Arjun Berera

We perform direct numerical simulation of the incompressible Navier-Stokes equation with forcing at different spatial dimensions and measure turbulent and chaotic properties. Lyapunov exponents, λ , decrease with dimension, and λ < 0 for all simulations in six dimensions up to Re λ = 21.2 . These six-dimensional simulations display non-Gaussian statistics and other behavior similar to well developed turbulence despite their lack of chaos. Further, we find that small scale perturbations do not extend to the largest scales and that this terminal scale between correlation and decorrelation shrinks with dimension. We theorize that this change is related to the increased rate of vortex stretching. We find the interplay between turbulent and chaotic properties changes with increasing dimension.

We investigate primordial magnetogenesis by assuming the gauge field is prepared in a thermal state during inflation rather than the standard Bunch-Davies vacuum. The temperature 𝒯 introduces a physical scale that breaks conformal invariance at the level of the state while preserving the standard Maxwell action. This modification results in a dissipative boost that alters the magnetic energy density scaling from a ^-4 to a ^-3 , resulting in a present-day magnetic field B ₀ enhancement that can potentially range from about 10 ⁸ to 10 ¹² on cosmological scales. While this toy model alone does not satisfy observational lower bounds, it demonstrates that thermal initial conditions can significantly mitigate the conformal obstruction. Our results suggest that embedding this mechanism within a fully dynamical warm inflation framework, where dissipation continuously maintains the thermal bath, provides a highly promising path towards successfully realizing a minimal model of inflationary magnetogenesis without the need to invoke non-minimal couplings, anomalous background dynamics or nonlinear extensions of electrodynamics.

A bstract: We propose a two-field model of warm inflation motivated by a heterotic string construction, involving an axion and a dilaton-like scalar field with non-trivial kinetic mixing. Gauge-field interactions generate dissipation and thermal corrections affecting both fields. A systematic numerical analysis reveals a range of dynamical regimes, including effectively single-field and multi-field behavior. We find that warm inflation is typically realized along the axion direction, while thermal corrections tend to hinder sustained dilaton-driven inflation over most of the parameter space. Although configurations exist in which the dilaton becomes dynamically relevant, particularly near the end of inflation, the majority of viable solutions are effectively single-field and axion-dominated. These results point to a dynamical mechanism in heterotic-inspired models that naturally favors axion-driven warm inflation while limiting the role of the dilaton.

The recently released data from the Atacama Cosmology Telescope (ACT) confirms that the primordial scalar spectrum is extremely flat. This, together with current upper bounds on the tensor-to-scalar ratio, implies that the simplest models of inflation coming from particle physics (for instance, a minimally-coupled scalar with monomial potentials) need additional ingredients in order to make them compatible with observations. Instead of invoking arbitrary new couplings or new interactions that are not protected symmetries, we argue that dissipation of the inflaton field with the radiation bath should be added as a new physical principle. Accordingly, we show that warm inflation provides the correct paradigm to explain the current observations, given very natural choices of dissipative terms. The model analyzed here has mirror and Z ₄ symmetries, which explicitly protect the inflaton potential from large quantum and thermal corrections. We use a recent precision numerical code designed for warm inflationary perturbations, improving on the determination of the cosmological observables previously obtained for such models.

In this paper we propose a two-field model of warm inflation motivated from a heterotic string construction. The model contains an axion and a dilaton-like field. We show that while warm inflation can take place in the axion-field direction, thermal corrections coming from the radiation gauge fields, which couples to both the axion and the dilaton, prevent warm inflation to happen in the dilaton-field direction. We explore the background dynamics for different parameters, and identify a diversity of dynamical behaviors allowed in this model, denoting different regimes of warm inflation.

Turbulence has associated chaotic features. In the past couple of decades, there has been growing interest in the study of these features as an alternative means of understanding turbulent systems. Our own input to this effort is in contributing to the initial studies of chaos in Eulerian flow using direct numerical simulation (DNS). In this review, we discuss the progress achieved in the turbulence community in understanding chaotic measures including our own work. A central relation between turbulence and chaos is one by Ruelle that connects the maximum Lyapunov exponent and the Reynolds number. The first DNS studies, ours amongst them, in obtaining this relation have shown the viability of chaotic simulation studies of Eulerian flow. Such chaotic measures and associated simulation methodology provides an alternative means to probe turbulent flow. Building on this, we analyze the finite-time Lyapunov exponent (FTLE) and study its fluctuations; we find that chaotic measures could be quantified accurately even at small simulation box sizes where for comparative sizes spectral measures would be inconclusive. We further highlight applications of chaotic measures in analyzing phase transition behavior in turbulent flow and two-dimensional thin-layer turbulent systems. This work shows that chaotic measures are an excellent tool that can be used alongside spectral measures in studying turbulent flow.