The vertical sea-level muon spectrum at energies above 1 GeV and the muon intensities at depths up to 18 km w.e. in different rocks and in water are calculated. The results are particularly collated with a great body of the ground-level, underground, and underwater muon data. In the hadron-cascade calculations, we take into account the logarithmic growth with energy of inelastic cross sections and pion, kaon, and nucleon generation in pion-nucleus collisions. For evaluating the prompt muon contribution to the muon flux, we apply the two phenomenological approaches to the charm production problem: the recombination quark-parton model and the quark-gluon string model. We give simple fitting formulas describing our numerical results. To solve the muon transport equation at large depths of a homogeneous medium, we use a semianalytical method, which allows the inclusion of an arbitrary (decreasing) muon spectrum at the medium boundary and real energy dependence of muon energy losses. Our analysis shows that at the depths up to 6-7 km w.e., essentially all underground data on the muon flux correlate with each other and with the predicted one for conventional (π, K)-muons, to within 10 %. However, the high-energy sea-level muon data as well as the data at high depths are contradictory and cannot be quantitatively described by a single nuclear-cascade model.
We calculate the frequency dependence of gravitational wave background
arising at second order of cosmological perturbation theory due to mixing of
tensor and scalar modes. The calculation of the induced gravitational
background is performed for two special cases: for the power spectrum of scalar
perturbations which has a peak at some scale and for the scalar spectrum
predicted by the inflationary model with the running mass potential. We show
that the amplitudes of the induced gravitational background, in the frequency
region $\sim 10^{-3} - 10^3 $Hz, are effectively constrained by results of
studies of primordial black hole production in early universe. We argue that
though today's LIGO bound on ${\cal P}_{\cal R}(k)$ is weaker than the PBH one,
Advanced LIGO will be able to set a stronger bound, and in future the
ground-based interferometers of LIGO type will be suitable for obtaining
constraints on PBH number density in the mass range $\sim 10^{11} - 10^{15}$ g.Comment: v2: 14 pages, 7 figures; revised version of the manuscript, accepted
for publication in Phys. Rev.
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