The signatures of Ultra High Energy (E >1 EeV) proton propagation through CMB radiation are pair-production dip and GZK cutoff. The visible characteristics of these two spectral features are ankle, which is intrinsic part of the dip, beginning of GZK
cutoff in the differential spectrum and E_{1/2} in integral spectrum. Measured by HiRes and Telescope Array (TA) these characteristics agree with theoretical predictions. However, directly measured mass composition remains a puzzle. While HiRes and TA detectors observe the proton dominated mass composition, the data of Auger detector strongly evidence for nuclei mass composition becoming progressively heavier at energy higher than 4 EeV and reaching Iron at energy about 35 EeV. The models based on the Auger and HiRes/TA data are considered independently and classified using the transition from galactic to extragalactic cosmic rays. The ankle cannot provide this transition. since data of all three detector at energy (1 - 3) EeV agree with pure proton composition (or at least not heavier than Helium). If produced in Galaxy these particles result in too high anisotropy. This argument excludes or strongly disfavours all ankle models with ankle energy E_a > 3 EeV. The calculation of elongation curves, X_{max}(E), for different ankle models strengthens further this conclusion. Status of other models, the dip, mixed composition and Auger based models are discussed.
The signatures of UHE proton propagation through CMB are pair-production dip and GZK cutoff. The visible manifestations of these spectral features are ankle, beginning of GZK cutoff in the differential spectrum and E_{1/2} in integral spectrum. Obser
ved in all experiments, the ankle is usually interpreted as transition from galactic to extragalactic cosmic rays. Using the mass composition measured by HiRes, Telescope Array (TA) and Auger detectors at energy (1-3) EeV, calculated anisotropy of galactic cosmic rays at these energies, and the elongation curves we strongly argue against the interpretation of the ankle given above. The transition must occur at lower energy, most probably at the second knee as the dip model predicts. The other prediction of this model, the shape of the dip, is well confirmed by HiRes, TA, AGASA and Yakutsk detectors, and, after recalibration of energies, by Auger detector. Predicted beginning of GZK cutoff and E_{1/2} agree well with HiRes and TA data. However, directly measured mass composition remains a puzzle. While HiRes and TA detectors observe the proton-dominated mass composition, as required by the dip model, the data of Auger detector strongly evidence for nuclei mass composition becoming steadily heavier at energy higher than 4 EeV and reaching Iron at energy about 35 EeV. The Auger-based scenario is consistent with another interpretation of the ankle at energy E_a=4 EeV as transition from extragalactic protons to extragalactic nuclei. The heavy- nuclei dominance at higher energies may be provided by low-energy of acceleration for protons E_{max} sim 4 EeV and rigidity-dependent E_{max}^A =Z E_{max}$ for nuclei. The highest energy suppression may be explained as nuclei-destroying cutoff.
The short review of theoretical aspects of ultra high energy (UHE) neutrinos. The accelerator sources, such as Supernovae remnants, Gamma Ray Bursts, AGN etc are discussed. The top-down sources include Topological Defects (TDs), Superheavy Dark Matte
r (SHDM) and Mirror Matter. The diffuse fluxes are considered accordingly as that of cosmogenic and top-down neutrinos. Much attention is given to the cascade upper limit to the diffuse neutrino fluxes in the light of Fermi-LAT data on diffuse high energy gamma radiation. This is most general and rigorous upper limit, valid for both cosmogenic and top-down models. At present upper limits from many detectors are close to the cascade upper limit, and 5 yr IceCube upper limit will be well below it.
We discuss the superluminal problem in the diffusion of ultra high energy protons with energy losses taken into account. The phenomenological solution of this problem is found with help of the generalized Juttner propagator, originally proposed for r
elativization of the Maxwellian gas distribution. It is demonstrated that the generalized Juttner propagator gives the correct expressions in the limits of diffusive and rectilinear propagation of the charged particles in the magnetic fields, together with the intermediate regime, in all cases without superluminal velocities. This solution, very general for the diffusion, is considered for two particular cases: diffusion inside the stationary objects, like e.g. galaxies, clusters of galaxies etc, and for expanding universe. The comparison with the previously obtained solutions for propagation of UHE protons in magnetic fields is performed.
We develop a model for explaining the data of Pierre Auger Observatory (Auger) for Ultra High Energy Cosmic Rays (UHECR), in particular, the mass composition being steadily heavier with increasing energy from 3 EeV to 35 EeV. The model is based on th
e proton-dominated composition in the energy range (1 - 3) EeV observed in both Auger and HiRes experiments. Assuming extragalactic origin of this component, we argue that it must disappear at higher energies due to a low maximum energy of acceleration, E_p^{max} sim (4 - 10) EeV. Under an assumption of rigidity acceleration mechanism, the maximum acceleration energy for a nucleus with the charge number Z is ZE_p^{max}, and the highest energy in the spectrum, reached by Iron, does not exceed (100 - 200) EeV. The growth of atomic weight with energy, observed in Auger, is provided by the rigidity mechanism of acceleration, since at each energy E=ZE_p^{max} the contribution of nuclei with Z < Z vanishes. The described model has disappointing consequences for future observations in UHECR: Since average energies per nucleon for all nuclei are less than (2 - 4) EeV, (i) pion photo-production on CMB photons in extragalactic space is absent; (ii) GZK cutoff in the spectrum does not exist; (iii) cosmogenic neutrinos produced on CMBR are absent; (iv) fluxes of cosmogenic neutrinos produced on infrared - optical background radiation are too low for registration by existing detectors and projects. Due to nuclei deflection in galactic magnetic fields, the correlation with nearby sources is absent even at highest energies.
