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I discuss the renormalization group approach to gravity, and its link to Weinberg's asymptotic safety scenario, and give an overview of results with applications to particle physics and cosmology.I discuss the renormalization group approach to gravity, and its link to Weinberg's asymptotic safety scenario, and give an overview of results with applications to particle physics and cosmology.

Motivated by several approaches to quantum gravity, there is a considerable literature on generalised uncertainty principles particularly through modification of the canonical position-momentum commutation relations. Some of these modified relations are also consistent with general principles that may be supposed of any physical theory. Such modified commutators have significant observable consequences. Here we study the noisy behaviour of an optomechanical system assuming a certain commonly studied modified commutator. From recent observations of radiation pressure noise in tabletop optomechanical experiments as well as the position noise spectrum of advanced LIGO we derive bounds on the modified commutator. We find how such experiments can be adjusted to provide significant improvements in such bounds, potentially surpassing those from sub-atomic measurements.

Based on the correspondence between operator commutative relations and Poisson brackets, we develop a framework of deformed Hamilton, Lagrange and Euler equations as well as their relations in the noncommutative phase space. We introduce a deformed factor and deformed matrix to measure the departure of the deformed symplectic structure from the canonical symplectic structure. We endow the noncommutative parameters with the Planck length, Planck constant and cosmological constant, which allows us to explore some puzzles from the Planck to cosmological scales. We find that there exist an observer-dependent effective force and moment of force break the translation and rotation symmetries. As a spacetime quantum fluctuation, these formulations and results provide some hints and insights into some unsolved phenomena such as intrinsic spacetime singularities, black hole radiation, dark matter and dark energy as well as anisotropic cosmic radiation background.

We are demonstrating new relationships among the Hawking temperature, the Cosmic Microwave Background (CMB) temperature, and the Planck scale. When understood deeply, these are in line with recent advancements in cosmological quantization and its connection to the Planck scale. This is also completely consistent with a recently published method for quantizing Einstein’s general theory of relativity.

Recent work showed that κ-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the Poincaré algebra of special-relativistic symmetries, one can toggle the curvature parameter Λ, the Planck scale quantum deformation parameter κ and the speed of light parameter c to move to the well-studied κ-Poincaré algebra, the (quantum) (A)dS algebra, the (quantum) Galilei and Carroll algebras and their curved versions. In this review, we survey the properties and relations of these algebras of relativistic symmetries and their associated noncommutative spacetimes, emphasizing the nontrivial effects of interplay between curvature, quantum deformation and speed of light parameters.

We have recently shown that the very low mechanical energy achieved and measured in the main vibration mode of gravitational wave bar detectors can set an upper limit to possible modifications of the Heisenberg uncertainty principle that are expected as an effect of gravity. Here we give more details on the data analysis procedure that allows one to deduce the energy of the bar mode (i.e., the meaningful parameter for our purpose). Furthermore, we extend the analysis of our results, discussing their implication for physical models that face quantum gravity from different points of view, e.g., proposing modified commutation relations or exploring spacetime discreteness.

We extend the Quantum Memory Matrix (QMM) framework, originally developed to reconcile quantum mechanics and general relativity by treating space–time as a dynamic information reservoir, to incorporate the full suite of Standard Model gauge interactions. In this discretized, Planck-scale formulation, each space–time cell possesses a finite-dimensional Hilbert space that acts as a local memory, or quantum imprint, for matter and gauge field configurations. We focus on embedding non-Abelian SU(3)c (quantum chromodynamics) and SU(2)L × U(1)Y (electroweak interactions) into QMM by constructing gauge-invariant imprint operators for quarks, gluons, electroweak bosons, and the Higgs mechanism. This unified approach naturally enforces unitarity by allowing black hole horizons, or any high-curvature region, to store and later retrieve quantum information about color and electroweak charges, thereby preserving subtle non-thermal correlations in evaporation processes. Moreover, the discretized nature of QMM imposes a Planck-scale cutoff, potentially taming UV divergences and modifying running couplings at trans-Planckian energies. We outline major challenges, such as the precise formulation of non-Abelian imprint operators and the integration of QMM with loop quantum gravity, as well as possible observational strategies—ranging from rare decay channels to primordial black hole evaporation spectra—that could provide indirect probes of this discrete, memory-based view of quantum gravity and the Standard Model.

A model of Planck cells structure on the hyphersurface of a de Sitter universe is proposed and compared with the cellular automata of 't Hooft. Processes of nucleation of particles since a “primordial” Wheeler-DeWitt equation which embeds, with a parameter of deformation, a “Quantum Boltzmann Statistics” leading to obtain bosons and fermions, are analysed. Finally, some conclusions about the fundamental role of non-locality and about the informational nature of Planck scale are made.

The standard model of cosmology, although very successful, has problems with the very initial phase, such as the existence of a singularity when the density and curvature becomes infinite. In this work we propose a possible non-singular beginning of the Universe. From quantum considerations we set the earliest epoch to be the Planck epoch, which implies that the Universe did not begin with a singularity but with a finite minimal size of 10−3cm. We suggest that the Universe initially began at the Planck length as a fluctuation having Planck energy expanding exponentially at constant Planck density, which then in turn accounts for the matter creation. All matter at the present epoch was created by the time the size of the Universe reached this minimal scale (10−3cm) starting from Planck length. We call this the Planck scale inflation. We also consider a time varying cosmological constant.

Modern cosmology has two competing theories of the origin of the universe: the \"Singularity theory\" and the \"Superstring theory\". Four Dilemmas of the \"Superstring theory\" are presented: the incompleteness of the eleven space–time dimensions, the inextricable dependence on the “Space–Time Background”, the \"Zero-Brane theory\" admitting stuff smaller than the Planck scale, and the pure mathematical theory that cannot be falsified by experiments. Although the \"Singularity theory\" is faced with many critiques from the \"Superstring theory\", from the perspective of Information Ontology, treating the \"Singularity\" as \"Origin Information\" can dissolve these troubles well. For the \"Singularity theory\", the new philosophical thinking framework effectively explains the parameter problems of the universe, and gives satisfied response to the challenges from the \"Superstring theory\". As a result, the \"Singularity theory\" has a more competitive advantage on the origin of the universe.