BingKan Xue

Evolution of curvature and anisotropy near a nonsingular bounce

We consider bouncing cosmologies in which an ekpyrotic contraction phase with w>>1 is followed by a bouncing phase with w<-1 that violates the null energy condition. The bouncing phase, induced by ghost condensation, is designed to produce a classically nonsingular bounce at a finite value of the scale factor. We show that the initial curvature and anisotropy, though diluted during the ekpyrotic phase, grow back exponentially during the bouncing phase. Moreover, curvature perturbations and anisotropy are generated by quantum fluctuations during the ekpyrotic phase. In the bouncing phase, however, an adiabatic curvature perturbation grows to dominate and contributes a blue spectrum that spoils the scale invariance. Meanwhile, a scalar shear perturbation grows nonlinear and creates an overwhelming anisotropy that disrupts the nonsingular bounce altogether.

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.

Unstable growth of curvature perturbations in nonsingular bouncing cosmologies.

Bouncing cosmologies require an ekpyrotic contracting phase (w≫1) in order to achieve flatness, homogeneity, and isotropy. Models with a nonsingular bounce further require a bouncing phase that violates the null energy condition (w<-1). We show that the transition from the ekpyrotic phase to the bouncing phase creates problems for cosmological perturbations. A component of the adiabatic curvature perturbations, though decaying and negligible during the ekpyrotic phase, is exponentially amplified just before w approaches -1, enough to spoil the scale-invariant perturbation spectrum.

Evolutionary learning of adaptation to varying environments through a transgenerational feedback

Significance Phenotypic diversification, a form of evolutionary bet hedging, is observed in many biological systems, ranging from isogenic bacteria to cell populations in a tumor. Such phenotypic diversity is adaptive only if it matches the statistics of local environmental variation. Often, the timescale of environmental variation can be much longer than the lifespan of individual organisms. Then how could organisms collect long-term environmental information to modulate their phenotypic diversity? We propose here a general mechanism of “evolutionary learning,” which could overcome the mismatch between the two timescales. The learning mechanism can in principle be realized through known molecular processes of epigenetic inheritance, suggesting experimental directions to probe the evolutionary significance of such processes. Organisms can adapt to a randomly varying environment by creating phenotypic diversity in their population, a phenomenon often referred to as “bet hedging.” The favorable level of phenotypic diversity depends on the statistics of environmental variations over timescales of many generations. Could organisms gather such long-term environmental information to adjust their phenotypic diversity? We show that this process can be achieved through a simple and general learning mechanism based on a transgenerational feedback: The phenotype of the parent is progressively reinforced in the distribution of phenotypes among the offspring. The molecular basis of this learning mechanism could be searched for in model organisms showing epigenetic inheritance.

Regularization of the big bang singularity with a time varying equation of state w > 1

We study the classical dynamics of the universe undergoing a transition from contraction to expansion through a big bang singularity. The dynamics is described by a system of differential equations for a set of physical quantities, such as the scale factor a, the Hubble parameter H, the equation of state parameter w, and the density parameter Ω. The solutions of the dynamical system have a singularity at the big bang. We study if the solutions can be regularized at the singularity in the sense of whether they have unique branch extensions through the singularity. In particular, we consider the model in which the contracting universe is dominated by a scalar field with a time varying equation of state w, which approaches a constant value wc near the singularity. We prove that, for , the solutions are regularizable only for a discrete set of wc values that satisfy a coprime number condition. Our result implies that the evolution of a bouncing universe through the big bang singularity does not have a continuous classical limit unless the equation of state is extremely fine-tuned.

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.

Regularization of the big bang singularity with random perturbations

We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result \cite{Xue:2014} that did not model random perturbations. This result implies that the extension from a contracting to an expanding universe for the discrete set of co-prime equation of state is robust, which is a surprising result. Implications for a purely expanding universe are discussed, such as a non-smooth, randomly varying scale factor near the big bang.