Jeans analysis with κ-deformed Kaniadakis distribution in f (R) gravity

Kaniadakis statistics is a widespread paradigm to describe complex systems in the relativistic realm. Recently, gravitational and cosmological scenarios based on Kaniadakis (κ-deformed) entropy have been considered, leading to generalized models that predict a richer phenomenology comparing to their standard Maxwell–Boltzmann counterparts. The purpose of the present effort is to explore recent advances and future challenges of Gravity and Cosmology in Kaniadakis statistics. More specifically, the first part of the work contains a review of κ-entropy implications on Holographic Dark Energy, Entropic Gravity, Black hole thermodynamics and Loop Quantum Gravity, among others. In the second part, we focus on the study of Big Bang Nucleosynthesis in Kaniadakis Cosmology. By demanding consistency between theoretical predictions of our model and observational measurements of freeze-out temperature fluctuations and primordial abundances of 4He and D, we constrain the free κ-parameter, discussing to what extent the Kaniadakis framework can provide a successful description of the observed Universe.

“…In [ 27 ], this criterion has been revisited in the context of Kaniadakis statistics, obtaining a

-deformed critical wavelength larger than the standard expression. Similar studies have also been developed in Eddington-inspired Born–Infeld [ 28 ] and

Section: Introductionmentioning

confidence: 59%

“…In [ 27 ], this criterion has been revisited in the context of Kaniadakis statistics, obtaining a

-deformed critical wavelength larger than the standard expression. Similar studies have also been developed in Eddington-inspired Born–Infeld [ 28 ] and

[ 29 ] gravity, and the dark-baryonic matter model [ 30 ], among others.…”

Section: Introductionmentioning

confidence: 59%

“…For instance, in [ 28 ], Jeans instability has been revisited in the framework of Eddington-inspired Born–Infeld gravity, showing that the

-deformed distribution may have non-negligible effects on the Jeans modes of the collisionless Eddington-inspired Born–Infeld gravitational systems. In a similar fashion, the influence of the

-generalized Jeans criterion has been examined in [ 29 ] in

gravity for both high and low frequency density perturbations. As a result, it has been proven that the range of the unstable modes and the growth rates decrease with increasing values of

.…”

Section: Gravity and Cosmology In Kaniadakis Statistical Theory: Rece...mentioning

confidence: 99%

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Gravity and Cosmology in Kaniadakis Statistics: Current Status and Future Challenges

Luciano

2022

“…However, this kind of approach is not directly applicable to nuclear reactor physics, given the impossibility of observing and measuring the distribution of relative velocities between neutrons and nuclei in a nuclear reactor. Therefore, one of the possible ways to validate the use of

-statistics is through numerical simulations, similar to in other scientific topics, e.g., relativistic plasmas under the effect of wave-particle interactions [ 3 ], non-extensive random matrix theories [ 17 ] and Jeans instability of self-gravitating systems [ 18 ].…”

Section: Introductionmentioning

confidence: 99%

Doppler Broadening of Neutron Cross-Sections Using Kaniadakis Entropy

Abreu

Maciel

Martinez

et al. 2022

In the last seven years, Kaniadakis statistics, or κ-statistics, have been applied in reactor physics to obtain generalized nuclear data, which can encompass, for instance, situations that lie outside thermal equilibrium. In this sense, numerical and analytical solutions were developed for the Doppler broadening function using the κ-statistics. However, the accuracy and robustness of the developed solutions contemplating the κ distribution can only be appropriately verified if applied inside an official nuclear data processing code to calculate neutron cross-sections. Hence, the present work inserts an analytical solution for the deformed Doppler broadening cross-section inside the nuclear data processing code FRENDY, developed by the Japan Atomic Energy Agency. To do that, we applied a new computational method called the Faddeeva package, developed by MIT, to calculate error functions present in the analytical function. With this deformed solution inserted in the code, we were able to calculate, for the first time, deformed radiative capture cross-section data for four different nuclides. The usage of the Faddeeva package brought more accurate results when compared to other standard packages, reducing the percentage errors in the tail zone in relation to the numerical solution. The deformed cross-section data agreed with the expected behavior compared to the Maxwell–Boltzmann.

“…The

-deformed distribution can be represented as a more universal form of the distribution functions mentioned in the above work. Consequently, many studies have been revisited under the

-deformed distribution, such as longitudinal plasma modes [ 52 ] and Jeans gravitational instability [ 53 , 54 , 55 ]. The

-deformed distribution as a generalized statistic may be able to characterize plasma waves in a fusion device.…”

Section: Introductionmentioning

confidence: 99%

The Longitudinal Plasma Modes of κ-Deformed Kaniadakis Distributed Plasmas Carrying Orbital Angular Momentum

Tan

Yang

Chen

et al. 2022

Based on plasma kinetic theory, the dispersion and Landau damping of Langmuir and ion-acoustic waves carrying finite orbital angular momentum (OAM) were investigated in the κ-deformed Kaniadakis distributed plasma system. The results showed that the peculiarities of the investigated subjects relied on the deformation parameter κ and OAM parameter η. For both Langmuir and ion-acoustic waves, dispersion was enhanced with increased κ, while the Landau damping was suppressed. Conversely, both the dispersion and Landau damping were depressed by OAM. Moreover, the results coincided with the straight propagating plane waves in a Maxwellian plasma system when κ=0 and η→∞. It was expected that the present results would give more insight into the trapping and transportation of plasma particles and energy.