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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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Gariazzo, S., de Salas, P. F., & Pastor, S. (2019). Thermalisation of sterile neutrinos in the early universe in the 3+1 scheme with full mixing matrix. J. Cosmol. Astropart. Phys., 07(7), 014–30pp.
Abstract: In the framework of a 3+1 scheme with an additional inert state, we consider the thermalisation of sterile neutrinos in the early Universe taking into account the full 4 x 4 mixing matrix. The evolution of the neutrino energy distributions is found solving the momentum-dependent kinetic equations with full diagonal collision terms, as in previous analyses of flavour neutrino decoupling in the standard case. The degree of thermalisation of the sterile state is shown in terms of the effective number of neutrinos, N-eff, and its dependence on the three additional mixing angles (theta(14), theta(24), theta(34)) and on the squared mass difference Delta m(41)(2) is discussed. Our results are relevant for fixing the contribution of a fourth light neutrino species to the cosmological energy density, whose value is very well constrained by the final Planck analysis. For the preferred region of active-sterile mixing parameters from short-baseline neutrino experiments, we find that the fourth state is fully thermalised (N-eff similar or equal to 4).
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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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Kim, J., Ko, P., & Park, W. I. (2017). Higgs-portal assisted Higgs inflation with a sizeable tensor-to-scalar ratio. J. Cosmol. Astropart. Phys., 02(2), 003–16pp.
Abstract: We show that the Higgs portal interactions involving extra dark Higgs field can save generically the original Higgs inflation of the standard model (SM) from the problem of a deep non-SM vacuum in the SM Higgs potential. Specifically, we show that such interactions disconnect the top quark pole mass from inflationary observables and allow multi-dimensional parameter space to save the Higgs inflation, thanks to the additional parameters (the dark Higgs boson mass m(phi), the mixing angle a between the SM Higgs H and dark Higgs Phi, and the mixed quartic coupling) affecting RG-running of the Higgs quartic coupling. The effect of Higgs portal interactions may lead to a larger tensor-to-scalar ratio, 0.08 less than or similar to r less than or similar to 0.1, by adjusting relevant parameters in wide ranges of alpha and m(phi), some region of which can be probed at future colliders. Performing a numerical analysis we find an allowed region of parameters, matching the latest Planck data.
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Mangano, G., Miele, G., Pastor, S., Pisanti, O., & Sarikas, S. (2011). Constraining the cosmic radiation density due to lepton number with Big Bang Nucleosynthesis. J. Cosmol. Astropart. Phys., 03(3), 035–18pp.
Abstract: The cosmic energy density in the form of radiation before and during Big Bang Nucleosynthesis (BBN) is typically parameterized in terms of the effective number of neutrinos N-eff. This quantity, in case of no extra degrees of freedom, depends upon the chemical potential and the temperature characterizing the three active neutrino distributions, as well as by their possible non-thermal features. In the present analysis we determine the upper bounds that BBN places on N-eff from primordial neutrino-antineutrino asymmetries, with a careful treatment of the dynamics of neutrino oscillations. We consider quite a wide range for the total lepton number in the neutrino sector, eta(nu) = eta(nu e) + eta(nu mu) + eta(nu tau) and the initial electron neutrino asymmetry eta(in)(nu e), solving the corresponding kinetic equations which rule the dynamics of neutrino (antineutrino) distributions in phase space due to collisions, pair processes and flavor oscillations. New bounds on both the total lepton number in the neutrino sector and the nu(e)-(nu) over bar (e) asymmetry at the onset of BBN are obtained fully exploiting the time evolution of neutrino distributions, as well as the most recent determinations of primordial H-2/H density ratio and He-4 mass fraction. Note that taking the baryon fraction as measured by WMAP, the H-2/H abundance plays a relevant role in constraining the allowed regions in the eta(nu)-eta(in)(nu e) plane. These bounds fix the maximum contribution of neutrinos with primordial asymmetries to N-eff as a function of the mixing parameter theta(13), and point out the upper bound N-eff less than or similar to 3.4. Comparing these results with the forthcoming measurement of N-eff by the Planck satellite will likely provide insight on the nature of the radiation content of the universe.
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