From wires to cosmology

Abstract

We provide a statistical framework for characterizing stochastic particle production in the early universe via a precise correspondence to current conduction in wires with impurities. Our approach is particularly useful when the microphysics is uncertain and the dynamics are complex, but only coarse-grained information is of interest. We study scenarios with multiple interacting fields and derive the evolution of the particle occupation numbers from a Fokker-Planck equation. At late times, the typical occupation numbers grow exponentially which is the analog of Anderson localization for disordered wires. Some statistical features of the occupation numbers show hints of universality in the limit of a large number of interactions and/or a large number of fields. For test cases, excellent agreement is found between our analytic results and numerical simulations.

Exponential Hierarchies from Anderson Localization in Theory Space

“…In particular, we exploit an analogy between the localization of electron energy eigenstates along a one-dimensional wire in the presence of disorder, and the localization of mass eigenstates along a local theory space with random mass parameters on each site. (Similar analogies have been made for inflation [20,21] and gravity [22].) All mass eigenstates are exponentially localized, and can thus have exponentially suppressed couplings to sites in the theory space-the lightest (and heaviest) eigenstates especially so.…”

Self-resonance after inflation: Oscillons, transients, and radiation domination

“…In particular, self-resonance, where the homogeneous inflaton condensate pumps energy into its own fluctuations, can lead to interesting nonlinear effects even in absence of couplings to other fields (e.g., [23][24][25]). Such explosive particle production, formation of nontopological and topological solitons (e.g., [23,26]), as well as relics such as black holes (e.g., [27]) and primordial gravitational waves (e.g., [28][29][30]), amongst others, make 1 See [12][13][14] for attempts at some model-independent approaches. reheating an exciting dynamical playground.…”

“…We also found that changing δ to 0.100 describes well the time the equation of state approaches w rad ¼ 1=3, as shown on the bottom. 12 For the calculation of the inflaton potential parameters in Sec. IV, we have used the value of A s measured at k ⋆ ¼ 0.05 Mpc −1 .…”

Enlarging the space of viable inflation models: A slingshot mechanism

“…It can therefore be shown that the problem of finding the Bogoliubov coefficients which relate these two sets of asymptotic solutions for ϕ k (t) is mathematically equivalent to the problem of determining the transmission coefficients for scattering off a potential V (x) ∝ −sech 2 (x) in non-relativistic quantum mechanics [54]. Thus, by analogy, we find that the differential energy density dρ (p) λ0 /dk of inflaton field quanta per unit comoving momentum k at the time the non-adiabatic evolution effectively ceases -which is roughly equivalent to the time at which φ λ0 is released from the slingshot -takes the form dρ (p) λ0 dk ≈ 4πk 2 cos 2 π 2 1 + λ 2 0 (t p )∆ 2 G (2π) 3 sinh 2 π 2 ∆ G k .…”