There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

https://arxiv.org/pdf/cond-mat/9806038.pdf

Theory of Bose-Einstein condensation in trapped gases

The theory of inflation with single and multiple fields is reviewed paying particular attention to the dynamics of adiabatic and entropy/isocurvature perturbations which provide the primary means of testing inflationary models. The theory and phenomenology of reheating and preheating after inflation is reviewed providing a unified discussion of both the gravitational and nongravitational features of multifield inflation. In addition inflation in theories with extra dimensions and models such as the curvaton scenario and modulated reheating which provide alternative ways of generating large-scale density perturbations are covered. Finally interesting observational implications are discussed that can result from adiabatic-isocurvature correlations and non-Gaussianity.

/pdf/inflation-dynamics-and-reheating-3rr302gbaj.pdf

Inflation dynamics and reheating

Mathematical Handbook for Scientists and Engineers

The Simons Observatory (SO) is a new cosmic microwave background experiment being built on Cerro Toco in Chile, due to begin observations in the early 2020s. We describe the scientific goals of the experiment, motivate the design, and forecast its performance. SO will measure the temperature and polarization anisotropy of the cosmic microwave background in six frequency bands centered at: 27, 39, 93, 145, 225 and 280 GHz. The initial configuration of SO will have three small-aperture 0.5-m telescopes and one large-aperture 6-m telescope, with a total of 60,000 cryogenic bolometers. Our key science goals are to characterize the primordial perturbations, measure the number of relativistic species and the mass of neutrinos, test for deviations from a cosmological constant, improve our understanding of galaxy evolution, and constrain the duration of reionization. The small aperture telescopes will target the largest angular scales observable from Chile, mapping ≈ 10% of the sky to a white noise level of 2 μK-arcmin in combined 93 and 145 GHz bands, to measure the primordial tensor-to-scalar ratio, r, at a target level of σ(r)=0.003. The large aperture telescope will map ≈ 40% of the sky at arcminute angular resolution to an expected white noise level of 6 μK-arcmin in combined 93 and 145 GHz bands, overlapping with the majority of the Large Synoptic Survey Telescope sky region and partially with the Dark Energy Spectroscopic Instrument. With up to an order of magnitude lower polarization noise than maps from the Planck satellite, the high-resolution sky maps will constrain cosmological parameters derived from the damping tail, gravitational lensing of the microwave background, the primordial bispectrum, and the thermal and kinematic Sunyaev-Zel'dovich effects, and will aid in delensing the large-angle polarization signal to measure the tensor-to-scalar ratio. The survey will also provide a legacy catalog of 16,000 galaxy clusters and more than 20,000 extragalactic sources.

/pdf/the-simons-observatory-science-goals-and-forecasts-4da1fcfijm.pdf

The Simons Observatory : Science goals and forecasts

https://wwwth.mpp.mpg.de/members/raffelt/mypapers/200203.pdf

Cosmological bounds on neutrino degeneracy improved by flavor oscillations

Non-equilibrium corrections to the spectra of massless neutrinos in the early universe

The process of condensation in the system of scalar bosons with weak {lambda}{phi}{sup 4} interaction is considered. The Boltzmann kinetic equation is solved numerically. We consider two kinetic stages. At the first stage condensate is still absent but there is nonzero inflow of particles towards p={bold 0} and the distribution function at p={bold 0} grows from finite values to infinity. At the second stage there are two components, condensate and particles, reaching their equilibrium values. We show that the evolution in both stages proceeds in a self-similar way and find the time needed for condensation.

Kinetics of bose condensation

Applying our recently developed propagation code we review extragalactic neutrino fluxes above ${10}^{14}\mathrm{eV}$ in various scenarios and how they are constrained by current data. We specifically identify scenarios in which the cosmogenic neutrino flux above $\ensuremath{\simeq}{10}^{18}\mathrm{eV},$ produced by pion production of ultrahigh energy cosmic rays outside their sources, is considerably higher than the ``Waxman-Bahcall bound.'' This is easy to achieve for sources with hard injection spectra and luminosities that were higher in the past. Such fluxes would significantly increase the chances to detect ultrahigh energy neutrinos with experiments currently under construction or in the proposal stage.

http://cds.cern.ch/record/550362/files/0205050.pdf

Ultrahigh-energy neutrino fluxes and their constraints

We study the kinetic regime of the Bose condensation of scalar particles. The Boltzmann equation is solved numerically. We consider two kinetic stages. At the first stage the condensate is absent but there is a nonzero inflow of particles towards {bold p}={bold 0} and the distribution function at {bold p}={bold 0} grows from finite values to infinity in a finite time. We observe a profound similarity between Bose condensation and Kolmogorov turbulence. At the second stage there are two components, the condensate and particles, reaching their equilibrium values. We show that the evolution in both stages proceeds in a self-similar way and find the time needed for condensation. We do not consider a phase transition from the first stage to the second. Condensation of self-interacting bosons is compared to the condensation driven by interaction with a cold gas of fermions; the latter turns out to be self-similar too. Exploiting the self-similarity we obtain a number of analytical results in all cases. {copyright} {ital 1997} {ital The American Physical Society}

Dmitry V. Semikoz

Papers

Cosmological bounds on neutrino degeneracy improved by flavor oscillations

Non-equilibrium corrections to the spectra of massless neutrinos in the early universe

Kinetics of bose condensation

Ultrahigh-energy neutrino fluxes and their constraints

Condensation of bosons in the kinetic regime