The cosmic microwave radiation illuminates all the sky with a uniformity of one part per hundred thousands. It has a black body spectrum in any direction with a peak energy of 6.626 × 10−4 eV . These highly specific features attest a thermodynamic equilibrium in a physical cavity like hollow radiators with internal black reflecting walls, common in physics laboratories. The present work identifies, for the first time, the cavity generating the cosmic microwave radiation. The cavity has a size of 9.311×1027 m, the material inside in thermodynamic equilibrium is unexcited neutral Hydrogen of total mass 6.269×1054 kg and, finally, the process maintaining the thermodynamic equilibrium is the light bending and trapping caused by gravity. The immaterial walls of the cavity relate to the minimum mass preventing light to escape which is 6.269 × 1054 kg. The matter density in the cavity is 0.0185 × 10−28 kg/m3 which evolved in recent times to higher density compatible with that measured in the local universe, close to 0.77 × 10−28 kg/m3.

The notion of Dark Matter originates from the violation of Virial Theorem in galaxy clusters and the empirical evidence of flat or increasing rotation curves in disk galaxies. From novel advances on basic properties of cosmic rays it emerges the necessity of ubiquitous electrostatic fields in disk galaxies and galaxy clusters. In this study it is argued that the electrostatic field in the Milky Way Galaxy exerts an attractive force on rotating stars and clouds which adds to gravity yielding slightly increasing rotation curves in the radial range from 8.5 to 15 kpc and decreasing curves beyond 15 kpc. Calculations are favorably compared with the rotation curves based on 21 cm HI gas emission, infrared emission from molecular clouds, Cepheid stars, Carbon stars, Planetary Nebulae and MASER from clouds excited by O and B stars. The results of this work interfuse with the numerous null results of Dark Matter quest in laboratories, caverns and particle accelerators during half a century and it is concluded that Dark Matter does not exist. It is a simple electrostatic effect of giant material bodies absorbing positive electric charge from extinguished cosmic rays.

The Voyager spacecrafts have been measuring since 2012 the rates of electron and nuclei of the cosmic radiation beyond the solar cavity at a distance of more than 10^13 meters from the Earth. A record of unique and notable findings have been reported and, among them, the electron-to-proton flux ratio of 50 to 100 below energies of 50 MeV. This ratio is thoroughly opposite of that of 0.01 measured at higher energies in the range 10 GeV to 10 TeV. The difference amounts to four orders of magnitude. Arguments and calculations to show how this surprising and fundamental ratio lends support to the empirical evidence of the ubiquitous electrostatic field in the Milky Way Galaxy are presented. In other respects this paper examines and calculates, for the first time, the electric charge balance in the solar system delimited by the termination shock of the solar wind.

Cosmic rays are fully ionized nuclei, electrons plus rare particles having extreme high energies with a characteristic energy spectrum up to 3 x 1020 eV. They move and reside in the Galaxy with a lifetime of 15 million years transporting a positive electric charge of about 1031-1032 C. The immense grid of positive electric charges of about 1050 particles necessarily generates an electrostatic field in the entire Galaxy. This work present five diverse models to quantitatively describe the Galactic electrostatic field and the related potential. Analytical formulae and tabulated values from computer calculation of the Galactic electric field are explicitly reported for the first time. Any of the five models have field intensities close to one V/m and electrostatic potentials in the range 1019-1020 V. The anchorage of the calculation to the observational data is delineated in the last Section.

Particles of the cosmic radiation, electrons and nuclei, transport a dominant positive electric charge. A tiny fraction of these particles of extremely high energies in favorable conditions overflow from galaxies. The overflowing of positively charged cosmic nuclei into the intergalactic space uncovers an equal amount of negative charge in the parent galaxy. Negative charge is mainly stored by quiescent electrons. After adequate particle propagation neither the negative electric charge located in the galaxies nor the positive electric charge of the overflowed cosmic nuclei can be neutralized due to the enormous distances. In several ways it is proved that the total electric charge retained by clusters of galaxies after an appropriate time interval generate a repulsive force between clusters which overwhelms gravity. After a few billions years of electrostatic repulsion, peripheral clusters attain relativistic velocities and their mutual distances increase accordingly. Several facts suggest that the expansion of the universe, as determined by optical observations since a century, has been caused by the electrostatic repulsion of the positively charged cosmic nuclei overflowed from galaxy clusters.

