ABSTRACTWe explore the implications of Branch‐Cut Quantum Gravity (BCQG), a novel framework leveraging non‐commutative geometry within a symplectic phase‐space, on the accelerated expansion of the universe. Non‐commutativity, introduced through a deformation of the Poisson algebra and enhanced by a symplectic metric, provides a robust mechanism for addressing key challenges in cosmology, such as the youngness paradox and the fine‐tuning of initial conditions in standard inflationary models. By embedding quantum dual‐field dynamics within a Riemannian‐foliated spacetime, BCQG naturally integrates short‐ and long‐range spacetime effects into a unified formalism. This approach offers an alternative to standard inflationary models by predicting cosmic acceleration through geometric restructuring rather than finely‐tuned initial states. In contrast to models like ΛCDM or String Theory, BCQG introduces unique corrections to cosmic scale factors and predicts a novel transition between contraction and expansion phases via topological branch‐cuts, circumventing the singularity problem. Moreover, BCQG's non‐commutative formulation provides testable predictions, such as modifications in cosmic microwave background (CMB) anisotropies and large‐scale structure evolution. We discuss the mathematical foundation, observational implications, and future avenues for validating BCQG through astrophysical data, positioning it as a promising theoretical alternative for understanding the universe's accelerated growth.

We propose a novel extension to the recently developed non-commutative Riemannian foliated branch-cut quantum gravity (BCQG). Based on 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. Based on a complementary analytically continued Friedmann-type equation, combined with a quantum approach based on the Hořawa-Lifshitz quantum gravity, we describe the dynamic evolution of the universe's wave function, unfolding unprecedented predictions for the cosmic evolution and inflation. The non-commutative foliated quantum gravity approach offers a new perspective on explaining the accelerated cosmic expansion of the universe, strongly suggesting that non-commutative algebra induces the late accelerated growth of both the universe's wave function and the corresponding scale factor, along with their 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. 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.

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 explore a noncommutative extension of branch-cut quantum gravity (BCQG), with a focus on its implications for early-universe inflation. Our framework builds on a three-field mini-superspace model involving a complex-valued cosmic-scale factor, a perfect-fluid field, and an inflaton-type scalar field. Using a Faddeev-Jackiw symplectic deformation of the conventional Poisson algebra, we construct a noncommutative phase space and derive a modified Wheeler-DeWitt equation. Analytic solutions to the wave function of the universe are obtained and analyzed. We show that noncommutativity induces coupling between ultraviolet and infrared modes, naturally leading to an inflationary phase without requiring fine-tuned initial conditions. This feature offers a novel alternative to standard inflationary models. We also discuss how the structure of the wave function in this framework may relate to primordial density perturbations. While some aspects of this theory remain speculative, the mathematical formulation provides a consistent path toward integrating quantum gravitational effects into early cosmological dynamics.

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.

This article focuses on the implications of a noncommutative formulation of branch-cut quantum gravity. Based on a mini-superspace structure that obeys the noncommutative Poisson algebra, combined with the Wheeler–DeWitt equation and Hořava–Lifshitz quantum gravity, we explore the impact of a scalar field of the inflaton-type in the evolution of the Universe's wave function. Taking as a starting point the Hořava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, the corresponding wave equations are derived and solved. The noncommutative quantum gravity approach adopted preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner Formalism. In this work we delve deeper into a mini-superspace of noncommutative variables, incorporating scalar inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions to the wave equations without resorting to numerical approximations. The results indicate that the noncommutative algebraic space captures low and high spacetime scales, driving the exponential acceleration of the Universe.

Based on an analytically continued Riemannian foliated quantum gravity super- Hamiltonian, known as branch cut quantum gravity (BCQG) we propose a novel approach to investigating the effects of noncommutative geometry on a minisuperspace of variables, influencing the acceleration behavior of the Universe's wave function and the cosmic scale factor. Noncommutativity is introduced through a deformation of the conventional Poisson algebra, enhanced with a symplectic metric. The resulting symplectic manifold provides a natural setting that enables an isomorphism between canonically conjugate dual vector spaces, spanning the BCQG cosmic scale factor and its complementary quantum counterpart. Using this formulation, we describe the dynamic evolution of the Universe's wave function, the cosmic scale factor, and its complementary quantum image. Our results strongly suggest that the non- commutative algebra induces late-time accelerated growth of the wave function, the Universe's scale factor, and its complementary quantum counterpart, offering a new perspective on explaining the accelerating cosmic expansion rate and the inflationary period. In contrast to the inflationary model, where inflation requires a remarkably fine-tuned set of initial conditions in a patch of the Universe, analytically continued non-commutative foliated quantum gravity captures short and long scales, driving the evolutionary dynamics of the Universe through a reconfiguration of the primordial cosmic content of matter and energy. This reconfiguration is encapsulated into a quantum field potential, which leads to the generation of relic gravitational waves, a topic for future investigation. Graphical representations and contour plots indicate a characteristic torsion (or twist) deformation of spacetime geometry. This result introduces new speculative elements regarding the reconfiguration of matter and energy as a driver of spacetime torsion deformation, generating relic gravitational waves and serving as an alternative topological mechanism for the Universe's acceleration. However, these assumptions require further investigation.

