Narrow Results

In this paper, we explore the influences of the higher-order Gauss–Bonnet (GB) correction terms on the growth of perturbations at the early stage of a $(n+1)$-dimensional Friedmann–Robertson–Walker (FRW) universe. Considering a cosmological constant in the FRW background, we study the linear perturbations by adopting the spherically symmetric collapse (SC) formalism. In light of the modifications that appear in the field equations, we disclose the role of the GB coupling constant $\alpha$, as well as the extra dimensions $n>3$ on the growth of perturbations. It, in essence, is done by defining a dimensionless parameter $\tilde{\beta }=(n-2)(n-3)\alpha H_0^2$ in which $H_0$ is the Hubble constant. We find that the matter density contrast starts growing at the early stages of the universe and, as the universe expands, it grows faster compared to the standard cosmology. Besides, in the framework of GB gravity, the growth of matter perturbations in higher dimensions is faster than its standard counterpart. Further, in the presence of $\alpha$, the growth of perturbations increases as it increases. This is an expected result, since the higher-order GB correction terms increase the strength of the gravity and thus support the growth of perturbations. For the existing cosmological model, we also investigate the behavior of quantities such as density abundance, deceleration and the jerk parameter. Finally, we study the imprint of the GB parameter and the higher dimensions in the evolution of the mass function of the dark matter halos.

We investigate Primordial Black Hole (PBH) formation by which we mean black holes produced in the early Universe during radiation domination. After discussing the range of PBH mass permitted in the original mechanism of Carr and Hawking, hybrid inflation with parametric resonance is presented as an existence theorem for PBHs of arbitrary mass. As proposed in arXiv:1510.00400, PBHs with many solar masses can provide a solution to the dark matter problem in galaxies. PBHs can also explain dark matter observed in clusters and suggest a primordial origin for Supermassive Black Holes (SMBHs) in galactic cores.

A generalization of the Press–Schechter (PS) formalism yielding the mass function of bound structures in the Universe is given. The extended formula is based on a power law distribution which encompasses the Gaussian PS formula as a special case. The new method keeps the original analytical simplicity of the PS approach and also solves naturally its main difficult (the missing factor 2) for a given value of the free parameter.

The Press–Schechter (PS) formalism yields the number density of bound objects formed during the evolution of the Universe, which should be compared to the great clusters of galaxies now observed. This basic approach has an intrinsic problem of normalization (the so-called missing factor 2). We argue here that such a problem is related to specific choices of the statistical distribution describing the initial density fluctuations. The fudge factor 2 occurs even in the context of the q-nonextensive statistics which is the simplest one-parametric extension of the Gaussian distribution. In general, other distributions require different corrections, such as the log-normal distribution. However, by assuming that the perturbations can be described by the Burr distribution, we prove that the PS approach in this case is not plagued with the normalization problem.

Several independent cosmological tests have shown evidences that the energy density of the universe is dominated by a dark energy component, which causes the present accelerated expansion. The large scale structure formation can be used to probe dark energy models, and the mass function of dark matter haloes is one of the best statistical tools to perform this study. We present here a statistical analysis of mass functions of galaxies under a homogeneous dark energy model, proposed in the work of Percival (2005), using an observational flux-limited X-ray cluster survey, and CMB data from WMAP. We compare, in our analysis, the standard Press–Schechter (PS) approach (where a Gaussian distribution is used to describe the primordial density fluctuation field of the mass function), and the PL (power–law) mass function (where we apply a non-extensive q-statistical distribution to the primordial density field). We conclude that the PS mass function cannot explain at the same time the X-ray and the CMB data (even at 99% confidence level), and the PS best fit dark energy equation of state parameter is ω = -0.58, which is distant from the cosmological constant case. The PL mass function provides better fits to the HIFLUGCS X-ray galaxy data and the CMB data; we also note that the ω parameter is very sensible to modifications in the PL free parameter, q, suggesting that the PL mass function could be a powerful tool to constrain dark energy models.

Clusters of galaxies are the most impressive gravitationally-bound systems in the universe, and their abundance (the cluster mass function) is an important statistic to probe the matter density parameter (Ω_m) and the amplitude of density fluctuations (σ₈). The cluster mass function is usually described in terms of the Press–Schecther (PS) formalism where the primordial density fluctuations are assumed to be a Gaussian random field. In previous works we have proposed a non-Gaussian analytical extension of the PS approach with basis on the q-power law distribution (PL) of the nonextensive kinetic theory. In this paper, by applying the PL distribution to fit the observational mass function data from X-ray highest flux-limited sample (HIFLUGCS), we find a strong degeneracy among the cosmic parameters, σ₈, Ω_m and the q parameter from the PL distribution. A joint analysis involving recent observations from baryon acoustic oscillation (BAO) peak and Cosmic Microwave Background (CMB) shift parameter is carried out in order to break these degeneracy and better constrain the physically relevant parameters. The present results suggest that the next generation of cluster surveys will be able to probe the quantities of cosmological interest (σ₈, Ω_m) and the underlying cluster physics quantified by the q-parameter.

Dark energy affects the abundance and evolution of clusters owing to their dependence on the geometry of the Universe and the power spectrum. Usually, there exits the degeneracy between σ₈ and the matter energy density contrast . We avoid this by using the explicit dark energy dependent rms linear mass fluctuation σ₈ which is consistent with the CMB normalization for general constant dark energy equation of state, ω_Q. When we use the correct value of the critical density threshold δ_c = 1.58 into the cluster number density n calculation in the Press–Schechter (PS) formalism, PS formalism predicts the cluster number consistent with both simulation and observed data at the high mass region. The improved coefficients of Sheth–Tormen (ST) formalism by using the correct δ_c is also obtained. We found that changing ω_Q by Δω_Q = -0.1 from ω_Q = -1.0 causes the changing of the comoving numbers of high mass clusters of M = 10¹⁶h^-1M_⊙ by about 20 and 40% at z = 0 and 1, respectively.

