High-energy muons loose their energy by ionization, pair production, bremsstrahlung and inelastic interaction with nuclei. The process with the largest uncertainty is the inelastic interaction with nuclei. Since the energy loss is dominated by soft interactions with small momentum transfer, parton distribution functions are not applicable and phenomenological parametrizations have to be used. The parametrizations of the proton structure functions that are commonly used in muon transport simulation tools such as PROPOSAL, MUM, MUSIC or Geant4 were determined on the basis of the data available about 20 years ago. In this contribution, we refit several commonly used parametrizations to the data on deep inelastic scattering available today, including the precise combined data from the HERA experiments H1 and ZEUS, which have become available a few years ago. We compare the goodness of fit and calculate the uncertainty of the average energy loss from the uncertainties and correlations of the fit parameters.

Nuclear shadowing corrections to the structure functions of deep inelastic scattering on intermediate-mass nuclei are calculated at very small values of Bjorken x and small values of Q^2 (Q^2<5 Gev^2). The two-component approach developed in previous works of authors for a description of the nucleon structure functions of deep inelastic scattering is used. It is shown that the hard component of the nucleon structure functions that arises, in terms of the colour dipole model, from qq-pairs with a high transverse momentum, is almost not shadowed. It is shown that a change of the slope of the shadowing curve with a decrease of x depends, at small values of x, on the relative contribution of the hard component to the nucleon structure function (this contribution is a function of x and Q^2) and on a size of gluon saturation effects. It is shown that an accounting for saturation effects becomes essential for predictions of shadowing at x<10^-4, depending on a value of Q^2. Results of numerical calculations of nuclear shadowing for several nuclei are compared with available data of the E665 and the NMC collaborations.

Primordial black holes (PBHs) are black holes which may form in the early Universe through the gravitational collapse of primordial cosmological density fluctuations. Due to Hawking radiation these PBHs are supposed to evaporate by emitting particles. Recent developments in the experimental searching for evaporating PBHs in the local Universe are reviewed. The multimessenger techniques of searching for signals from evaporating PBHs are discussed.

We consider the inflationary model in which the inflaton $\ensuremath{\phi}$ couples to another scalar field $\ensuremath{\chi}$ via the interaction ${g}^{2}(\ensuremath{\phi}\ensuremath{-}{\ensuremath{\phi}}_{0}{)}^{2}{\ensuremath{\chi}}^{2}$ with a small coupling constant $g$ (${g}^{2}\ensuremath{\sim}{10}^{\ensuremath{-}7}$). We assume that there is a sequence of ``trapping points'' ${\ensuremath{\phi}}_{0i}$ along the inflationary trajectory where particles of the $\ensuremath{\chi}$ field become massless and are rather effectively produced. We calculate the power spectrum of inflaton field fluctuations originating from a backreaction of $\ensuremath{\chi}$ particles produced using the Schwinger's ``in-in'' formalism. We show that the primary curvature power spectrum produced by these backreaction effects is blue, which leads to a strong overproduction of primordial black holes (PBHs) in the subsequent radiation era.

Nuclear shadowing corrections to the structure functions of deep inelastic scattering of intermediate-mass nuclei are calculated at very low values of Bjorken x and small values of Q^2 (Q^2<5 GeV^2). The two-component approach (generalized VMD plus hard pomeron) is used for a description of the underlying virtual photon - nucleon interaction. The hard component of the nucleon structure function is calculated in a framework of the colour dipole model with dipole cross section having Regge-type energy dependence. Numerical results for nuclear shadowing corrections are compared with available data of E665 and NMC collaborations.

We study the process of primordial black hole (PBH) formation at the beginning of radiation era for the cosmological scenario in which the inflaton is a pseudo-Nambu-Goldstone boson (axion) and there is a coupling of the inflaton with some gauge field. In this model inflation is accompanied by the gauge quanta production and a strong rise of the curvature power spectrum amplitude at small scales (along with non-Gaussianity) is predicted. We show that data on PBH searches can be used for a derivation of essential constraints on the model parameters in such an axion inflation scenario. We compare our numerical results with the similar results published earlier, in the work by Linde et al.

