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It is found that the suppression due to two-body LambdaN-SigmaN coupling solves the overbinding problem in (5)(Lambda)He but it, in turn, causes a severe underbinding in the four-body systems. The shortage of this binding is overcome by introducing explicitly the Lambda-Sigma coupling which is equivalent to the LambdaNN three-body force. This three-body force becomes strong in the 0(+) states of (4)(Lambda)H and (4)(Lambda)He according to the coherently added enhancement. The 0(+)-1(+) splitting in (4)(Lambda)H and (4)(Lambda)He is found partly due to the LambdaN spin-spin interaction and partly due to the Lambda-Sigma coupling in the recent Nijmegen soft-core potential.

We investigate neutron stars in scalar-tensor theories. We examine their secular stability against spherically symmetric perturbations by use of a turning point method. For some choices of the coupling function contained in the theories, the number of the stable equilibrium solutions changes and the realized equilibrium solution may change discontinuously as the asymptotic value of the scalar field or total baryon number is changed continuously. The behavior of the stable equilibrium solutions is explained by fold and cusp catastrophes. Whether or not the cusp catastrophe appears depends on the choice of the coupling function. These types of catastrophes are structurally stable. Recently discovered spontaneous scalarization, which is a nonperturbative strong-field phenomenon due to the presence of the gravitational scalar field, is well described in terms of the cusp catastrophe.

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The production rate of primordial black holes is often calculated by considering a nearly Gaussian distribution of cosmological perturbations, and assuming that black holes will form in regions where the amplitude of such perturbations exceeds a certain threshold. A threshold ζ th for the curvature perturbation is somewhat inappropriate for this purpose, because it depends significantly on environmental effects, not essential to the local dynamics. By contrast, a threshold δ th for the density perturbation at horizon crossing seems to provide a more robust criterion. On the other hand, the density perturbation is known to be bounded above by a maximum limit δ max at the horizon entry, and given that δ th is comparable to δ max , the density perturbation will be far from Gaussian near or above the threshold. In this paper, we provide a new plausible estimate for the primordial black hole abundance based on peak theory. In our approach, we assume that the curvature perturbation is given as a random Gaussian field with the power spectrum characterized by a single scale, while an optimized criterion for PBH formation is imposed, based on the locally averaged density perturbation around the nearly spherically symmetric high peaks. Both variables are related by the full nonlinear expression derived in the long-wavelength approximation of general relativity. We do not introduce a window function which is usually introduced to obtain the scale dependence of the spectrum. The scale of the inhomogeneity is introduced as a random variable in the peak theory, and the scale dependent PBH fraction is automatically induced. We find that the mass spectrum is shifted to larger mass scales by one order of magnitude or so, compared to a conventional calculation. The abundance of PBHs becomes significantly larger than the conventional one, by many orders of magnitude, mainly due to the optimized criterion for PBH formation and the removal of the suppression associated with a window function.