We study the structure of compact objects that contain non-self annihilating, self-interacting dark matter admixed with ordinary matter made of neutron star and white dwarf materials. We extend the previous work Phys. Rev. D 92 123002 (2015) on these dark compact objects by analyzing the effect of weak and strongly interacting dark matter with particle masses in the range of 1-500 GeV, so as to set some constraints in the strength of the interaction and the mass of the dark matter particle. We find that the total mass of the compact objects increases with decreasing dark matter particle mass. In the strong interacting case and for dark matter particle masses in the range 1-10 GeV, the total mass of the compact objects largely exceeds the 2M constraint for neutron star masses and the nominal 1M for white dwarfs, while for larger dark matter particle masses or in the weakly interacting case the compact objects show masses in agreement or smaller than these constraints, thus hinting at the exclusion of strongly self-interacting dark matter of masses 1-10 GeV in the interior of these compact objects. Moreover, we observe that the smaller the dark matter particle mass, the larger the quantity of dark matter captured is, putting constraints on the dark matter mass trapped in the compact objects so as to fullfill 2M observations. Finally, the inhomogeneity of distribution of dark matter in the Galaxy implies a mass dependence of compact objects from the environment which can be used to put constraints on the characteristics of the Galaxy halo DM profile and on particle mass. In view of the these results, we discuss the formation of the dark compact objects in an homogeneous and non-homogeneous dark matter environment. In the ΛCDM model, a parameterization of the big-bang cosmology with six parameters, the DE is associated with the cosmological constant Λ, and the material components of the Universe are the ones indicated previously. The quoted ΛCDM paradigm, describes correctly many of the observations[2, 6-9], but has some drawbacks. On large scale CMB shows some anomalies, such as that the Planck 2015 data are in tension with the CFHTLenS weak lensing [10], and σ 8 [11]. There is also another tension with the value of the Hubble parameter measured by SNIa 1 . Another big issue of the paradigm is the nature of DM. A "zoo" of candidates have been proposed, with masses in the range of 10 −33 GeV (Fuzzy DM) to 10 15 GeV (Wimpzillas). In that large "zoo", 1 The ΛCDM paradigm has some other drawbacks, as the cosmological constant problem [12,13], the unknown nature of DE [14-16] and the so called "small scale problems" [17].

We study the near-threshold η production mechanism in nucleon-nucleon and πN collisions under the assumption that subthreshold resonance N * (1535) is predominant. In an effective Lagrangian approach that gives a reasonable description to the pN → pNη and π − p → nη reactions, we find that the excitation of N * (1535) resonance from the t-channel π exchange makes the dominate contribution to the pN → pNη process, and a value of 6.5 for the ratio of σ (pn → pnη ) to σ (pp → ppη ) is predicted. A strongcoupling strength of N * (1535) to η N (g 2 η NN * /4π = 1.1) is extracted from a combined analysis to pp → ppη and πN → Nη , and the possible implication to the intrinsic component of N * (1535) is explored.

In terms of the quantitative causal principle, this paper obtains a general variational principle, gives unified expressions of the general, Hamilton, Voss, Hölder, Maupertuis-Lagrange variational principles of integral style, the invariant quantities of the general, Voss, Hölder, Maupertuis-Lagrange variational principles are given, finally the Noether conservation charges of the general, Voss, Hölder, Maupertuis-Lagrange variational principles are deduced, and the intrinsic relations among the invariant quantities and the Noether conservation charges of the all integral variational principles are achieved.