A Numerical Simulation of Chern-Simons Inflation

We present results of numerical simulations of the Chern-Simons inflation model proposed by Alexander, Marciano, and Spergel. According to this model, inflation begins with a fermion condensate interacting with a gauge field. Crucial to the success of this mechanism is the assumption that the Chern-Simons interaction would drive energy from the initial random spectrum into a narrow band of frequencies at superhorizon scales. In this work, we numerically confirm this expectation. These gauge fields and currents, when combined with the Friedmann equations, were broken into a system of hyperbolic equations and numerically simulated. It was found in our simulation that, by including the effects of the chiral anomaly for the axial vector current, inflation can end satisfactorily after approximately 60 e-folds. 1. Introduction and Motivation Our understanding of the early universe is based on the phenomenon of cosmic inflation [1]. It is well known that inflation resolves most of the problems of the standard big-bang scenario, such as the horizon problem. Although there are many successes of inflation, there are hundreds of scalar field models of inflation which have proven difficult to distinguish with data. Moreover, scalar field driven inflation is fraught with conceptual and technical issues. Recently Chen and Wang demonstrated that the primordial power spectrum in scalar field inflation has anomalous sensitivity to high energy physics [2]. These issues have motivated Alexander et al. [3] to provide an inflationary mechanism that is driven by an interaction between vector and spinor fields, otherwise known as Chern-Simons inflation. This is somewhat similar in concept to the vector field inflation model proposed by Ford in which the vector field self-couples in order to form an effective scalar field [4]. For an overview of Chern-Simons modified gravity, see the paper by Alexander and Yunes [5]. Alexander et al. propose a model in which the early universe is dominated by a gauge field that interacts with a fermion current. This interaction results in an equation of state with consistently negative pressure, the condition needed for inflation [3]. In this model, the gauge field begins as a random, white noise spectrum; the authors assume that this evolves into a spectrum of superhorizon modes. Even though gauge fields and currents dilute with the expansion of space, their interaction energy is found to provide enough negative pressure to fuel an exponential expansion of spacetime. Because of the complexity of the differential equations, they were not able