Branch-cut gravity (BCG) is an extended version of the ontological domain of General Relativity, which is analytically continued to the complex plane. When combined with the Hawking-Hertog multiverse conception, BCG successfully addresses the issue of the primordial singularity. It consistently portrays the early Universe as a Riemannian foliation in which the singularities of the multiverse merge, giving rise to a smooth branching topological structure that resembles continuously connected Riemann surfaces. This structure introduces a new cosmic scale factor that is analytically continued into the complex plane. In this contribution, we start with the recently developed Wheeler DeWitt-Horava-Lifshitz non-commutative BCG formulation of quantum gravity. We investigate the impact of a non-commutative mini-superspace of variables obeying Poisson algebra on the accelerated behavior of the branch-cutting cosmic scale factor. drive spacetime acceleration, offering a new perspective on explaining the accelerating expansion rate of our Universe. As far as primordial relic gravitational waves are concerned, our predictions reveal an intricate transition between the two phases of the branched Universe: a contraction phase preceding the conventional concept of a primordial singularity and a subsequent expansion phase whose transition region is characterized by a Riemannian topological foliation structure. Furthermore, this transition is characterized by asymmetric distributions of gravitational wave intensities.

This article focuses on a recently developed formulation based on the noncommutative branch-cut cosmology, the Wheeler-DeWitt (WdW) equation, the Horava-Lifshitz quantum gravity, chaotic and the coupling of the corresponding Lagrangian approach with the inflaton scalar field. Assuming a mini-superspace of variables obeying the noncommutative Poisson algebra, we examine the impact of the inflaton scalar field on the evolutionary dynamics of the branch-cut Universe scale factor, characterized by the dimensionless helix-like function ln(-1) left perpendicular beta(t)right perpendicular. This scale factor characterizes a Riemannian foliated spacetime that topologically overcomes the primordial singularities. We take the Horava-Lifshitz action modeled by branch-cut quantum gravity as our starting point, which depends on the scalar curvature of the branched Universe and its derivatives and which preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt-Deser-Misner formalism. We then investigate the sensitivity of the scale factor of the branch-cut Universe's dynamics.

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigated a formulation of quantum gravity based on the Wheeler-DeWitt (WDW) equation combined with the classical concepts of the branch-cut cosmology, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction phase, prior to the primordial singularity, and the subsequent expansion phase. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched cosmology as well as the corresponding conjugate momentum to the category of quantum operators. As a novelty, ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted to the integers α=[0,1,2], since non-integers have no physical meaning, allowing this way a broader class of solutions for the wave function of the Universe. As another novelty, additional energy-dependent parametrizations are considered, more specifically, in addition to a branched universe filled with underlying background vacuum energy, matter and radiation, in order to make contact with standard model calculations, we additionally supplement the formulation with baryon matter, dark matter and quintessence contributions. As an additional novelty, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate this way, as a novelty conclusion, the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early universe in contrast to the classic branched cosmology view of a smooth transition.

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigate a formulation of quantum gravity using the Hořava–Lifshitz theory of gravity, which is General Relativity augmented by counter-terms to render the theory regularized. We are then led to the Wheeler–DeWitt (WDW) equation combined with the classical concepts of the branch-cut gravitation, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction and expansion phases. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched gravitation as well as the corresponding conjugate momentum to the category of quantum operators. Ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted, to make contact with similar approaches, to the integers α=[0,1,2], allowing this way a broader class of solutions for the wave function of the Universe. In addition to a branched universe filled with underlying background vacuum energy, primordial matter and radiation, in order to connect with standard model calculations, we additionally supplement this formulation with baryon matter, dark matter and quintessence contributions. Finally, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early Universe in contrast to the classic branched cosmology view of a smooth transition.

In this contribution, motivated by the quest to understand cosmic acceleration, based on the theory of Hořava–Lifshitz and on the branch-cut gravitation, we investigate the effects of non-commutativity of a mini-superspace of variables obeying the Poisson algebra on the structure of the branch-cut scale factor and on the acceleration of the Universe. We follow the guiding lines of a previous approach, which we complement to allow a symmetrical treatment of the Poisson algebraic variables and eliminate ambiguities in the ordering of quantum operators. On this line of investigation, we propose a phase-space transformation that generates a super-Hamiltonian, expressed in terms of new variables, which describes the behavior of a Wheeler–DeWitt wave function of the Universe within a non-commutative algebraic quantum gravity formulation. The formal structure of the super-Hamiltonian allows us to identify one of the new variables with a modified branch-cut quantum scale factor, which incorporates, as a result of the imposed variable transformations, in an underlying way, elements of the non-commutative algebra. Due to its structural character, this algebraic structure allows the identification of the other variable as the dual quantum counterpart of the modified branch-cut scale factor, with both quantities scanning reciprocal spaces. Using the iterative Range–Kutta–Fehlberg numerical analysis for solving differential equations, without resorting to computational approximations, we obtained numerical solutions, with the boundary conditions of the wave function of the Universe based on the Bekenstein criterion, which provides an upper limit for entropy. Our results indicate the acceleration of the early Universe in the context of the non-commutative branch-cut gravity formulation. These results have implications when confronted with information theory; so to accommodate gravitational effects close to the Planck scale, a formulation à la Heisenberg’s Generalized Uncertainty Principle in Quantum Mechanics involving the energy and entropy of the primordial Universe is proposed.