UHE neutrinos with $E>10^{17}$ eV can be produced by ultra-high energy cosmic rays (UHECR) interacting with CMB photons (cosmogenic neutrinos) and by top-down sources, such as topological defects (TD), superheavy dark matter (SHDM) and mirror matter.
Cosmogenic neutrinos are reliably predicted and their fluxes can be numerically evaluated using the observed flux of UHECR. The lower limit for the flux is obtained for the case of pure proton composition of the observed UHECR. The rigorous upper limit for cosmogenic neutrino flux also exists. The maximum neutrino energy is determined by maximum energy of acceleration, which at least for the shock acceleration is expected not to exceed $10^{21} - 10^{22}$ eV. The top-down sources provide neutrino energies a few orders of magnitude higher, and this can be considered as a signature of these models. Oscillations play important role in UHE neutrino astronomy. At production of cosmogenic neutrinos $tau$-neutrinos are absent and $bar{ u}_e$ neutrinos are suppressed. These species, important for detection, appear in the observed fluxes due to oscillation. Mirror neutrinos cannot be observed directly, but due to oscillations to ordinary neutrinos they can provide the largest neutrino flux at the highest energies.
The status of the Greisen-Zatsepin-Kuzmin (GZK) cutoff and pair-production dip in Ultra High Energy Cosmic Rays (UHECR) is discussed.They are the features in the spectrum of protons propagating through CMB radiation in extragalactic space, and discov
ery of these features implies that primary particles are mostly extragalactic protons. The spectra measured by AGASA, Yakutsk, HiRes and Auger detectors are in good agreement with the pair-production dip, and HiRes data have strong evidences for the GZK cutoff. The Auger spectrum,as presented at the 30th ICRC 2007, agrees with the GZK cutoff, too. The AGASA data agree well with the beginning of the GZK cutoff at E leq 80 EeV, but show the excess of events at higher energies, the origin of which is not understood. The difference in the absolute fluxes measured by different detectors disappears after energy shift within the systematic errors of each experiment.
We discuss the production of ultra high energy secondary protons by cosmic ray primary nuclei propagating in the intergalactic space through Cosmic Microwave Background (CMB) and Infrared (IR) radiations. Under the assumption that only primary nuclei
with a fixed atomic mass number $A_0$ are accelerated, the spectrum of secondary protons is calculated. It is found that for all $A_0$ the diffuse flux of secondary protons starts to dominate over that of primary nuclei at energy $E sim (1 - 2)times 10^{19}$ eV, and thus the standard Greisen-Zatsepin -Kuzmin (GZK) cutoff is produced.
Puzzles often give birth to the great discoveries, the false discoveries sometimes stimulate the exiting ideas in theoretical physics. The historical examples of both are described in Introduction and in section ``Cosmological Puzzles. From existing
puzzles most attention is given to Ultra High Energy Cosmic Ray (UHECR) puzzle and to cosmological constant problem. The 40-years old UHECR problem consisted in absence of the sharp steepening in spectrum of extragalactic cosmic rays caused by interaction with CMB radiation. This steepening is known as Greisen-Zatsepin-Kuzmin (GZK) cutoff. It is demonstrated here that the features of interaction of cosmic ray protons with CMB are seen now in the spectrum in the form of the dip and beginning of the GZK cutoff. The most serious cosmological problem is caused by large vacuum energy of the known elementary-particle fields which exceeds at least by 45 orders of magnitude the cosmological vacuum energy. The various ideas put forward to solve this problem during last 40 years, have weaknesses and cannot be accepted as the final solution of this puzzle. The anthropic approach is discussed.
The transition from galactic to extragalactic cosmic rays is discussed. One of critical indications for transition is given by the Standard Model of Galactic cosmic rays, according to which the maximum energy of acceleration for iron nuclei is of ord
er of $E_{rm Fe}^{rm max} approx 1times 10^{17}$ eV. At $E > E_{rm Fe}^{rm max}$ the spectrum is predicted to be very steep and thus the Standard Model favours the transition at energy not much higher than $E_{rm Fe}^{rm max}$. As observations are concerned there are two signatures of transition: change of energy spectra and elongation rate (depth of shower maximum in the atmosphere $X_{rm max}$ as function of energy). Three models of transition are discussed: dip-based model, mixed composition model and ankle model. In the latter model the transition occurs at the observed spectral feature, ankle, which starts at $E_a approx 1times 10^{19}$ eV and is characterised by change of mass compostion from galactic iron to extragalactic protons. In the dip model the transition occures at the second knee observed at energy $(4 -8)times 10^{17}$ eV and is characterised by change of mass composition from galactic iron to extragalactic protons. The mixed composition model describes transition at $E sim 3times 10^{18}$ eV with mass composition changing from galactic iron to extragactic mixed composition of different nuclei. These models are confronted with observational data on spectra and elongation rates from different experiments, including Auger.