The mechanism accelerating cosmic rays in the Milky Way Galaxy and galaxy clusters is identified and described. The acceleration of cosmic rays is a purely electrostatic process which operates up to the maximum energies of $10^{23}$ eV in galaxy clusters. Galactic cosmic rays are accelerated in a pervasive electrostatic field active in the whole Galaxy except in restricted regions shielded by interstellar and stellar plasmas as, for instance, the region occupied by the solar system. It is proved that the energy spectrum of the cosmic radiation in the Milky Way Galaxy, in the region where the solar system resides, has a constant spectral index comprised between 2.64-2.68 and the maximum energies of Galactic protons are $3.0 \times 10^{19}$ eV. The agreement of these results with the experimental data is discussed in detail and underlined. The various physical processes that maintain the stability of the electrostatic structure in the Milky Way Galaxy are the same that generate the Galactic magnetic field. Accordingly, the intensity, orientation and direction of the Galactic magnetic field are evaluated. The results of the calculation are compared with the observational data, optical and mostly radio astronomy data. The accord of the intensity, orientation and direction of the observed magnetic field with calculation is excellent.

Cosmic ray abundances, A(cr), are compared with those of quiescent matter in the Galaxy, A(g), for 40 nuclei from Hydrogen to Zirconium via the abundance ratios A(cr)/A(g). Secondary nuclei generated by spallation reactions in the interstellar medium are removed from the analysis reducing the sample to primary nuclei. The abundance ratios of primary nuclei obey a simple rule depending on the atomic number Z, namely A(cr)/A(g) = aZ(2) - b Z where a and b are numerical constants. This study suggests that the physical mechanism giving the correct, quantitative explanation of the above rule is the photoionization of the quiescent, cold interstellar matter. The ultraviolet light spectrum causing photoionization of neutral atoms is highly characteristic and concentrated in a very restricted band, namely 3-250 nm. It is argued that such an ultraviolet spectrum and the related absolute intensity can be generated by O and B stars. It is concluded that the sources of cosmic rays are located in cold zones, at adequate distances from O and B stars beyond the fully ionized Stromgren shells. Previous explanations of the universal A(cr)/A(g) abundance ratios are discussed.

A major feature of the energy spectrum of the cosmic radiation above 1019 eV is the increasing fraction of heavy nuclei with respect to light nuclei. This fact, along with other simple assumptions, is adopted to calculate the energy spectrum of the cosmic radiation up to 2.4 × 1021 eV. The predicted spectrum maintains the index of 2.67 observed at lower energies which is the basic, known, empirical well-assessed feature of the physical mechanism accelerating cosmic rays in the Galaxy. Indeed above 1019 eV the injection of nuclei is inhibited by some filter and this inhibition causes a staircase profile of the energy spectrum. It is argued that particle injection failure versus energy commences with protons, followed by Helium and then by other heavier nuclei up to Uranium. Around 7.5 × 1020 the cosmic radiation consists solely of nuclei heavier than Copper and the estimated intensity is 1.8 × 10-30 particles/GeV s sr m2.

The energy spectrum of the cosmic radiation in the range 10^19-2.4×10^21 eV has been recently predicted showing a rich and distinctive staircase profile. In order to check the prediction, the spectra measured by running and past experiments above 10^19 eV are examined. The computed spectrum compares more favourably with the Telescope Array, HiRes I and Yakutsk data rather than with the Auger data in the range (1-20)×10^19 eV. Previous flux measurements by Haverah Park, sugar, agasa and Fly's Eye experiments are above the predicted spectrum in the limited band (1-30)×10^19 eV. The flux measured by the Auger Group in the band (8-18)×10^19 eV is below those of all other experiments and below the prediction. The energy scales of the instruments might be at the origin of the flux mismatch among the experiments. Accordingly, the energy scales of all the eleven instruments operating above 10^20 eV are examined and the major inconsistencies discerned. The paucity of events above 10^20 eV of the Auger experiment with respect to all others is by far the major puzzle emerging from this scrutiny. The Auger instrument recorded only 4 events above 10^20 eV with an exposure exceeding 42500 km^2 sr year while the Telescope Array recorded 13 events with an exposure of 8100 km^2 sr year. A tentative solution of this puzzle is ventilated.

According to recent measurements the tendency of the chemical composition above the ankle is characterized by increasing fractions of intermediate and heavy nuclei and a dominance of light nuclei around the ankle. Calculation of the chemical composition in the range 3.5 × 1018 - 5 × 1019 eV according to new principles explains both the rising tendency of the heavy component. The calculation is prolonged to the adjacent interval 5 × 1019- 2.4 × 1021 eV using the same theoretical background and some features of the observed cosmic-ray spectrum. It results that above the energy of 6.7 × 1020 eV, where the flux is estimated to be 1.8 × 10?30 particles/m2 s sr GeV, the cosmic radiation consists only of nuclei heavier than Zinc. Measurements of the spectrum of present and past experiments are compared with the calculations.

