In recent years, a new class of exact solutions of the Einstein field
equations of general relativity in the presence of matter, in the static
and spherically symmetric case, was discovered and analyzed by analytical
and numerical means. In this talk, these new solutions are described in the
case of the polytropic equations of state, and their main conceptual
consequences for the structure of the theory are discussed.

As a consequence of the development of these solutions, new aspects of the
concept of spacetime singularity were uncovered, namely that there exist
previously unsuspected repulsive singularities, as well as new facts about
the existence and character of the gravitational field within spherically
symmetric vacuous cavities. The existence of these new solutions also led
to new and radically different conclusions about the concept of
gravitational collapse, as well as about the internal geometry and
structure of black holes.

The analysis of limits of sequences of shell solutions that approach the
exterior geometries of black holes and the formation of event horizons led
to a completely unexpected connection with the quantum aspects of
physics. We were able to reproduce, by purely classical means, the two
main conclusions of the study of quantum mechanics in the background
geometry of the exterior Schwarzschild solution, representing a naked
black hole. This led to the conclusion that general relativity seems to
contain remnants of some underlying quantum structure.

There is some ongoing work further exploring this connection of general
relativity with quantum field theory, for which it is necessary to use the
Euclidean lattice formulation of this theory. This connection is
made directly with the standard model of particle physics through the
spontaneous symmetry breaking mechanism involving the Higgs field. This
can be qualitatively commented on if there is time and interest.

The infall of a dipole and anti-dipole towards a Schwarzschild Black Hole (SBH), within the context of spherically symmetric spacetime, serves as a model for understanding the gravitational behavior of matter and antimatter. SBH is chosen as a prototype to represent the gravity of our Earth or any spherically symmetric heavenly object. Our findings indicate that in the geometrical units, the acceleration of dipoles and anti-dipoles can be either attracted or repelled, depending on the mass ($m$) of the gravitating center, dipole moment ($P$), and distance ($r$). In the physical units, however, the difference is far from being detectable, at least with the present technology. Therefore, the assumption that they always fall down is valid only by virtue of the huge mass of the Earth. Consequently, the detectability of the dipole correction is highly suppressed for massive central bodies such as the Earth, whereas satellite-based experiments in low-gravity environments may offer the sensitivity required to observe the effect. These results may shed light on the question of what happened to antimatter believed to have formed in the stages of the Big Bang. By providing new insights on the universe's imbalance between matter and antimatter, they may be able to clarify why matter eventually took over and gave rise to planets, stars, and galaxies, as well as our own existence.

Recent BAO (Baryonic Acoustic Oscillation) observations—large-scale clustering features of galaxies that act as a standard ruler for cosmic expansion—from dark energy surveys have reignited the debate over the dynamical nature of dark energy, revealing deviations from the standard LambdaCDM model at more than the 4sigma level. To capture departures from a cosmological constant, several parametric models of the dark energy equation of state have been proposed, often based on series expansions in redshift. These studies consistently suggest phantom behavior, characterized by an equation-of-state parameter, at higher redshifts. Such behavior is theoretically problematic, as it can lead to ghost instabilities, namely negative-energy degrees of freedom that render the theory unstable at the perturbative level.

Since the influence of dark energy naturally weakens at high redshifts, we propose a double-crossing, bell-shaped parametrization of the dark energy equation of state, where the cosmological constant boundary is crossed twice during cosmic evolution. This form is more sensitive to low-redshift dynamics compared to conventional series-based parametrizations. We show that this model exhibits transient phantom behavior (w<-1) near the matter–dark energy equality epoch, but evolves into a quintessential regime (w>-1) at present and at higher redshifts, thereby avoiding ghost-related instabilities. Such short-lived phantom behavior at low redshifts may arise from mechanisms such as non-minimally coupled gravity theories. Furthermore, we demonstrate that non-canonical scalar field models interacting with dark matter, when constrained by multiple cosmological probes, favor a quintessential-like evolution with no evidence for phantom behavior, supporting the possibility that modified gravity effects play a role primarily at low-redshift epochs.

