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A precise measurement of the proton flux in primary cosmic rays with rigidity (momentum/charge) from 1 GV to 1.8 TV is presented based on 300 million events. Knowledge of the rigidity dependence of the proton flux is important in understanding the origin, acceleration, and propagation of cosmic rays. We present the detailed variation with rigidity of the flux spectral index for the first time. The spectral index progressively hardens at high rigidities.

Precision measurements by the Alpha Magnetic Spectrometer on the International Space Station of the primary cosmic-ray electron flux in the range 0.5 to 700 GeV and the positron flux in the range 0.5 to 500 GeV are presented. The electron flux and the positron flux each require a description beyond a single power-law spectrum. Both the electron flux and the positron flux change their behavior at $\sim 30\mathrm{GeV}$ but the fluxes are significantly different in their magnitude and energy dependence. Between 20 and 200 GeV the positron spectral index is significantly harder than the electron spectral index. The determination of the differing behavior of the spectral indices versus energy is a new observation and provides important information on the origins of cosmic-ray electrons and positrons.

We present a measurement of the cosmic ray $(e^{+}+e^{-})$ flux in the range 0.5 GeV to 1 TeV based on the analysis of 10.6 million $(e^{+}+e^{-})$ events collected by AMS. The statistics and the resolution of AMS provide a precision measurement of the flux. The flux is smooth and reveals new and distinct information. Above 30.2 GeV, the flux can be described by a single power law with a spectral index $\gamma =-3.170\pm 0.008(\text{stat}+\text{syst})\pm 0.008(\text{energy}\text{scale})$.

A precision measurement by AMS of the positron fraction in primary cosmic rays in the energy range from 0.5 to 500 GeV based on 10.9 million positron and electron events is presented. This measurement extends the energy range of our previous observation and increases its precision. The new results show, for the first time, that above $\sim 200\mathrm{GeV}$ the positron fraction no longer exhibits an increase with energy.

A precision measurement by the Alpha Magnetic Spectrometer on the International Space Station of the positron fraction in primary cosmic rays in the energy range from 0.5 to 350 GeV based on $6.8\times {10}^6$ positron and electron events is presented. The very accurate data show that the positron fraction is steadily increasing from 10 to $\sim 250\mathrm{GeV}$, but, from 20 to 250 GeV, the slope decreases by an order of magnitude. The positron fraction spectrum shows no fine structure, and the positron to electron ratio shows no observable anisotropy. Together, these features show the existence of new physical phenomena.

In this paper we analyze the Bianchi IX Universe dynamics within the corner region associated to the potential term which the spatial curvature induces in the minisuperspace. We investigate the dynamics in terms of the WKB scenario: the isotropic Misner variable ($\alpha$) and one of the two anisotropic variables (${\beta }_{+}$) are treated as semiclassical, while the remaining anisotropy (${\beta }_{-}$) is described on a pure quantum level. The quantum dynamics always reduces to the one of a time-dependent Schrödinger equation for a harmonic potential with a time dependent frequency. The study is done in the vacuum and in the presence of a massless scalar field $\varphi$ and a cosmological constant term $\mathrm{\Lambda }$. The vacuum case is treated in the limits of a collapsing and an expanding Universe, while the dynamics in presence of $\varphi$ and $\mathrm{\Lambda }$ is studied only for $t\to \infty$. In both analyses the quantum dynamics of the anisotropy variable ${\beta }_{-}$ suggests a suppression of the quantum anisotropy associated. In the vacuum case the corner configuration becomes an attractor for the dynamics and the evolution resembles that of a Taub cosmology in the limit of a nonsingular initial Universe. This suggests that if the Bianchi dynamics enters deeply enough in the potential corner the initial singularity is removed and a Taub picture emerges. The case when $\varphi$ is present well mimics the de Sitter phase of an inflationary Universe. Here we show that both the classical and quantum anisotropies are exponentially suppressed and therefore the resulting dynamics corresponds to an isotropic closed Robertson-Walker geometry.