The model of a flat (Euclidean) expansive homogeneous and isotropic relativistic universe in the light of the general relativity,quantum mechanics,and observations

Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial solutions: Einstein special theory of relativity and Newton gravitation theory), quantum mechanics, and observations, too.     

All-sky ultraviolet surveys: the needs and the means

This is a crucial time in the history of astronomy with major all-sky surveying work being carried out in all spectral bands, as well as in astrometry. The results of this activity are advancing all fields of astrophysical research, from the investigation of exo-planetary systems to the study of the chemical evolution of the Universe. Full sky surveys are available from the radio domain to X-ray wavelengths but not in the ultraviolet range (UV). While large UV missions are currently under discussion within the astrophysical community and at the major Space Agencies, the efficient use of resources requires preparatory work that can fill the UV surveying gap. This article summarizes the research and on-going activities in this field.     

Exact solution of anisotropic compact stars via mass function

Studying relativistic compact objects is important in modern astrophysics to understand several astrophysical issues. It is therefore natural to ask for an internal structure and physical properties of specific classes of compact stars from astrophysical observations. We obtain a class of new relativistic solutions with anisotropic distribution of matter for compact stars. More specifically, stellar models, described by an anisotropic fluid, establishing a relation between metric potentials and generating a specific form of mass function, are explicitly constructed within the framework of General Relativity. New solutions can be used to model compact objects, which adequately describe compact strange star candidates like SMC X-1, Her X-1 and 4U 1538-52, with observational data taken from Gangopadhyay et al. (Mon. Not. R. Astron. Soc. 431:3216, 2013). As a possible astrophysical application the obtained solutions could explain the physics of selfgravitating objects, and might be useful for strong-field regimes where data are currently inadequate.     

New UV-source catalogs,UV spectral database,UV variables and science tools from the GALEX surveys

We present a new, expanded and improved catalog of Ultraviolet (UV) sources from the GALEX All-Sky Imaging survey: GUVcat_AIS (Bianchi et al. in Astrophys. J. Suppl. Ser. 230:24, 2017). The catalog includes 83 million unique sources (duplicate measurements and rim artifacts are removed) measured in far-UV and near-UV. With respect to previous versions (Bianchi et al. in Mon. Not. R. Astron. Soc. 411:2770 2011a, Adv. Space Res. 53:900–991, 2014), GUVcat_AIS covers a slightly larger area, 24,790 square degrees, and includes critical corrections and improvements, as well as new tags, in particular to identify sources in the footprint of extended objects, where pipeline source detection may fail and custom-photometry may be necessary. The UV unique-source catalog facilitates studies of density of sources, and matching of the UV samples with databases at other wavelengths.We also present first results from two ongoing projects, addressing respectively UV variability searches on time scales from seconds to years by mining the GALEX photon archive, and the construction of a database of ～120,000 GALEX UV spectra (range ～1300–3000 Å), including quality and calibration assessment and classification of the grism, hence serendipitous, spectral sources.     

Study of some chaotic inflationary models in $$ gravity

In this paper, we discuss an inflationary scenario via scalar field and fluid cosmology for an anisotropic homogeneous universe model in \(f(R)\) gravity. We consider an equation of state which corresponds to a quasi-de Sitter expansion and investigate the effect of the anisotropy parameter for different values of the deviation parameter. We evaluate potential models like linear, quadratic and quartic models which correspond to chaotic inflation. We construct the observational parameters for a power-law model of \(f(R)\) gravity and construct the graphical analysis of tensor–scalar ratio and spectral index which indicates the consistency of these parameters with Planck 2015 data.     