We argued that deep inelastic scattering (DIS) at small values of Q squared is an essentially nonperturbative process and can be described, partially at least, by the vector meson dominance (VMD) model. We showed by the straightforward calculation that VMD model alone can successfully explain data on structure functions of DIS in a broad interval of x (5e-2 - 1e-4) for the region Q squared < 1 GeV squared. For a description of data at larger Q squared we used the two-component (VMD + perturbative QCD) approach. We showed that these two components can be separated if VMD is used in the aligned jet version. We took into account, in calculations of VMD component of structure functions, the excited states of the rho-meson and nondiagonal transitions between different members of the rho-meson family. Amplitudes of these transitions were obtained using a formalism of the light-front Bethe-Salpeter equation and the method of diffraction-scattering eigenstates. The perturbative QCD component was calculated using a framework of the colour dipole model with the dipole cross section having a Regge-type energy dependence. We presented results of the detailed comparison of our predictions with experimental data for structure functions of the nucleon. We obtained also approximate predictions for the structure functions in the region of very small x, up to 1e-9, and showed that nonperturbative component at such values of x is still relatively large and must be taken into account if Q squared is about few GeV squared or less.

We consider the early Universe scenario which allows for production of non-Gaussian curvature perturbations at small scales. We study the peculiarities of a formation of primordial black holes (PBHs) connected with the non-Gaussianity. In particular, we show that PBH constraints on the values of curvature perturbation power spectrum amplitude are strongly dependent on the shape of perturbations and can significantly (by two orders of magnitude) deviate from the usual Gaussian limit P-zeta less than or similar to 10(-2). We give examples of PBH mass spectra calculations and PBH constraints for the particular case of the curvaton model.

We show that nucleon electromagnetic structure functions of deep inelastic scattering in Regge-Gribov limit (fixed Q-squared, asymptotically large 1/x and s) can be well described in the two-component (soft + hard) approach. In the concrete model elaborated by authors, the soft part of the virtual photon-nucleon scattering is given by the vector meson dominance, with taking into account the radial excitations of the rho-meson and nondiagonal transitions in meson-nucleon interactions. The hard part is calculated by using the dipole factorization, i.e., the process is considered as the dissociation of the photon into a -pair (the "color dipole") and the subsequent interaction of this dipole with the nucleon. The dipole cross section has a Regge-type s-dependence and vanishes in the limit of large transverse sizes of the dipole. We give the brief description of the model and present results of the detailed comparison of model predictions with experimental data for electromagnetic structure functions of the nucleon.

It is shown that experimental data on the electromagnetic structure functions of a nucleon in the kinematic region of low x can be described in terms of a two-component approach in which the nonperturbative part of photon-nucleon interaction is described in terms of a updated variant of the generalized model of vector dominance that includes the radial excitations of mesons and off-diagonal elements of the matrix of meson-nucleon scattering. The perturbative component is described using the color-dipole model.

We consider the mixed inflaton-curvaton scenario in which quantum fluctuations of the curvaton field during inflation lead to a relatively large curvature perturbation spectrum at small scales. We use the model of chaotic inflation with quadratic potential including supergravity corrections leading to a large positive tilt in the power spectrum of the curvaton field. The model is characterized by the strongly inhomogeneous curvaton field in the Universe and large non-Gaussianity of curvature perturbations at small scales. We obtained the constraints on the model parameters considering the process of primordial black hole (PBH) production in radiation era.

We consider several early Universe models that allow for production of large curvature perturbations at small scales. As is well known, such perturbations can lead to formation of primordial black holes (PBHs). We briefly review the today's situation with PBH constraints and then focus on two models in which strongly non-Gaussian curvature perturbations are predicted: the hybrid inflation waterfall model and the curvaton model. We show that PBH constraints on the values of curvature perturbation power spectrum amplitude are strongly dependent on the shape of perturbations and can significantly (by two orders of magnitude) deviate from the usual Gaussian limit P_ζ≲ 10^-2. We give examples of PBH mass spectra calculations for both inflationary models.

