We follow scale invariant perturbations generated in a matter-like contraction phase through the bounce. Their amplitude in the expansion phase is determined by the growing mode in the contraction phase, and the scale invariance is well preserved across the bounce.Comment: 38 pages + appendices, 22 figure

Muon Charge Information from Geomagnetic Deviation in Inclined Extensive Air Showers

We propose to extract the charge information of high energy muons in very inclined extensive air showers by analyzing their relative lateral positions in the shower transverse plane. We calculate the muon lateral deviation under the geomagnetic field and compare it to dispersive deviations from other causes. By our criterion of resolvability, positive and negative muons with energies above $10^4$ GeV will be clearly separated into two lobes if the shower zenith angle is larger than $70^\circ$. Thus we suggest a possible approach to measure the $\mu^+ / \mu^-$ ratio for high energy muons.Comment: 21 latex pages, 9 figures, to appear in Astroparticle Physic

Geometry of environment-to-phenotype mapping: Unifying adaptation strategies in varying environments

Biological organisms exhibit diverse strategies for adapting to varying environments. For example, a population of organisms may express the same phenotype in all environments (`unvarying strategy'), or follow environmental cues and express alternative phenotypes to match the environment (`tracking strategy'), or diversify into coexisting phenotypes to cope with environmental uncertainty (`bet-hedging strategy'). We introduce a general framework for studying how organisms respond to environmental variations, which models an adaptation strategy by an abstract mapping from environmental cues to phenotypic traits. Depending on the accuracy of environmental cues and the strength of natural selection, we find different adaptation strategies represented by mappings that maximize the longterm growth rate of a population. The previously studied strategies emerge as special cases of our model: the tracking strategy is favorable when environmental cues are accurate, whereas when cues are noisy, organisms can either use an unvarying strategy or, remarkably, use the uninformative cue as a source of randomness to bet-hedge. Our model of the environment-to-phenotype mapping is based on a network with hidden units; the performance of the strategies is shown to rely on having a high-dimensional internal representation, which can even be random.Comment: 12 pages, plus supplemental figure

The four fixed points of scale invariant single field cosmological models

We introduce a new set of flow parameters to describe the time dependence of the equation of state and the speed of sound in single field cosmological models. A scale invariant power spectrum is produced if these flow parameters satisfy specific dynamical equations. We analyze the flow of these parameters and find four types of fixed points that encompass all known single field models. Moreover, near each fixed point we uncover new models where the scale invariance of the power spectrum relies on having simultaneously time varying speed of sound and equation of state. We describe several distinctive new models and discuss constraints from strong coupling and superluminality.Comment: 24 pages, 6 figure

Nonsingular Bouncing Cosmology

This thesis studies the cosmological theory in which the universe transitions from a contraction phase into an expansion phase through a big bounce. Primordial fluctuations that seed structure formation in the expansion phase arise from adiabatic perturbations in the preceding contraction phase. The purpose of this study is to understand how the properties of the adiabatic perturbations are affected by the bounce. In particular, a nonsingular type of bounce is considered in which the universe ceases contraction and reverses to expansion at a finite size, fully described by known theories of classical gravity and effective field theory. Two major aspects of such a nonsingular bounce are studied -- the stability of the bounce against inhomogeneities, and the power spectrum of adiabatic perturbations after the bounce. Results show that a class of bouncing models based on ghost condensation are subject to unstable growth of curvature and anisotropy, which alters the adiabatic perturbations and disrupts the nonsingular bounce. Another class of models with a ghost field are shown to have limited instability, though the contraction phase requires fine-tuning; sufficiently small perturbations can pass through the bounce and maintain a nearly scale-invariant power spectrum, consistent with observational constraints. Incorporating features of both models and resolving their problems, an ekpyrotic nonsingular bounce is proposed to support stable contraction and bouncing phases yet produce scale-invariant perturbations. Thus the nonsingular bouncing cosmology provides a possible explanation for the early universe