FLRW cosmological models with quark and strange quark matters in $$ gravity

In this paper, we have studied the magnetized quark matter (QM) and strange quark matter (SQM) distributions in the presence of \(f(R,T)\) gravity in the background of Friedmann-Lemaître-Robertson-Walker (FLRW) metric. To get exact solutions of modified field equations we have used \(f(R,T ) = R + 2 f(T)\) model given by Harko et al. with two different parametrization of geometrical parameters i.e. the parametrization of the deceleration parameter \(q \), and the scale factor \(a \) in hybrid expansion form. Also, we have obtained Einstein Static Universe (ESU) solutions for QM and SQM distributions in \(f(R,T)\) gravity and General Relativity (GR). All models in \(f(R,T)\) gravity and GR for FRW and ESU Universes with QM also SQM distributions, we get zero magnetic field. These results agree with the solutions of Akta? and Aygün in \(f(R,T)\) gravity. However, we have also discussed the physical consequences of our obtained models.     

A model of the late universe with viscous Zel’ldovich fluid and decaying vacuum

Many have speculated about the presence of a stiff fluid in very early stage of the universe. Such a stiff fluid was first introduced by Zel’dovich. Recently the late acceleration of the universe was studied by taking bulk viscous stiff fluid as the dominant cosmic component, but the age predicted by such a model is less than the observed value. We consider a flat universe with viscous stiff fluid and decaying vacuum energy as the cosmic components and found that the model predicts a reasonable background evolution of the universe with de Sitter epoch as end phase of expansion. More over, the model also predicts a reasonable value for the age of the present universe. We also performed a dynamical system analysis of the model and found that the end de Sitter phase predicted by the model is stable.     

An interacting new holographic dark energy in the framework of fractal cosmology

In this paper, we study an interacting holographic dark energy model in the framework of fractal cosmology. The features of fractal cosmology could pass ultraviolet divergencies and also make a better understanding of the universe in different dimensions. We discuss a fractal FRW universe filled with the dark energy and cold dark matter interacting with each other. It is observed that the Hubble parameter embraces the recent observational range while the deceleration parameter demonstrates an accelerating universe and a behavior similar to \(\Lambda \mbox{CDM}\). Plotting the equation of state shows that it lies in phantom region for interaction mode. We use \(\mathit{Om}\)-diagnostic tool and it shows a phantom behavior of dark energy which is a condition of avoiding the formation of black holes. Finally we execute the StateFinder diagnostic pair and all the trajectories for interacting and non-interacting state of the model meet the fixed point \(\Lambda \mbox{CDM}\) at the start of the evolution. A behavior similar to Chaplygin gas also can be observed in statefinder plane. We find that new holographic dark energy model (NHDE) in fractal cosmology expressed the consistent behavior with recent observational data and can be considered as a model to avoid the formation of black holes in comparison with the main model of NHDE in the simple FRW universe. It has also been observed that for the interaction term varying with matter density, the model generates asymptotic de-Sitter solution. However, if the interaction term varies with energy density, then the model shows Big-Rip singularity. Using our modified CAMB code, we observed that the interacting model suppresses the CMB spectrum at low multipoles \(l<50\) and enhances the acoustic peaks. Based on the observational data sets used in this paper and using Metropolis-Hastings method of MCMC numerical calculation, it seems that the best value with \(1\sigma \) and \(2\sigma \) confidence interval are \(\Omega _{m0}=0.278^{+0.008~+0.010} _{-0.007~-0.009}\), \(H_{0}=69.9^{+0.95~+1.57}_{-0.95~-1.57}\), \(r_{c}=0.08^{+0.02~+0.027}_{-0.002~-0.0027}\), \(\beta =0.496^{+0.005~+0.009} _{-0.005~-0.009}\), \(c= 0.691^{+0.024~+0.039}_{-0.025~-0.037}\) and \(b^{2}=0.035\) according to which we find that the proposed model in the presence of interaction is compatible with the recent observational data.     

Fuel optimization for low-thrust Earth–Moon transfer via indirect optimal control

The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun–Earth–Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin’s Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem’s state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth–Moon and Sun–Earth is presented leading to a physical interpretation of the different families of trajectories.