Dimiter Hadjimichef

We investigate how neutrino oscillations are modified in a non‐commutative spacetime characterized by a minimal length scale, described by the Quesne–Tkachuk algebra. By incorporating the algebra's deformation parameter into the effective neutrino mass, we derive the two‐flavor oscillation probability in this non‐commutative setting. The resulting probability depends not only on the usual mass‐squared difference but also on a fourth‐order mass difference scaled by . A comparison between the standard and non‐commutative oscillation probabilities reveals a beat pattern arising from the additional non‐commutative phase, which induces a small shift in the oscillation profiles. Finally, we extend our analysis to include the effects of a magnetic field on neutrino propagation in an extreme astrophysical environment.

A novel approach to cosmic inflation within the framework of a noncommutative Riemannian foliated quantum gravity, built upon a reverse Faddeev–Jackiw symplectic spacetime deformation of the conventional Poisson algebra, is investigated. Friedmann‐type dynamical equations, analytically continued to a complex noncommutative framework, incorporate a modified energy‐momentum Riemann tensor and a noncommutative matter‐energy potential, highlighting the emergence of quantum gravity topological fluctuation effects on the expansion dynamics of the universe. In this realm, the coupling of UV and IR scales plays a central role, providing a natural topological mechanism for inflation and recursal evidence for the generation of relic gravitational waves. These predictions align with a self‐consistent description of the transition between the primordial mirror‐universe deceleration and present‐universe acceleration phases as predicted by the Riemann foliated quantum gravity, offering potential connections to observational cosmology.

We investigate pseudo-complex General Relativity (pcGR)—a coordinate-extended formulation of General Relativity (GR)—within the framework of Hořava-Lifshitz gravity, a regularized theory featuring anisotropic scaling. The pcGR framework bridges GR with modified gravitational theories through the introduction of a minimal length scale. Focusing on Schwarzschild black holes, we derive the Wheeler-deWitt equation, obtaining a quantized description of pcGR. Using perturbative methods and semi-classical approximations, we analyze the solutions of the equations and their physical implications. A key finding is the avoidance of the central singularity due to nonlinear interaction terms in the Hořava-Lifshitz action. Notably, extrinsic curvature (kinetic energy) contributions prove essential for singularity resolution, even in standard GR. Furthermore, the theory offers new perspectives on dark energy, proposing an alternative mechanism for its accumulation.

We present a study of relic gravitational waves based on a foliated gauge field theory defined over a spacetime endowed with a noncommutative algebraic–geometric structure. As an ontological extension of general relativity—concerning manifolds, metrics, and fiber bundles—the conventional space and time coordinates, typically treated as classical numbers, are replaced by complementary quantum dual fields. Within this framework, consistent with the Bekenstein criterion and the Hawking–Hertog multiverse conception, singularities merge into a helix-like cosmic scale factor that encodes the topological transition between the contraction and expansion phases of the universe analytically continued into the complex plane. This scale factor captures the essence of an intricate topological quantum-leap transition between two phases of the branching universe: a contraction phase preceding the now-surpassed conventional concept of a primordial singularity and a subsequent expansion phase, whose transition region is characterized by a Riemannian topological foliated structure. The present linearized formulation, based on a slight gravitational field perturbation, also reveals a high sensitivity of relic gravitational wave amplitudes to the primordial matter and energy content during the universe’s phase transition. It further predicts stochastic homogeneous distributions of gravitational wave intensities arising from the interplay of short- and long-spacetime effects within the non-commutative algebraic framework. These results align with the anticipated future observations of relic gravitational waves, expected to pervade the universe as a stochastic, homogeneous background.

We investigate the effects of a minimal measurable length on neutron stars, within the quantum hadrodynamics (QHD‐I) model modified by the Generalized Uncertainty Principle (GUP). Working in a deformed Poisson algebra framework, we incorporate GUP effects via a time‐invariant transformation of the phase space volume, effectively reducing the number of accessible quantum states at high momentum. We focus specifically on two observables critical to this star physics, the compressibility, which encapsulates how stiff EOS become, and the speed of sound, which imposes a causality constraint. Using this model as an exploratory study, due to its simplicity and structured description, we perform a preliminary analysis of GUP effects with a minimum spacetime length on these compact objects. This deformation increases the speed of sound while decreasing the compressibility, and we identify critical values of the Fermi momentum beyond which both quantities become nonphysical. These results underscore the potential role of a minimal length scale in shaping the bulk properties and possible phase structures of dense matter in neutron stars.

A novel approach to cosmic inflation within the framework of a non-commutative Riemannian foliated quantum gravity, built upon a reverse Faddeev–Jackiw symplectic spacetime deformation of the conventional Poisson algebra, is investigated. Friedmann-type dynamical equations, analitycally continued to a complex non-commutative framework, incorporate a modified energy-momentum Riemann tensor and a non-commutative matter-energy potential, highlighting the emergence of quantum gravity topological fluctuation effects on the expansion dynamics of the universe. In this realm, the coupling of UV and IR scales play a central role, providing a natural topological mechanism for inflation and recursal evidences for the generation of relic gravitational waves. These predictions align with a self-consistent description of the transition between the primordial mirror-universe deceleration and present-universe acceleration phases as predict by the Riemann foliated quantum gravity, offering potential connections to observational cosmology.

