Persistent tensions in the Hubble parameter ($H_0$) and the matter clustering amplitude ($S_8$) motivate theoretical extensions beyond the non-interacting dark sector assumed in $\Lambda$CDM. From an effective field theory perspective, a non-zero Yukawa interaction between a scalar dark-energy field $\phi$ and fermionic dark matter $\psi$ is technically natural unless prohibited by symmetry. In this work, we construct a microphysically consistent framework in which such an interaction emerges dynamically rather than being imposed phenomenologically.

We model the dark sector as an open quantum system, in which the scalar field constitutes a reduced subsystem that exchanges energy and information with an environmental dark-matter bath. Unlike a closed (unitary) quantum system, tracing over the fermionic degrees of freedom induces irreversible effects captured by a Lindblad evolution equation for the scalar density matrix. The scalar potential undergoes spontaneous symmetry breaking once the dark-matter density falls below a critical scale, inducing a time-dependent vacuum expectation value. The resulting interaction kernel $Q(a)$ and coupling profile $\beta(a)$ are therefore not free parameters, but consequences of the underlying symmetry-breaking and dissipative microphysics.

The resulting phenomenology is distinctive: the expansion history remains close to $\Lambda$CDM, while structure growth is modified through a late-time activation of the coupling. We test this against current large-scale structure and background probes using RSD, BAO, SN Ia, and CMB priors. A dynamical analysis—which self-consistently evolves both the background and perturbations—favours a late transition ($a_c \simeq 0.47$) and ($\beta_0 \simeq 0.52$). The model naturally suppresses the growth amplitude to $\sigma_{8,0} \simeq 0.59$ while simultaneously raising the inferred Hubble constant to $H_0 \simeq 69.6\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, suggesting that the $H_0$ and $S_8$ discrepancies may trace distinct physical origins. This places observationally inferred coupling strengths in direct correspondence with radiative stability constraints, making the next generation of spectroscopic surveys a decisive test of this class of models.

The Barrow holographic dark energy (BHDE) framework arises from Barrow entropy \cite{ Phys. Rev. D 102 (2020) 123525, Phys. Lett. B 808 (2020) 135643 }, which incorporates possible fractal deformations of the horizon surface and is characterized by the Barrow exponent Δ, thereby modifying the standard holographic dark energy scenario. We have studied the effect of dynamical radiation in the interacting Barrow holographic dark energy (BHDE) model for a non-flat universe. For both open and closed universes (“open” and “closed” refer explicitly to the sign of the spatial curvature parameter $k$ present in the FLRW metric ), we derived the evolution equations for the energy density parameters of dark energy, dark matter, and radiation by considering four different types of interactions among the other possible linear phenomenological forms. These coupled differential equations were then solved numerically to examine their behavior with respect to the redshift parameter. The variation of the dark energy equation-of-state parameter with redshift was also explored for the different interaction models. For all four interaction cases, we found that higher values of the Barrow exponent lead to a transition of the dark energy equation-of-state parameter from the quintessence region to the phantom region at late times, corresponding to lower redshift values. We also identified distinct epochs corresponding to dark energy–dark matter, dark energy–radiation, and dark matter–radiation crossings.

Using data from the Cosmic Chronometer, Baryon Acoustic Oscillation, and Pantheon+ samples, we constrained several cosmological parameters of the interacting BHDE model. The estimated Hubble parameter values in our model are higher than those predicted by the ΛCDM model. This result suggests that our framework could provide useful insights for future studies involving high-redshift data and may contribute to resolving the Hubble tension problem. A statistical comparison between our models and the ΛCDM model has also been carried out.

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.

In this presentation, I will demonstrate a natural and seamless occurrence of remnant scenarios within the confines of the original computation of Hawking. Hawking in his seminal work demonstrated that the black-hole evaporates thermally at a temperature inversely proportional to its mass $T_H = 1/M$; hence, it is unclear as to what happens in the final stages of the black-hole evaporation as $M \to 0$ due to it being a divergence of the black-hole temperature. A natural resolution to this issue is via remnant scenarios where a black-hole ceases evaporation at some temperature. There have been several attempts over the years to improve upon the computations of Hawking and realize the remnant scenario. However, these attempts rely on implementing extra constraints inspired from various theories of Quantum Gravity or Generalized Uncertainty Principles (GUPs). But we have demonstrated that these constraints are not essential and the remnant configuration can arise simply from the conformal symmetry that emerge in the $M\to 0$ limit of the theory. I will also show that the event horizon is dual to a matrix model which provides a physical mechanism for the formation of remnants. Note that matrix models are actually fermionic theories; therefore, this is suggestive of fermionization of the black-hole event horizon as well.