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Figueroa, D. G., Florio, A., Torrenti, F., & Valkenburg, W. (2021). The art of simulating the early universe. Part I. Integration techniques and canonical cases. J. Cosmol. Astropart. Phys., 04(4), 035–108pp.
Abstract: We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of O(delta t(2)) accuracy like staggered leapfrog and Verlet integration, to Runge-Kutta methods up to O(delta t(4)) accuracy, and the Yoshida and Gauss-Legendre higher-order integrators, accurate up to O(delta t(10)) We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in 3+1 dimensions, including the case of 'self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: i) Interacting scalar fields, ii) Abelian U(1) gauge theories, and iii) Non-Abelian SU(2) gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from O(delta t(2)) up to O(delta t(10)) For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. We note that all our algorithms for gauge theories always respect the Gauss constraint to machine precision, including when 'self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under SU(2) x U(1). We note that the present manuscript is meant to be part of the theoretical basis for the code CosmoLattice, a multi-purpose MPI-based package for simulating the non-linear evolution of field theories in an expanding universe, publicly available at http://www.cosrnolattice.net.
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Jeong, K. S., & Park, W. I. (2023). Cosmology with a supersymmetric local B – L model. J. Cosmol. Astropart. Phys., 11(11), 016–34pp.
Abstract: We propose a minimal gauged U(1)(B-L) extension of the minimal supersymmetric Standard Model (MSSM) which resolves the cosmological moduli problem via thermal inflation, and realizes late-time Affleck-Dine leptogensis so as to generate the right amount of baryon asymmetry at the end of thermal inflation. The present relic density of dark matter can be explained by sneutrinos, MSSM neutralinos, axinos, or axions. Cosmic strings from U(1)(B-L) breaking are very thick, and so the expected stochastic gravitational wave background from cosmic string loops has a spectrum different from the one in the conventional Abelian-Higgs model, as would be distinguishable at least at LISA and DECIGO. The characteristic spectrum is due to a flat potential, and may be regarded as a hint of supersymmetry. Combined with the resolution of moduli problem, the expected signal of gravitational waves constrains the U(1)(B-L) breaking scale to be O(10(12-13)) GeV. Interestingly, our model provides a natural possibility for explaining the observed ultra-high-energy cosmic rays thanks to the fact that the core width of strings in our scenario is very large, allowing a large enhancement of particle emissions from the cusps of string loops. Condensation of LHu flat-direction inside of string cores arises inevitably and can also be the main source of the ultra-high-energy cosmic rays accompanied by ultra-high-energy lightest supersymmetric particles.
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Maji, R., & Park, W. I. (2024). Supersymmetric U(1)B-L flat direction and NANOGrav 15 year data. J. Cosmol. Astropart. Phys., 01(1), 015–19pp.
Abstract: We show that, when connected with monopoles, the flat D-flat direction breaking the local U(1)B-L symmetry as an extension of the minimal supersymmetric standard model can be responsible for the signal of a stochastic gravitational wave background recently reported by NANOGrav collaborations, while naturally satisfying constraints at high frequency band. Thanks to the flatness of the direction, a phase of thermal inflation arises naturally. The reheating temperature is quite low, and suppresses signals at frequencies higher than the characteristic frequency set by the reheating temperature. Notably, forthcoming spaced based experiments such as LISA can probe the cutoff frequency, providing an indirect clue of the scale of soft SUSY-breaking mass parameter.
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