We present a study of relic gravitational waves based on a foliated gauge field theory defined over a spacetime endowed with a noncommutative algebraic-geometric structure. As an ontological extension of general relativity concerning manifolds, metrics and fiber bundles, the space and time coordinates, which conventionally correspond to classical numbers, are replaced in this formulation by complementary quantum dual fields. In this framework, consistently complying within the Bekenstein criterion, combined with the Hawking-Hertog multiverse conception, singularities merge, portrayed into a new cosmic helix-like scale factor, analytically continued to the complex plane. This scale-factor captures the essence of an intricate topological quantum-leap transition between two phases of the branching universe: a contraction phase preceding the surpassed conventional concept of a primordial singularity and a subsequent expansion phase whose transition region between the two phases is characterized by a Riemannian topological foliated structure. The present linearized formulation, underlying a slightly gravitational field perturbation reveals, during the universe phase transition, high sensitivity of the relic gravitational waves amplitudes to the primordial matter and energy content. The present formulation reveals a stochastic homogeneous distributions of gravitational-wave intensities arising from the capture of short and long spacetime scales within the noncommutative algebraic framework. These results are consistent with the expected anticipated future observations of relic gravitational waves, which are expected to fill the universe as a stochastic homogeneous background.

This Conference Proceedings volume contains the written versions of most of the contributions presented during the 11th International Workshop on Astronomy and Relativistic Astrophysics (IWARA 2024). The Workshop took place in Machupicchu Pueblo (Aguas Calientes), Peru, from September 2–6, 2024. The Workshop provided a setting for discussing recent developments in a wide variety of topics, including Archaeoastronomy and Cognition, the Kerr metric and the Hawking temperature, Damour‐Solodukhin‐type Wormholes, Stellar Physics and General Relativity, Stochastic Quantum Mechanics in Curved Spaces, Gauss‐Bonnet Theory, Quantum Gravity, Black Holes, Fast Radio Bursts, Neutron Stars, Strange Stars, X‐ray Binaries, Pulsars, Gravitational Waves, and Dark Matter, among others. Most of these contributions are included in this volume.

We propose a novel extension to the recently developed non-commutative Riemannian foliated branch-cut quantum gravity (BCQG). On basis in an extended Faddeev–Jackiw symplectic deformation of the conventional Poisson algebra, we investigate non-commutativity effects on a symplectic topological manifold that provides a natural isomorphic setting composed by a triad of canonically conjugate scalar complex fields which comprise quantum complementary dualities. The resulting extended manifold spans the canonical BCQG cosmic scale factor and, in addition to its complementary quantum counterpart, outlined in the perfect fluid domain of Hermann Weyl, a scalar-complex inflaton-inspired field. By constructing a triad of quantized fields underlying a noncommutative spacetime, this extension allows the elaboration of a scenario where the original branch-cut domain coexists with a complex scalar inflaton-type field, settled on a plateau of a strong gravity interaction structure. Alongside shaping this structure settled on a background composed by the primordial energy, radiation-, quintessence-, stiff-, baryon- and dark matter, combined with the spacetime components of the scalar Ricci curvature at different orders, cosmic inflation is driven. The presence of the inflaton field in the present formulation transcends the character of a simple reference field, to the extent that its original motivation has been to driven inflation, a role played by the original formulation of the BCQG. The resulting symplectic algebraic extension allows additionally a liaison with primordial cosmic density perturbation predictions based on heuristic derivations of the scale invariance of the primordial spectrum of the Universe, as well as with eternal inflation and primordial chaotic cosmic mechanisms proposals. Given the peculiar characteristic of BCQG in overcoming the primordial singularity, the non-commutative symplectic extension proposal, due to the complex character of the constituent fields, additionally outlines the evolutionary process of the mirror Universe that encompasses analytically continued complex conjugate Friedmann's-type equations. This brings unique characteristics to the main scenario for the BCQG cosmic evolution, with a mirrored parallel evolutionary Universe, adjacent to ours, nested in the structure of space and time. The evolutionary process of the mirror Universe occurs in the negative sector of cosmological thermal time, and is characterized by a continuous cosmic contraction, with a systematic and continuous increase in temperature and a decrease in entropy before reaching the transition region to the current stage of the Universe. In contrast, the subsequent present evolutionary stage of cosmic expansion is characterized by a positive complex cosmological-time sector, accompanied by a systematic decrease in temperature and increase in entropy. On basis on complementary analytically continued Friedmann’s-type equation, combined with a quantum approach based on the Ho\v{r}awa-Lifshitz quantum gravity, we describe the dynamic evolution of the Universe’s wave function, unfolding unprecedented predictions for the cosmic evolution and inflation. This approach offers a new perspective to explain the accelerated cosmic expansion of the Universe, strongly suggesting that non-commutative algebra induces the late accelerated growth of the wave function of the Universe as well as of the corresponding scale factor and its complementary quantum counterparts. In contrast to the conventional inflationary model, where inflation requires a remarkably fine-tuned set of initial conditions in a patch of the Universe, non-commutative foliated quantum gravity, analytically continued to the complex plane, captures short and long scales of spacetime, leading to an evolutionary cosmic dynamic through a topological reconfiguration of the primordial cosmic matter and energy content. Still, we consider in this work the interplay between naturalness and a fine-tuning set constraining of the cosmological initial conditions. This result introduces new speculative framework elements regarding the reconfiguration of matter and energy due to an underlying non-commutative spatio-temporal structure as a driver of spacetime cosmic acceleration.