The discovery of dark matter (DM) by Zwicky (1933) remains inconsistent within known physics. Astonishingly, a number of solar system observables exhibit unexpected “planetary dependencies”, even though no remote force beyond gravity exists. Question: Are persisting local mysteries also signals from the dark sector? Gravitational focusing of DM streams has short focal ranges since the impact goes with 1/(speed)2. Also, the inner mass distribution of solar system bodies acts as a gravitational lens, with amplification of streams being up to ~109, compared to few % for isotropic DM. The analysis of a number of observations within the solar system fits in the streaming DM scenario following gravitational lensing effects by solar system bodies. More specifically, analyzing secondaries from cosmic rays (CRs) points to streaming DM with the secondaries coming from the parent massive DM due to their self-annihilation, decay or interaction with ordinary matter. The secondaries provide the time stamp of the DM. New direct measurements of more CRs species can strengthen this result. All CR telescopes may have taken relevant data worth re-analyzing; the same applies to the data from direct DM searches. This is because only streaming DM can result occasionally in otherwise anomalous “planetary dependencies”. This is a new opportunity to unravel DM signatures hidden in existing data. This proposal is model-independent. So far the direct DM searches expect an annual distribution, while the underlying noise usually has a seasonal variation. In this proposal we overcome this noise problem by projecting the measured events (signal and noise), e.g., instead of on365 days, on the 88 and 225 days of the orbital periodicity of Mercury and Venus, respectively. So far the DM Axionantiquarknugget model by ZHITNITSKY is the inspiring favourite, while this approach is open to any other DM model.

Further reading: https://doi.org/10.22323/1.474.0035; https://arxiv.org/abs/2506.17676v2

Integrable quantum spin chains are fundamental models that are also widely used for the exploration of foundational aspects of quantum mechanics, offering a perfect arena to study key quantities such as entanglement, information scrambling, and quantum correlations. Yet, the utilised theoretical methods here still face major obstacles, especially for the computation of correlation functions. Recent years have seen substantial progress in the development of the powerful separation of variables (SoV) approach to quantum integrable models, which allows one to factorise the wavefunctions, opening gateways to many applications as well as clarifying the structure of the model's Hilbert space. In this talk, I will review the main results achieved in this program based on a series of recent papers with my collaborators. In particular, I will present the explicit construction of the SoV framework for integrable spin chains with gl(N) symmetry. I will explain how the SoV basis arises in this general setting, providing a representation-theoretic understanding of the method. I will then address a longstanding problem in the field, namely the computation of the SoV measure. I will show how our approach leads to a complete solution of this problem and, as a direct consequence, to new highly compact determinant representations for a broad class of physical quantities, including correlation functions and wavefunction overlaps. Furthermore, I will demonstrate the power and versatility of SoV in four-dimensional integrable conformal field theories, with a particular emphasis on the fishnet theory. In this context, I will present new results on the Yangian symmetry for a large and previously unexplored class of Feynman graphs. Finally, I will outline promising applications of these methods to the computation of exact correlators in planar N=4 super Yang–Mills theory and discuss several open directions for future research.

In the context of the theory of minimally modified gravity known as VCDM, one can realize any cosmological behavior at the level of the homogeneous and isotropic background without introducing fatal instabilities for perturbations. The ‘V’ in VCDM represents the variable function ?(?) that is introduced in this framework. Therefore, VCDM provides a theoretically consistent and observationally testable framework of dynamical dark energy parameterizations with or without phantom behaviors. In this paper, we propose the VCDM realizations of various phenomenological parameterizations present in the literature: the Chevallier–Polarski–Linder (CPL), Barboza–Alcaniz (BA), Jassal–Bagla–Padmanabhan (JBP), Exponential (EXP), and Logarithmic (LOG) models. Using the VCDM equations for cosmological perturbations, we test them against the recent cosmological datasets, Planck 2018 and DESI BAO DR2, and then discuss their implications. We find that the equation of state crosses the phantom regime (w < -1) at higher redshifts for all the paramterizations, as is also indicated by the DESI DR2 results. In principle, we confirm the phantom crossing of dynamical dark energy in a more stable theoretical framework of VCDM. Moreover, our approach does not rely on prior assumptions regarding the dynamics or microphysical origin of the equation of state, enabling a purely observational investigation into whether the dark energy transition favors a quintessence-like or phantom-like behavior. Together, these developments set the stage for a transformative decade in cosmology, one that may ultimately challenge and reshape our current theoretical paradigm.

Standard inflationary models, while successful, often require fine-tuned potentials to satisfy current observational constraints on the spectral index (n_s) and the tensor-to-scalar ratio (r). In this work, we propose a generalized cosmological framework based on fractional calculus, where the effective action includes non-local memory terms arising from a modified gravitational coupling. We investigate the dynamics of a scalar field against an n-dimensional Friedmann–Lemaitre–Robertson–Walker (FLRW) background, demonstrating that the fractional order parameter, α, introduces a cumulative friction term, (1 - α)/H^-1, into the background equations.

