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Register a new userReal scalar field, non-relativistic limit, and cosmological expansion
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The existing transformation from a relativistic real scalar field to a complex non-relativistic scalar field by Namjoo, Guth, and Kaiser is generalized from Minkowski space to a more general background metric. In that case the transformation is not purely algebraic any more but determined by a differential equation. We apply the generalized transformation to a real scalar with $phi^4$ interaction on an Friedmann-Lema^itre-Robertson-Walker cosmologically expanding background and calculate the resulting non-relativistic action up to second order in small parameters. We also show that the transformation can be interpreted as a Bogoliubov transformation between relativistic and non-relativistic creation and annihilation operators and comment on emerging symmetries in the non-relativistic theory.
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We derive non-relativistic equations of motion for the formation of cosmological structure in a Scalar Field Dark Matter (SFDM) model corresponding to a complex scalar field endowed with a quadratic scalar potential. Starting with the full equations of motion written in the Newtonian gauge of scalar perturbations, we separate out the fields involved into relativistic and non-relativistic parts, and find the equations of motion for the latter that can be used to build up the full solution. One important assumption will also be that the SFDM field is in the regime of fast oscillations, under which its behavior is exactly that of cold dark matter. The resultant equations are quite similar to the Schrodinger-Poisson system of Newtonian boson stars plus relativistic leftovers. We exploit that similarity to show how to simulate, with minimum numerical effort, the formation of cosmological structure in SFDM models and others alike, and ultimately prove their viability as complete dark matter models.
We study exclusive quarkonium production in the dipole picture at next-to-leading order (NLO) accuracy, using the non-relativistic expansion for the quarkonium wavefunction. This process offers one of the best ways to obtain information about gluon distributions at small $x$, in ultraperipheral heavy ion collisions and in deep inelastic scattering. The quarkonium light cone wave functions needed in the dipole picture have typically been available only at tree level, either in phenomenological models or in the nonrelativistic limit. In this paper, we discuss the compatibility of the dipole approach and the non-relativistic expansion and compute NLO relativistic corrections to the quarkonium light-cone wave function in light-cone gauge. Using these corrections we recover results for the NLO decay width of quarkonium to $e^{+}e^{-}$ and we check that the non-relativistic expansion is consistent with ERBL evolution and with B-JIMWLK evolution of the target. The results presented here will allow computing the exclusive quarkonium production rate at NLO once the one loop photon wave function with massive quarks, currently under investigation, is known.
We show that the combined minimal and non minimal interaction with the gravitational field may produce the generation of a cosmological constant without self-interaction of the scalar field. In the same vein we analyze the existence of states of a scalar field that by a combined interaction of minimal and non minimal coupling with the gravitational field can exhibit an unexpected property, to wit, they are acted on by the gravitational field but do not generate gravitational field. In other words, states that seems to violate the action-reaction principle. We present explicit examples of this situation in the framework of a spatially isotropic and homogeneous universe.
We consider a novel baryogenesis mechanism in which the asymmetry is sourced from heavy particles which either gain their mass or are created during bubble expansion in a strong first order phase transition. The particles are inherently out-of-equilibrium and sufficiently dilute after wall crossing so -- even with order one gauge interactions -- the third Sakharov condition is easily met. Washout is avoided provided the reheat temperature is sufficiently below the scale of the heavy particles. The mechanism relies on moderate supercooling and relativistic walls which -- in contrast to electroweak baryogenesis -- leads to a sizable gravitational wave signal. We present a simple example model and discuss the restrictions on the parameter space for the mechanism to be successful. We find that high reheat temperatures $T_{rm RH} gtrsim 10^{10}$ GeV are generally preferred, whereas stronger supercooling allows for temperatures as low as $T_{rm RH} sim 10^{6}$ GeV, provided the vacuum energy density is sufficiently suppressed.
Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well-separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a 1D plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may be computed using quantum parallelism in the future.
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