Abstract:
We derive a constraint on the cosmic density of string moduli fields in gauge-mediated supersymmetry-breaking theories by requiring that photons emitted from the unstable moduli fields should not exceed the observed X-ray backgrounds. Since mass of the moduli field lies in the range between $O(0.1)$keV and $O(1)$MeV and the decay occurs through a gravitational interaction, the lifetime of the moduli field is much longer than the age of the present universe. The obtained upperbound on their cosmic density becomes more stringent than that from the unclosure condition for the present universe for the mass greater than about 100keV.

Abstract:
We study a double inflation model (a preinflation + a new inflation) in supergravity and discuss the formation of primordial black holes which may be identified with massive compact halo objects (MACHOs) observed in the halo of our galaxy. The preinflation drives an inflaton for the new inflation close to the origin through supergravity effects and the new inflation naturally occurs. If the total e-fold number of the new inflation is smaller than $\sim 60$, both inflations produce cosmologically relevant density fluctuations. If the coherent inflaton oscillation after the preinflation continues until the beginning of the new inflation, density fluctuations on small cosmological scales can be set suitably large to produce black holes MACHOs of masses $\sim 1 M_{\odot}$ in a wide region of parameter space in the double inflation model.

Abstract:
We investigate the electromagnetic cascade initiated by injection of very high energy photons in the early Universe and calculate the cascade spectrum by solving a set of Boltzmann equations numerically. In the calculation we take account of Compton scattering off the background electrons and pair creation off the background nucleons as well as photon-photon processes and inverse Compton scattering. We also apply our cascade spectrum to the big bang nucleosynthesis with photo-dissociation processes due to heavy unstable particles and obtain the constraint on their lifetime and abundance.

Abstract:
Gravitino produced in the inflationary universe are studied. When the gravitino decays into a neutrino and a sneutrino, the emitted high energy neutrinos scatter off the background neutrinos and produce charged leptons (mainly electrons and positrons), which cause the electro-magnetic cascades and produce many soft photons. We obtain the spectra of the high energy neutrinos as well as the spectrum of the high energy photon by integrating a set of Boltzmann equations. Requiring these photons should not alter the abundances of the light elements (D, $^3$He, $^4$He) in the universe, we can set the stringent upperbound on the reheating temperature after the inflation. We find that $T_R \lesssim (10^{10}-10^{12})$GeV for $m_{3/2}\sim (100\GEV - 1\TEV)$, which is more stringent than the constraints in the previous works.

Abstract:
Gravitino production and decay in the inflationary universe are reexanimed. Assuming that gravitino mainly decays into photon and photino, we have calculated the upperbound of the reheating temperature. Compared to previous works, we have essentially improved the following two points; (i) the helicity $\pm\frac{3}{2}$ gravitino production cross sections are calculated by using the full relevant terms in the supergravity lagrangian, and (ii) high energy photon spectrum is obtained by solving the Boltzmann equations numerically. Photo-dissociation of the light elements (D, T, $^3$He, $^4$He) leads to the most stringent upperbound of the reheating temperature, which is given by ($10^{6}$--$10^{9}$)GeV for the gravitino mass 100GeV--1TeV. On the other hand, requiring that the present mass density of photino should be smaller than the critical density, we find that the reheating temperature have to be smaller than ($10^{11}$--$10^{12}$)GeV for the photino mass (10--100)GeV, irrespectively of the gravitino mass. The effect of other decay channel is also considered.

Abstract:
Gravitino production and decay in the inflationary universe are reexamined. Assuming that the gravitino mainly decays into a photon and a photino, we calculate the upperbound on the reheating temperature. Compared to previous works, we have essentially improved the following two points: (i) the helicity $\pm\frac{3}{2}$ gravitino production cross sections are calculated by using the full relevant terms in the supergravity lagrangian, and (ii) the high energy photon spectrum is obtained by solving the Boltzmann equations numerically. Photo-dissociation of the light elements (D, T, $^3$He, $^4$He) leads to the most stringent upperbound on the reheating temperature, which is given by ($10^{6}$--$10^{9}$)GeV for the gravitino mass 100GeV--1TeV. On the other hand, requiring that the present mass density of photino should be smaller than the critical density, we find that the reheating temperature have to be smaller than ($10^{11}$--$10^{12}$)GeV for the photino mass (10--100)GeV, irrespectively of the gravitino mass. The effect of other decay channels is also considered.

Abstract:
Banks and Dine have recently shown that the M theory naturally accommodates the Peccei-Quinn axion. Since the decay constant $F_a$ of the axion is large as $F_a \simeq 10^{15}-10^{16}$GeV, the halo axion is hardly detected in coming axion-search experiments. However, we show that isocurvature fluctuations of the M-theory axion produced at the inflationary epoch are most likely detectable in future satellite experiments on anisotropies of the cosmic microwave background radiation.

Abstract:
In superstring theories, there exist various dilaton and modulus fields which masses are expected to be of the order of the gravitino mass $m_{3/2}$. These fields lead to serious cosmological difficulties, so called ``cosmological moduli problem'', because a large number of moduli particles are produced as the coherent oscillations after the primordial inflation. We make a comprehensive study whether the thermal inflation can solve the cosmological moduli problem in the whole modulus mass region $m_\phi \sim 10 eV - 10^4 GeV$ predicted by both hidden sector supersymmetry (SUSY) breaking and gauge-mediated SUSY breaking models. In particular, we take into account the primordial inflation model whose reheating temperature is so low that its reheating process finishes after the thermal inflation ends. We find that the above mass region $m_\phi (\simeq m_{3/2}) \sim 10 eV - 10^4 GeV$ survives from various cosmological constraints in the presence of the thermal inflation.

Abstract:
We review the studies on the emergent phases of superconductvity and magnetism in the $f$-electron derived heavy-fermion (HF) systems by means of the nuclear-quadrupole-resonance (NQR) under pressure. These studies have unraveled a rich variety of the phenomena in the ground state of HF systems. In this article, we highlight the novel phase diagrams of magnetism and unconventional superconductivity (SC) in CeCu$_2$Si$_2$, HF antiferromagnets CeRhIn$_5$, and CeIn$_3$. A new light is shed on the difference and common features on the interplay between magnetism and SC on the magnetic criticality.

Abstract:
We study the Polonyi problem in the framework of no-scale type supergravity models. We show that the lightest superparticle (LSP) produced in the decay of the Polonyi field may contribute too much to the present density of the universe. By requiring that LSP should not overclose the universe, we obtain a stringent constraint on the reheating temperature after the decay of the Polonyi field. We calculate the LSP density with physical parameters obtained by solving renormalization group equations in the minimal supersymmetric SU(5) model and find that the reheating temperature should be greater than about 100MeV which corresponds to $O$(100)TeV of the Polonyi mass.