A major feature of the energy spectrum of the cosmic radiation above 10^19 eV is the increasing fraction of heavy nuclei with respect to light nuclei. This fact, along with other simple assumptions, is adopted to calculate the energy spectrum of the cosmic radiation up to 2.4×10^21 eV. The predicted spectrum maintains the index of 2.67 observed at lower energies which is the basic, known, empirical well-assessed feature of the physical mechanism accelerating cosmic rays in the Galaxy. Indeed above 10^19 eV the injection of nuclei is inhibited by some filter and this inhibition causes a staircase profile of the energy spectrum. It is argued that particle injection failure versus energy commences with protons, followed by Helium and then by other heavier nuclei up to Uranium. Around 7.5×10^20 the cosmic radiation consists solely of nuclei heavier than Copper and the estimated intensity is 1.8×10^-30 particles/GeV s sr m^2.

The dominance of secondary nuclei in the cosmic radiation and the modulation of the nuclear species at the injection of the galactic accelerator

The proton flux and the chemical composition of the cosmic radiation measured, respectively, by the Kascade and Auger experiments entail radical changes in Cosmic Ray Physics. A large discrepancy emerges by comparing the proton flux predicted by the dip model and that measured by Kascade in the critical energy interval 5 x 10 ** 16 - 10 ** 17 eV. It is mentioned and substantiated that the proton flux measurements of the Kascade experiment are consistent with other pertinent empirical observations. It is shown that the chemical composition measured by Auger by two independent procedures, using the mean depth reached by cosmic nuclei in giant air cascades, is incompatible with that predicted by the dip model. A notable consequence suggested here based on the failures of the dip model is that the spectral index softening of the primary cosmic radiation above 6 x 10 ** 19 eV observed by HiRes and Auger experiments, is not due to the extragalactic cosmological protons suffering energy losses in the intergalactic space via the reactions, p gamma -> pi0 p, pi+ n, but to some physical phenomena occurring in the cosmic vicinity.

The differential energy spectrum of the cosmic radiation from solar modulation energies tip to 5 x 10(19) eV is correctly predicted by a recent theory of the knee and ankle which uses only one normalization point. This remarkable quantitative result, spanning over many decades in energy and intensity, along with the existence of the second knee at 6 x 10(17) eV, is obtained assuming constant spectral indices of individual ions at the cosmic-ray sources and no other critical hypotheses. In this study the chemical composition of the cosmic radiation is evaluated as a direct consequence of the theory. The computed mean logarithmic mass exhibits a rising trend from 1.8 to 3.0 in the range 10(15) - 10(17) eV, a maximum value of 3.2 at 3 x 10(17) eV, and a characteristic lightening above 3 x 10(17) eV up to 4 x 10(18) eV. All of these distinctive features are in accord with the data of many experiments. Two additional consequences intrinsic to the theory are qualitatively discussed: (1) some limitative bounds on the mechanism accelerating cosmic rays; (2) the degree of isotropy implied by the residence time of the cosmic rays in the Galaxy.

Some recent measurements of the chemical composition of the cosmic radiation indicate that at the energy of 3 x 10 **18 eV, around the ankle, light cosmic ions dominate the spectrum as it occurs in the preknee energy region. Taking advantage of a recent theory of cosmic radiation which provides a quantitative explanation of the knee, the second knee and the ankle, the chemical composition of cosmic radiation is explicitly calculated giving individual ion spectra and ion fractions from 10 ** 12 eV to 5 x 10 ** 19 eV. The calculation assumes two components of the cosmic radiation feeding the ion flux at Earth: one originated in the disc volume and another one, called extradisc component, which from the disc boundaries traverses the Galaxy reaching the solar system. Data above 10 ** 17 eV collected during half century of experimentation by Auger, HiRes, Agasa, Akeno, Fly' s Eye, Yakutsk, Haverah Park and Volcano Ranch experiments are reviewed, examined and compared with the theoretical . The comparison between computed and measured exhibits a good global accord up to 2 x 10 ** 19 eV except with the HiRes experiment and an excellent agreement in the range 10 ** 15 - 10 ** 17 eV with Kascade, Eas-top, Tunka and other experiments. The accord requires a flux of the extradisc component of 1.8 x 10 ** 14 particles / m ** 2 sr s eV **(1.5) at 10 ** 19 eV, twice that generated by disc sources.

Many experimental results around and above the energies where the solar modulation affects cosmic ion fluxes were quantified, conceptualized and debated using leaky box models. These models exploit the notion of equilibrium between creation and destruction processes of cosmic ions in an undifferentiated arbitrary volume representing the Galaxy, ignoring the galactic magnetic field, the size of the Galaxy, the position of the solar cavity, the spatial distribution of the sources, the space variation of the interstellar matter and other pertinent observations. Progress in the measurements of the quoted observational parameters rendes obsolete the use of the leaky box models. Specific examples substantiating the inadequacy of the leaky box models are analyzed such as the conversion of the boron-to-carbon flux ratio into grammage and the residence times of cosmic ions in the Galaxy. The unphysical and misleading nature of the leaky box models is ascertained and illustrated at very high energy.