Crucially, we extend this analysis to linear cosmological perturbations. By enforcing variational consistency, we derive the Fractional Mukhanov–Sasaki equation, which explicitly incorporates memory effects. We solve this equation analytically for power-law inflation, obtaining exact mode functions in terms of Hankel functions. The resulting power spectra reveal that the spectral index and tensor-to-scalar ratio are modified by the fractional parameter, taking the form n_s(α, m) and r(α). We show that these memory effects can naturally suppress the tensor-to-scalar ratio without requiring complex potentials, bringing power-law inflation back into agreement with recent Planck and BICEP/Keck data. This framework offers a novel, mathematically rigorous mechanism to address the "fine-tuning" problems of standard inflation through the lens of non-local gravity.

The Heisenberg–Robertson uncertainty relation is a standard tool in quantum mechanics, but its use in non-Hermitian settings is not straightforward, especially in regimes with complex spectra and exceptional points. In this context, we study uncertainty relations for pseudo-Hermitian, in particular PT-symmetric Hamiltonians by introducing a metric operator in all spectral regimes. As a simple and widely used test case, we focus on a non-Hermitian two-level toy model with balanced gain and loss, which shows the transition from an exact PT-symmetric phase to a symmetry-broken phase through an exceptional point.

The chosen method is based on the explicit construction, in each regime, of a positive-definite metric operator that induces a modified inner product and defines the physical expectation values and variances. On this basis, we derive generalized Heisenberg–Robertson uncertainty relations for selected observables of the two-level model and compute their behavior in the exact, broken, and exceptional-point regions. In parallel, we construct a description in terms of a Lindblad master equation for the corresponding open two-level system and use it as a reference to compare with the non-Hermitian effective dynamics.

We find that the metric-based formulation restores an uncertainty relation with the same formal structure as in the Hermitian case, whereas the direct use of the standard inner product can lead to ill-defined quantities, in particular in the symmetry-broken phase and at the exceptional point. The comparison with Lindblad dynamics shows agreement between the metric-based description and features such as PT-symmetry breaking and decoherence. These results indicate that, even for a two-level toy model, an appropriate metric is necessary to obtain consistent uncertainty bounds and dynamical predictions from pseudo-Hermitian Hamiltonians.

Our research explores the sensitivity of satellite constellations to fluctuations in the quantum gravitational field, with the aim of quantifying their potential impact on critical operations and precision measurements. The main objective is to quantify the potential impact of hypothetical quantum effects on the precise orbital dynamics of satellite constellations. The methods employed will involve the development of a sophisticated computational model using MATLAB. Our model will simulate the trajectories of various satellite constellation configurations in two distinct gravitational frameworks: one based on classical general relativity and the other incorporating theoretical models of quantum gravitational fluctuations. The main task is to meticulously analyze and compare the resulting differences in key orbital parameters, including position, velocity, and orbital period, between these two scenarios. This comparative analysis is crucial in determining whether the minute stochastic perturbations resulting from quantum gravity could accumulate over time and measurably affect the performance and objectives of current and future high-precision satellite missions, such as those related to Earth observation, global navigation satellite systems (GNSSs), or space-based gravitational wave detectors. The expected results have provided essential insights into the potential need to integrate quantum gravitational corrections into very high-precision astrodynamics and will contribute significantly to ongoing theoretical and experimental efforts to unify quantum mechanics and general relativity at the macroscopic scale.

In this talk, I will discuss the notion of thermally averaged mean energy of a quantum harmonic oscillator strongly coupled to a heat bath, defined as the expectation value of the bare-system Hamiltonian in the canonical Gibbs state of the composite system, i.e., the system and bath taken together with their interactions. This quantity differs fundamentally from the thermodynamic internal energy obtained from the reduced partition function and provides an alternative perspective on the strong-coupling energetics. Using the Brownian quantum oscillator as a paradigmatic example, I will show how this mean energy can be consistently interpreted within the frameworks of quantum thermodynamics and stochastic energetics.

Based on the fluctuation–dissipation theorem, I will first show how the Lehmann–Kubo representation of the generalized susceptibility allows one to interpret the mean energy as the bare oscillator's energy contained within the dressed eigenmodes of the composite system. I will then show, using the quantum Langevin equation, that the mean energy obeys an exact energy-balance relation consistent with the framework of stochastic energetics, even in the presence of non-Markovian dissipation.

Finally, I will discuss analytical results for Ohmic dissipation with a Drude cutoff and show that, at low temperatures, the thermal part of the mean energy exhibits the same universal power-law behavior as the thermodynamic internal energy. The remaining difference between these two notions of energy is a temperature-independent contribution originating from system-bath correlations, highlighting the persistent role of the environment deep into the quantum regime.