Abstract. We propose the disappearance of "the hyperon puzzle" in neutron star (NS) by invoking two new-physics prescriptions: modified gravity theory and braneworld scenario. By assuming that NS lives on a 3-brane within a 5d empty AdS bulk, gravitationally governed by Eddington-inspired Born-Infeld (EiBI) theory, the field equations can be effectively cast into the usual Einstein's with "apparent" anisotropic energy-momentum tensor. Solving the corresponding brane-TOV equations numerically, we study its mass-radius relation. It is known that the appearance of finite brane tension λ reduces the compactness of the star. The compatibility of the braneworld results with observational constraints of NS mass and radius can be restored in our model by varying the EiBI's coupling constant, κ. We found that within the astrophysically-accepted range of parameters (0 < κ < 6 × 10 6 m 2 and λ 1 MeV 4 ) the NS can have mass ∼ 2.1 M and radius ∼ 10 km.

The isotropy of space is not a logical requirement but rather is an empirical question; indeed there is suggestive evidence that universe might be anisotropic. A plausible source of these anisotropies could be quantum gravity corrections. If these corrections happen to be between the electroweak scale and the Planck scale, then these anisotropies can have measurable consequences at short distances and their effects can be measured using ultra sensitive condensed matter systems. We investigate how such anisotropic quantum gravity corrections modify low energy physics through an anisotropic deformation of the Heisenberg algebra. We discuss how such anisotropies might be observed using a scanning tunnelling microscope.

Loop Quantum Gravity has become one of the alternative solutions to quantum gravity. This formulation introduced geometrical operators which successfully used to model that in the quantum scale, the space is actually discretized in the order of Planck length. These operators are area and volume operator. The regularization process of these operators came from the classical definition of area and volume, thus, the eigenvalues of area operator and volume operator are respectively the area and volume of the space. However, there exists two types of volume operator, the Ashtekar-Lewandowski operator and the Rovelli-Smolin operator. The significant difference between these two operators is the fact that Ashtekar-Lewandowski operator is sensitive to the direction of the spin networks link, while Rovelli-Smolin operator is not. This difference will produce different spectral. In this article, we compare the resulting spectral of the two volume operators, where both of them is used to calculate the volume of the monochromatic 4-valent and 6-valent spin network for the kinematical case.

Triangular inequality is an important relation in geometry such that this relation, intuitively, is a statement that the direct line connecting two points is the shortest one. Loop quantum gravity is presented after a reformulation of gravity using Ashtekar variables. The quantization follows the Dirac procedures, which results in the existence of state of quanta of 3d space as an element of Hilbert space. Spin network states has become the basis state for quanta of space in loop quantum gravity. In loop quantum gravity space is discrete and the geometrical quantity is quantized at the Planck scale. In 3d space, we can define triangular discretization of the hypersurface. In this article we discuss the length spectrum and check whether the triangular inequality is satisfied by the quantum length. The answer to the question is positive, such that even at the Planck scale the triangular inequality is still valid.