arXiv subjects

Hal Finkel

Publications and source records attributed to Hal Finkel.

42 records · Page 3Linked to original sources

arXiv2011

Oscillons After Inflation

Oscillons are massive, long-lived, localized excitations of a scalar field. We show that in a large class of well-motivated single-field models, inflation is followed by self-resonance, leading to copious oscillon generation and a lengthy period of oscillon domination. These models are characterized by an inflaton potential which has a quadratic minimum and is shallower than quadratic away from the minimum. This set includes both string monodromy models and a class of supergravity inspired scenarios, and is in good agreement with the current central values of the concordance cosmology parameters. We assume that the inflaton is weakly coupled to other fields, so as not to quickly drain energy from the oscillons or prevent them from forming. An oscillon-dominated universe has a greatly enhanced primordial power spectrum on very small scales relative to that seen with a quadratic potential, possibly leading to novel gravitational effects in the early universe.

astro-ph.CO↗

arXiv2011

An Iterated, Multipoint Differential Transform Method for Numerically Evolving PDE IVPs

Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time step. Although redundant in the dx->0 limit, what if spatial derivatives were also stored? This paper presents an iterated, multipoint differential transform method (IMDTM) for numerically evolving PDE IVPs. Using this scheme, it is demonstrated that stored spatial derivatives can be propagated in an efficient and self-consistent manner; and can effectively contribute to the evolution procedure in a way which can confer several advantages, including aiding solution verification. Lastly, in order to efficiently implement the IMDTM scheme, a generalized finite-difference stencil formula is derived which can take advantage of multiple higher-order spatial derivatives when computing even-higher-order derivatives. As is demonstrated, the performance of these techniques compares favorably to other explicit evolution schemes in terms of speed, memory footprint and accuracy.

math.NA↗

arXiv2010

Inflaton Fragmentation and Oscillon Formation in Three Dimensions

Analytical arguments suggest that a large class of scalar field potentials permit the existence of oscillons -- pseudo-stable, non-topological solitons -- in three spatial dimensions. In this paper we numerically explore oscillon solutions in three dimensions. We confirm the existence of these field configurations as solutions to the Klein-Gorden equation in an expanding background, and verify the predictions of Amin and Shirokoff for the characteristics of individual oscillons for their model. Further, we demonstrate that significant numbers of oscillons can be generated via fragmentation of the inflaton condensate, consistent with the analysis of Amin. These emergent oscillons can easily dominate the post-inflationary universe. Finally, both analytic and numerical results suggest that oscillons are stable on timescales longer than the post-inflationary Hubble time. Consequently, the post-inflationary universe can contain an effective matter-dominated phase, during which it is dominated by localized concentrations of scalar field matter.

astro-ph.CO↗

arXiv2010

PSpectRe: A Pseudo-Spectral Code for (P)reheating

PSpectRe is a C++ program that uses Fourier-space pseudo-spectral methods to evolve interacting scalar fields in an expanding universe. PSpectRe is optimized for the analysis of parametric resonance in the post-inflationary universe, and provides an alternative to finite differencing codes, such as Defrost and LatticeEasy. PSpectRe has both second- (Velocity-Verlet) and fourth-order (Runge-Kutta) time integrators. Given the same number of spatial points and/or momentum modes, PSpectRe is not significantly slower than finite differencing codes, despite the need for multiple Fourier transforms at each timestep, and exhibits excellent energy conservation. Further, by computing the post-resonance equation of state, we show that in some circumstances PSpectRe obtains reliable results while using substantially fewer points than a finite differencing code. PSpectRe is designed to be easily extended to other problems in early-universe cosmology, including the generation of gravitational waves during phase transitions and pre-inflationary bubble collisions. Specific applications of this code will be pursued in future work.

astro-ph.CO↗

arXiv2010

The differential transformation method and Miller's recurrence

The differential transformation method (DTM) enables the easy construction of a power-series solution to a nonlinear differential equation. The exponentiation operation has not been specifically addressed in the DTM literature, and constructing it iteratively is suboptimal. The recurrence for exponentiating a power series by J.C.P. Miller provides a concise implementation of exponentiation by a positive integer for DTM. An equally-concise implementation of the exponential function is also provided.

math.CA↗

arXiv2006

Stochastic Evolution of Graphs using Local Moves

Inspired by theories such as Loop Quantum Gravity, a class of stochastic graph dynamics was studied in an attempt to gain a better understanding of discrete relational systems under the influence of local dynamics. Unlabeled graphs in a variety of initial configurations were evolved using local rules, similar to Pachner moves, until they reached a size of tens of thousands of vertices. The effect of using different combinations of local moves was studied and a clear relationship can be discerned between the proportions used and the properties of the evolved graphs. Interestingly, simulations suggest that a number of relevant properties possess asymptotic stability with respect to the size of the evolved graphs.

hep-th↗