We consider the process of primordial black hole (PBH) formation originated from primordial curvature perturbations produced during waterfall transition (with tachyonic instability), at the end of hybrid inflation. It is known that in such inflation models, rather large values of curvature perturbation amplitudes can be reached, which can potentially cause a significant PBH production in the early Universe. The probability distributions of density perturbation amplitudes in this case can be strongly non-Gaussian, which requires a special treatment. We calculated PBH abundances and PBH mass spectra for the model, and analyzed their dependence on model parameters. We obtained the constraints on the parameters of the inflationary potential, using the available limits on $\beta_{PBH}$.

We carried out numerical calculations of a contribution of the waterfall field to the primordial curvature perturbation (on uniform density hypersurfaces) ζ, which is produced during waterfall transition in hybrid inflation scenario. The calculation is performed for a broad interval of values of the model parameters. We show that there is a strong growth of amplitudes of the curvature perturbation spectrum in the limit when the bare mass-squared of the waterfall field becomes comparable with the square of Hubble parameter. We show that in this limit the primordial black hole constraints on the curvature perturbations must be taken into account. It is shown that, in the same limit, peak values of the curvature perturbation spectra are far beyond horizon, and the spectra are strongly non-Gaussian.

We study, by numerical methods, the time evolution of scalar perturbations in radiation era of Randall-Sundrum braneworld cosmology. Our results confirm an existence of the enhancement of perturbation amplitudes (near horizon crossing), discovered recently. We suggest the approximate solution of equations of the perturbation theory in the high-energy regime, which predicts that the enhancement factor is asymptotically constant, as a function of scale. We discuss the application of this result for the problem of primordial black hole production in braneworld cosmology.

We perform a consistent calculation of primordial black hole (PBH) mass spectrum and second-order induced gravitational wave (GW) background produced from primordial scalar perturbations in radiation era of the early Universe. It is shown that the maximal amplitudes of the second-order GW spectrum that can be approached without conflicting with the PBH data do not depend significantly on the shape of primordial perturbation spectrum. The constraints on the GW background obtained in previous works are extended to a wider GW frequency range. We discuss the applicability of the currently available pulsar timing limits for obtaining the constraints on scalar power spectrum and PBH abundance and show that they can be used for strongly constraining the PBH number density in the PBH mass range similar to(0.03 - 10)M-circle dot.

The today's energy density of the induced (second order) gravitational wave background in the frequency region ∼10−3–103 Hz is constrained using the existing limits on primordial black hole production in the early Universe. It is shown, in particular, that at frequencies near ∼40 Hz (which is the region explored by LIGO detector), the value of the induced part of ΩGW cannot exceed (1−3) × 10−7. The spread of values of the bound is caused by the uncertainty in parameters of the gravitational collapse of black holes.

Cosmic gamma-ray bursts with primary-photon energies > 10 GeV are sought in the data from the Andyrchy array obtained in the mode of detection of a single cosmic-ray component during a net observation period of 2005.4 d. The distribution of fluctuations of the detector counting rate agrees with the expected cosmic-ray background, the only exception being an event with a deviation of 7.9 sigma. Constraints on the number density of evaporating primordial black holes in a local region of the Galaxy are obtained for the chromospheric evaporation models.

We calculate differential energy spectra (xF-distributions) of charmed particles produced in proton–nucleus collisions, assuming the existence of intrinsic heavy quark components in the proton wavefunction. For the calculation, the recently proposed factorization scheme is used, based on the colour glass condensate theory and specially suited for predictions of a production of particles with large rapidities. It is argued that the intrinsic charm component can, if it exists, dominate in a sum of two components, intrinsic + extrinsic, of the inclusive spectrum of charmed particles produced in proton–nucleus collisions at high energies, in the region of medium xF, 0.15 < xF < 0.7, and can give noticeable contribution to atmospheric fluxes of prompt muons and neutrinos.