Compact stars consisting of strange quark matter and strange matter with admissible dark matter are studied by solving the Tolman-Oppenheimer-Volkoff equations for two fluids interacting only by gravity, with the dark-matter EoS obtained by means of galaxy rotation curves. The properties of these stars are explored by means of the modeling of their mass-radius relations and gravitational redshifts.

In this article, we follow a previously developed theoretical approach, based on the tools of the singular semi-Riemannian geometry, to push the limits of time beyond the primordial spacetime singularity. By complexifying the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and Friedmann's equations, we model a branch cut universe, in which the cosmic FLRW metric scale factor is analytically continued to the complex plane, and becomes equivalent from a conceptual point of view of describing a hypothetical general metric of maximally symmetric and homogeneous superposed multiple universes.

In this contribution, we identify two scenarios for the evolutionary branch cut universe. In the first scenario, the universe evolves continuously from the negative complex cosmological time sector, prior to a primordial singularity, to the positive one, circumventing continuously a branch cut, and no primordial singularity occurs in the imaginary sector, only branch points. In the second scenario, the branch cut and branch point disappear after the realization of the imaginary component of the complex time by means of a Wick rotation, which is replaced by the thermal time. In the second scenario, the universe has its origin in the Big Bang, but the model contemplates simultaneously a mirrored parallel evolutionary universe going backwards in the cosmological thermal time negative sector. A quantum formulation based on the Wheeler–DeWitt equation is sketched and preliminary conclusions are drawn.

The predictions of General Relativity suggest a universe in which, as we follow time backward, the hotter and the more dense it was, and the more rapidly it was expanding and that, around 13.7 billion years ago, at the extreme gravitational regime of its evolutionary process, the density, temperature, and expansion rate of the universe would start off as infinite. The General Relativity prediction of a singularity in the early universe would impose a limitation to our understanding of the cosmos and gravity, implying loss of logic and of formal consistency and predictability, making it impossible to impose initial conditions. These extreme conditions of the initial state of the universe are very far from our experimental possibilities, and presently, theoretical models allow only speculations about the avoidance of physical singularities or about the physical conditions that circumvented this drastic consequence of General Relativity. Speculations aside, in this study, we follow an analytical line in which we apply the tools of singular semi-Riemannian geometry to push the limits of General Relativity beyond the Big Bang singularity.

In this investigation, we study the structure of ultra-compact stars in the framework of semiclassical gravity, an extension of Einstein's general relativity (GR), in which a classical spacetime metric is coupled to the quantum expectation value of the stress tensor and that incorporates the polarization of the quantum vacuum in the presence of a gravitational field. In this approach, a generalization of the classical Tolman-Oppenheimer-Volkoff (TOV) equations may be derived. Unlike most theoretical treatments based on GR, this formulation allows a wider range of consistent equation of state (EoS) solutions with enough compactness to produce a photon sphere without violating the Buchdahl limit, an upper bound on the compactness, thus motivating future studies to investigate if ultra-compact stars could act as black hole mimickers. The main novelty of this extended formalism, when compared to the conventional form of the TOV equations, is the presence of an additional repulsive term-due to quantum corrections originated by the phenomenon of quantum vacuum polarization-that can withstand, under certain conditions, the gravitational collapse. Although the quantum corrections furnished by semiclassical gravity are negligible in most compact stars scenarios, for ultra-compact configurations, where the star radius is not much larger than its gravitational radius, such effects may be relevant.

Neutron stars are the most compact objects in nature widely used in the study of dense matter physics. In this work we investigate the structure of these stars, described by the Tolman-Openheimer-Volkof equations, using equations of state for both symmetric nuclear matter and quark matter. We obtain results for the mass-radius relation and then we compared ours results with the actual pulsar data recently observed PSR J1614-2230 with a mass $1.97pm 0.04 M_{odot}$.

Compact objects are the name used to classify the following objects: white dwarf, neutron star and black holes. In addition to them, some authors have suggested that in the core of a neutron star we may have the quarks u,d,s and c. In this work we investigate the structure of neutron star and strange star, described by the Tolman-Openheimer-Volkof equations. For the neutron star, we used the relativistic EoS from Walecka's model and the non-relativistic EoS PAL model. For the strange star, we used the M.I.T. bag model. We obtain results for the mass-radius relation and then we compared ours results with the actual pulsar data recently observed PSR J1614-2230 with a mass 1.97± 0.04M_⊙.