Higher-order Generalized Uncertainty Principle Research Articles

Higher-order generalized uncertainty principle applied to gravitational baryogenesis

The gravitational baryogenesis plays an important role in the study of baryon asymmetry. However, the original mechanism of gravitational baryogenesis in the radiation-dominated era leads to the asymmetry factor η equal to zero, which indicates this mechanism may not generate a sufficient baryon asymmetry in the early Universe. In this paper, we investigate the gravitational baryogenesis for the generation of baryon asymmetry in the early Universe by using a new higher-order generalized uncertainty principle (GUP). It is demonstrated that the entropy and the Friedman equation of the Universe deviate from the original cases due to the effect of the higher-order GUP. Those modifications break the thermal equilibrium of the Universe, and in turn produce a non-zero asymmetry factor η. In particular, our results satisfy all of Sakharov's conditions, which indicates that the scheme of explaining baryon asymmetry in the framework of higher-order GUP is feasible. In addition,combining our theoretical results with the observational data, we constraint the GUP parameter β 0, whose bound is between 8.4 × 1010 ∼ 1.1 × 1013.

Higher-order GUP black hole based on COW experiment and Einstein–Bohr’s photon box

In this work, we have explored the effects of the higher-order generalized uncertainty principle (GUP), inspired by the quantum gravity COW experiment and Einstein–Bohr’s photon box thought experiment, on the properties of a black hole. Two different GUP models, namely GUP to all orders in the Planck length model and GUP with minimal length uncertainty and maximal momentum model, are considered for our study. For each model, we have investigated the modified de Broglie formula, modification in gravitational phase shift, Einstein–Bohr’s photon box, and the modified Hawking temperature and the tidal force of the GUP modified black hole.

Higher-order generalized uncertainty principle corrections to the Jeans mass

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 by applying various data of Bok globules, and find that the range of magnitude of gamma _0 is {10^{11}} {-} {10^{12}}.

Extended GUP corrected thermodynamics, shadow radius and quasinormal modes of charged AdS black holes in Gauss–Bonnet gravity

This paper explores the influence of special type of higher order generalized uncertainty principle on the thermodynamics of five-dimensional black hole in Einstein–Gauss–Bonnet gravity coupled to nonlinear electrodynamics. We examine the corrected thermodynamical properties of the black hole with some interesting limiting cases [Formula: see text] and [Formula: see text] and compared our results with usual thermodynamical relations. We observe that the influence of GUP correction stabilizes the BH and BH solution remains physical throughout the region of horizon radius. In this framework, we also uncover the relationship of shadow radius and quasinormal modes of the mentioned black hole. We conclude that shadow radius of our considered black hole is a perfect circle and it decreases with increasing values of charge and Gauss–Bonnet parameter. We also verify the inverse relation between the quasinormal modes frequencies and shadow radius, i.e. quasinormal modes should increase with increasing values of Gauss–Bonnet parameter and electric charge.

Analysis of black hole thermodynamics with a new higher order generalized uncertainty principle

This research explores a unified expression for the black hole thermodynamics in the presence of a special generalized uncertainty principle (GUP). We have considered a heuristic analysis versus behavior of a particle which is absorbed by the black hole. Then we investigate the thermodynamic properties of the topological charged black hole under the consideration of GUP and we obtain the GUP-corrected temperature, entropy and heat capacity and we compare the behaviors of the usual temperature and the corrected temperature for the charged black hole in the spherical horizon case.

On the Position Representation of Pedram’s Higher Order GUP

In this paper we show that the position representation of the higher order generalized uncertainty principle (HGUP) is also well defined without approximation. We find the simpler form of this representation with a help of the signature of the discriminant of the cubic equation. Using this we discuss the HGUP derivative, HGUP exponential and HGUP trigonometric functions and HGUP-corrected Bohr atom model. Finally we discuss the D-dimensional HGUP algebra and compute the cosmological constant.

Some applications of the most general form of the higher-order GUP with minimal length uncertainty and maximal momentum

In this paper, using the new type of D-dimensional nonperturbative Generalized Uncertainty Principle (GUP) which has predicted both a minimal length uncertainty and a maximal observable momentum,1 first, we obtain the maximally localized states and express their connections to [P. Pedram, Phys. Lett. B 714, 317 (2012)]. Then, in the context of our proposed GUP and using the generalized Schrödinger equation, we solve some important problems including particle in a box and one-dimensional hydrogen atom. Next, implying modified Bohr–Sommerfeld quantization, we obtain energy spectra of quantum harmonic oscillator and quantum bouncer. Finally, as an example, we investigate some statistical properties of a free particle, including partition function and internal energy, in the presence of the mentioned GUP.

Generalized uncertainty principle: Approaches and applications

In this paper, we review some highlights from the String theory, the black hole physics and the doubly special relativity and some thought experiments which were suggested to probe the shortest distances and/or maximum momentum at the Planck scale. Furthermore, all models developed in order to implement the minimal length scale and/or the maximum momentum in different physical systems are analyzed and compared. They entered the literature as the generalized uncertainty principle (GUP) assuming modified dispersion relation, and therefore are allowed for a wide range of applications in estimating, for example, the inflationary parameters, Lorentz invariance violation, black hole thermodynamics, Saleker–Wigner inequalities, entropic nature of gravitational laws, Friedmann equations, minimal time measurement and thermodynamics of the high-energy collisions. One of the higher-order GUP approaches gives predictions for the minimal length uncertainty. A second one predicts a maximum momentum and a minimal length uncertainty, simultaneously. An extensive comparison between the different GUP approaches is summarized. We also discuss the GUP impacts on the equivalence principles including the universality of the gravitational redshift and the free fall and law of reciprocal action and on the kinetic energy of composite system. The existence of a minimal length and a maximum momentum accuracy is preferred by various physical observations. The concern about the compatibility with the equivalence principles, the universality of gravitational redshift and the free fall and law of reciprocal action should be addressed. We conclude that the value of the GUP parameters remain a puzzle to be verified.

A higher order GUP with minimal length uncertainty and maximal momentum II: Applications

In a recent paper, we presented a nonperturbative higher order Generalized Uncertainty Principle (GUP) that is consistent with various proposals of quantum gravity such as string theory, loop quantum gravity, doubly special relativity, and predicts both a minimal length uncertainty and a maximal observable momentum. In this Letter, we find exact maximally localized states and present a formally self-adjoint and naturally perturbative representation of this modified algebra. Then we extend this GUP to D dimensions that will be shown it is noncommutative and find invariant density of states. We show that the presence of the maximal momentum results in upper bounds on the energy spectrum of the free particle and the particle in box. Moreover, this form of GUP modifies blackbody radiation spectrum at high frequencies and predicts a finite cosmological constant. Although it does not solve the cosmological constant problem, it gives a better estimation with respect to the presence of just the minimal length.