arXiv subjects

Naouel Boulkaboul

Publications and source records attributed to Naouel Boulkaboul.

3 recordsLinked to original sources

arXiv2022

$3n+3^k$: New Perspective on Collatz Conjecture

Collatz conjecture is generalized to $3n+3^k$ ($k\in N$). Operating as usual, every sequence seems to reach $3^k$ and end up in the loop $3^k, 4.3^k, 2.3^k,3^k$. The usual $3n+1$ conjecture is recovered for $k=0$. For $k>0$, we noticed the existence of a sequence of period 3, namely, $3^{k-1}, 2.3^k, 3^k$, alongside the cycle $4.3^k, 2.3^k,3^k$ encountered in the $3n+1 (k=0)$ sequence. A term formula of the $3n+3^k$ conjecture has been derived, and hence the total stopping time.

math.GM↗

arXiv2022

Interacting Tsallis holographic dark energy in $q$-modified DGP braneworld

We explore the cosmological aspects of interacting Tsallis holographic dark energy (THDE) in a $q$-modified DGP braneworld setup emerging from non-Gaussian statistical mechanics.To this end, three classes of superstatistics, that is, log-normal, inverse $χ^2$ and $χ^2$ superstatistics were incorporated into the model. We examined the implication of the three superstatistics on different cosmological parameters, namely, the dimensionless energy density and the equation-of-state (EoS) of THDE, along with the deceleration parameter and the squared speed of sound. As a result, we noted that the cosmological parameters stemming from the $χ^2$ superstatistics, with a parameter $q > 1$, represent the highest deviation from those ascribed to the standard DGP model. While the system parameters show appropriate behavior in all three cases, the model cannot achieve stability throughout the history of the Universe. It is probably the outcome of setting the Hubble horizon as the infrared cutoff. Furthermore, the behavior of EoS was found to be governed by the value of the THDE parameter $δ$. That is to say, for $δ > 2$ THDE exhibits a phantom-like behavior while for $δ < 2$ it displays a quintessence behavior. Constrained by the dominant energy condition, an upper bound on $δ$ $(δ < 2)$ has been imposed.

gr-qc↗

arXiv2020

Can Gibbons-Hawking Radiation and Inflation Arise Due to Spacetime Quanta?

In this study, we provide an alternatively reformulated interpretation of Gibbons-Hawking radiation as well as inflation. By using a spacetime quantization procedure, proposed recently by L.C. Céleri et al., in anti-de Sitter space we show that Gibbons-Hawking radiation is an intrinsic property of the concerned space, that arises due to the existence of a scalar field whose quanta "carry" a length $l$ (i.e. the radius of the hyperboloid curvature). Furthermore, within the context of Tsallis q-framework, we propose an inflationary model that depends on the non-extensive parameter $q$. The main source of such an inflation is the same scalar field mentioned before. Being constrained by the observational data, the q-parameter along with the rest of the model's parameters has been used to estimate the time at which inflation ends as well as the reheating temperature. The latter is found to be related to Gibbons-Hawking temperature. Thus, the present model offers an alternative perspective regarding the nature of the cosmic background radiation (CMB).

gr-qc↗