There has been immense interest in uncertainty measurement because most real-world problems are accompanied by uncertain events. Therefore, Deng entropy has been proposed to measure the uncertainty in the probability theory and evidence theory. In this paper, we show that the uncertainty of the basic probability assignment (BPA) separated through the maximum Deng entropy separation rule (MDESR) is larger than the maximum Deng entropy of the original BPA. In addition, when the cardinality of the frame of discernment increases, the maximum information volume becomes larger and converges slower. The information volume fractal dimension is then proposed to describe the fractal property of uncertainty about the separated BPA distribution, which indicates the inherent physical meanings of Deng entropy from the perspective of statistics. This work can inspire further research on the fractal property of Deng entropy. Some experiments are applied to show the applicability of our proposed information volume fractal dimension.

Fractals play an important role in nonlinear science. The most important parameter when modeling a fractal is the fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, calculating the fractal dimension given a mass function, which is the generalization of probability, is still an open problem of immense interest. The main contribution of this work is to propose an information fractal dimension of mass function. Numerical examples are given to show the effectiveness of our proposed dimension. We discover an important property in that the dimension of mass function with the maximum Deng entropy is $\frac{ln3}{ln2}\approx 1.585$, which is the well-known fractal dimension of Sierpiski triangle. The application in complexity analysis of time series illustrates the effectiveness of our method.

The application of multi-sensor fusion, which aims at recogizing a state among a set of hypotheses for object classification, is of major interest as regards the performance improvement brought by the sensor complementarily. Nevertheless this needs to take into account the more accurate as possible information and take advantage of the statistical learning of the previous measurements acquired by sensors. The classical probabilistic fusion methods lack of performance when the previous learning is not representative of the real measurements provided by sensors. The theory of evidence is then introduced to face this disadvantage by integrating a further information which is the context of the sensor acquisitions. In this paper, we propose a formalism of modeling of the sensor reliability to the context that leads to two methods of integration when all the hypotheses, associated to the objects of the scene acquired by sensors, are previously learnt: the first one amounts to integrate this further information in the fusion rule as degrees of trust and the second models the sensor reliability directly as mass functions. These two methods are based on the theory of fuzzy events. Afterwards, we are interested in the evolvement of these two methods in the case where the previous learning is unavailable for a hypothesis associated to an object of the scene and compare these two methods in order to deduce a global method of contextual information integration in the fusion process.

With the development of uncertainty reasoning and information fusion, there have emerged several theories including fuzzy set theory, Dempster-Shafer evidence theory, probability theory and rough set theory, etc., for representing and dealing with the uncertain information. When the fusion of the uncertain information originated from different sources is needed, how to construct a general framework for different theories of uncertainty or how to establish the connection between different theoretical frameworks has become a crucial problem. Particularly, to combine two kinds of information represented respectively by the BPA and the FMF, this paper proposes two transformations of an FMF into a BPA by solving a constrained maximization or minimization optimization problem. The objective function is the uncertainty degree of the body of evidence (BOE) and the corresponding constraints are established based on the given FMF. In fact the transformation of an FMF into a BPA is the transformation of fuzzy sets into random sets, which is currently accepted as a unified framework for several theories of uncertainty. Our proposed approaches have no predefinition of focal elements and they can be used as the general transformations of fuzzy sets into random sets. Some examples and analyses are provided to illustrate and justify the rationality and effectiveness of the proposed approaches.

In this paper, a class of anisotropic compact stars is analyzed in Heintzmann geometry. The Einstein field equations (EFEs) have been solved to obtain the stellar model in presence of pressure anisotropy. We have considered the $g_{tt}$ metric component as proposed by Heintzmann, and by solving the EFEs, the $g_{rr}$ metric component is evaluated in the presence of pressure anisotropy. It is noted that for an isotropic star ($\alpha =0$), the maximum mass lies within the range 1.87–3.04$M_{\odot }$ for radii ranging between 8–13 km. For anisotropic compact stars, the maximum mass increases with $\alpha$ and lies within the range 1.99–3.23 $M_{\odot }$ for anisotropy parameter $\alpha =0.5$. The physical viability of the model is examined by applying our model to study the properties of a few known compact objects. All the stability conditions are fulfilled in the proposed model. It is also interesting to note that the maximum mass calculated from our model from geometrical consideration and solving the TOV equation is approximately equal, and the radii predicted from the present model comply with the estimated radius from observations of recently observed pulsars and lighter compact objects of GW events such as GW 190814 and GW 170817.

In this paper we consider the problem of how to derive mass functions systematically from data samples, and the ensuing problem of how to combine different mass functions thus derived. We show that a mass function can be efficiently, systematically derived from multivariate data space. We also show that combining mass functions thus derived appears trial, but this approach opens door for a potentially completely new rule for combining mass functions.

We study the diffuse NIR background light associated with the cluster of high velocity stars at the Galactic Center, known as the S-stars. We use the luminosity function of the cluster members, the distribution of the diffuse background light and the stellar number density counts to investigate the amount of stellar and dark mass associated with the cluster in the immediate vicinity of the supermassive black hole. We show that both the total mass, and the number, of objects within an S-star's orbit can be constrained using observed changes in the star's orbital elements.