Higher-order generalized uncertainty principle corrections to the Jeans mass

Abstract

The Jeans instability is regarded as an important tool for analyzing the dynamics of a self-gravitating system. However, this theory is challenging since astronomical observation data show some Bok globules, whose masses are less than the Jeans mass and still have stars or at least undergo the star formation process. To explain this problem, we investigate the effects of the higher-order generalized uncertainty principle on the Jeans mass of the collapsing molecular cloud. The results in this paper show that the higher order generalized uncertainty principle has a very significant effect on the canonical energy and gravitational potential of idea gas, and finally leads to a modified Jeans mass lower than the original case, which is conducive to the generation of stars in small mass Bok globules. Furthermore, we estimate the new generalized uncertainty principle parameter $$\gamma _0$$ γ 0 by applying various data of Bok globules, and find that the range of magnitude of $$\gamma _0$$ γ 0 is $${10^{11}} {-} {10^{12}}$$ 10 11 - 10 12 .

The effect of different generalized uncertainty principles on Jeans mass modification

“…Due to the efforts of the researchers, the theoretical value of nebula collapse mass (Jeans mass) was put forward in the literature [9]. However, [9,10] show that the modified Jeans mass based on the generalized uncertainty principle (GUP) is smaller than the original condition, which is consistent with the conclusion that the observed value is smaller than the theoretical value.…”

“…In addition, people have done more in-depth research and proposed different expressions of the GUP model based on HUP. At present, studies have shown that [10,20,21], combining the GUP with thermodynamics, the modification of Jeans mass is achieved, and the results show that GUP can reduce Jeans mass. For example, the literature [9,10] explores the Jeans mass using the generalized and extended uncertainty principles and the higher-order GUP, respectively, and the Friedmann equation derived from Gauss-born gravity was used to modify the area law of entropy by GUP to realize the pair Jeans mass amendment in [10].…”

“…At present, studies have shown that [10,20,21], combining the GUP with thermodynamics, the modification of Jeans mass is achieved, and the results show that GUP can reduce Jeans mass. For example, the literature [9,10] explores the Jeans mass using the generalized and extended uncertainty principles and the higher-order GUP, respectively, and the Friedmann equation derived from Gauss-born gravity was used to modify the area law of entropy by GUP to realize the pair Jeans mass amendment in [10]. Most previous works modified the Jeans mass through a single different GUP form, and the calculated value of Jeans mass theory after modification was smaller than the original value.…”

Higher-order generalized uncertainty principle applied to gravitational baryogenesis

“…This indicates the bound of GUP parameter is depended on the its model, and the high-order terms O (β 0 ) have an inportant impact on the effect of QG. Recently, many higher-order GUP [39][40][41][42][43] and extended uncertainty principle models [65,66] have been proposed. By combining them with baryon asymmetry could help us have a deeper understanding of the Universe and QG.…”

“…This heuristic work of Pedram is considered as an important step towards establishing a physically reasonable theory of QG. Therefore, many studies have converged on the construction and application of high-order GUP [39][40][41][42]. Recently, according to the commutator [x, p] = i 1 − 2βp 2 , Petruzziello [43] constructed a new higher-order GUP, viz.…”