We study the origin of non-thermal emissions from the Galactic black hole X-ray binary Cygnus X-1 which is a confirmed high mass microquasar. By analogy with those methods used in studies of active galactic nuclei, we propose a two-dimensional, time-dependent radiation model from the microquasar Cygnus X-1. In this model, the evolution equation for relativistic electrons in a conical jet are numerically solved by including escape, adiabatic and various radiative losses. The radiative processes involved are synchrotron emission, its self-Compton scattering, and inverse Compton scatterings of an accretion disk and its surrounding stellar companion. This model also includes an electromagnetic cascade process of an anisotropic γ-γ interaction. We study the spectral properties of electron evolution and its emission spectral characteristic at different heights of the emission region located in the jet. We find that radio data from Cygnus X-1 are reproduced by the synchrotron emission, the Fermi LAT measurements by the synchrotron emission and Comptonization of photons of the stellar companion, the TeV band emission fluxes by the Comptonization of the stellar photons. Our results show that: (1) Radio emission region extends from the binary system scales to the termination of the jet. (2) The GeV band emissions should originate from the distance close to the binary system scales. (3) The TeV band emissions could be inside the binary system, and these emissions could be probed by the upcoming CTA telescope. (4) The MeV tail emissions, which produces a strongly linearly polarized signal, are emitted inside the binary system. The location of the emissions is very close to the inner region of the jet.

We perform observational tests on the f(T) gravity with the BAO data (including the BOSS DR 12 galaxy sample, the DR12 Lyα-Forests measurement, the new eBOSS DR14 quasar sample, the 6dFGS, and the SDSS), the CMB distance priors from the Planck 2015, the SNIa data from the joint light-curve analysis, the latest H(z) data, and the local value of the Hubble constant. Six different f(T) models are investigated. Furthermore, the ΛCDM is also considered. All models are compared by using the Akaike information criteria (AIC) and the Bayesian information criteria (BIC). Our results show that the ΛCDM remains to be the most favored model by current observations. However, there are also the Hubble constant tension between the Planck measurements and the local Universe observations and the tension between the CMB data and the H(z) data in the ΛCDM. For f(T) models considered in this paper, half, which can reduce to the ΛCDM, have values of smaller than that of the ΛCDM and can relieve the tensions existing in the ΛCDM. However, they are punished slightly by the BIC due to one extra parameter. Two of six f(T) models, in which the crossing of the phantom divide line can be realized for the equation of state of the effective dark energy and this crossing is shown in this paper to be favored by current observations, are punished by the information criteria. In addition, we find that the logarithmic f(T) model is excluded by cosmological observations.

Based on the holographic principle and the Barrow entropy, Barrow holographic dark energy had been proposed. In order to analyze the stability and the evolution of Barrow holographic dark energy, we, in this paper, apply the dynamical analysis and statefinder methods to Barrow holographic dark energy with different IR cutoff and interacting terms. In the case of using Hubble horizon as IR cutoff with the interacting term $$Q=\frac{\lambda }{H}\rho _{m}\rho _{D}$$ Q = λ H ρ m ρ D , we find this model is stable and can be used to describe the whole evolution of the universe when the energy transfers from the pressureless matter to the Barrow holographic dark energy. When the dynamical analysis method is applied to this stable model, an attractor corresponding to an accelerated expansion epoch exists and this attractor can behave as the cosmological constant. Furthermore, the coincidence problem can be solved in this case. Then, after using the statefinder analysis method to this model, we find this model can be discriminated from the standard $$\Lambda $$ Λ CDM model. Finally, we have discussed the turning point of Hubble diagram in Barrow holographic dark energy and find the turning point does not exist in this model.

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We give negative answers to Lin-Ni's conjecture for any four and six dimensional domains. No condition on the symmetry, geometry and topology of the domain is needed.