When investigating various issues in cosmology and other areas of general relativity, a perfect fluid is usually considered. A perfect fluid is one with negligible viscosity and heat conduction. However, this is only an idealisation, and in more realistic situations, dissipative effects need to be considered. Secondly, there are several "constants of nature" such as Newton's gravitational constant $G$, the cosmological constant $\Lambda$, the speed of light $c$, the fine-structure constant $\alpha$, Boltzmann’s constant $\Bar{h}$, Planck’s constant and Fermi’s constant $G_F$, which may not necessarily be constant, but could be varying. There have been several studies carried out with bulk viscosity together with variable $G$ and $\Lambda$. In these studies, the modified energy conservation equation can be split up into the traditional equation, plus an equation involving the parameters $G$ and $\Lambda$. However, many authors have split the full equation in such a way that the viscosity appears in the wrong equation. In such a situation, it is not possible to obtain the correct general relativistic limiting case. In this work, the relevant equations are re-analysed, showing that the bulk viscosity needs to be incorporated into the other equation and highlighting how the general relativistic limit is obtained.

I will discuss recent progress in string cosmology. Incorporating all-order α′ corrections leads to a far richer and more self-consistent picture of the pre-Big Bang universe. Within this more complete framework, the early universe can evolve smoothly through a genuinely non-singular bounce, allowing a continuous transition between two dual cosmological phases without encountering the usual curvature singularity. This mechanism provides a natural way to resolve the classical Big Bang singularity while remaining firmly grounded in string-theoretic principles. Moreover, when an appropriate potential is introduced for the dilaton, the same setup can stabilize the string coupling at late times, preventing it from running to strong coupling. This dynamical stabilization enables the emergence of realistic cosmological epochs, such as matter domination or even a period of de Sitter-like accelerated expansion, within a unified string-inspired description. These theoretical developments significantly broaden the phenomenological landscape. During the high-curvature string phase, small variations in the sound speed of cosmological perturbations can dramatically boost the production of primordial black holes, potentially bringing their abundance into the open window for dark matter. Likewise, recent hints from NANOGrav of a stochastic gravitational-wave background can be naturally accommodated by non-minimal versions of the pre-Big Bang scenario, in which stringy corrections enhance gravitational wave production. Taken together, these results suggest that genuinely stringy effects may leave measurable traces in today’s universe, offering a promising bridge between fundamental theory and near-future observations.

Lepton Flavour Violation (LFV) is one of the important topics of High-Energy Physics in recent days
and $\Upsilon$ is one of the suited candidates to explore the early universe. Upsilons decay into muons through the annihilation of the bound state of quarks and gluons. Since the discovery of these particles,
they have drawn much attention in understanding their characteristics experimentally and theoretically. The radiative and the lepton flavour-conserving decays are already well established via observations in small systems. On the other hand, their lepton flavour violating part is still unexplored in colliders and also in BSM physics. Also, this quarkonium candidate shows
unique behaviour at high temperatures and densities. The colliders are also probing the LFV decays in the search of NP. Motivated by the study of the LFV decays, we will present and discuss various LFV decays of Upsilons, incorporating the contribution of the Z' boson. Here, we have also constrained the maximum allowed values of the New Physics (NP) quark couplings to predict the upper
bound of the LFV branching ratios. The NP couplings are constrained with the available experimental data using the chi-square fitting technique. Connections of BSM physics with QCD avenues will be also presented and discussed.

The nature of dark energy (DE) challenges our comprehension of the cosmos, appearing as the source responsible for the Universe’s accelerating expansion. This work considers the Einstein Cosmological Constant (Λ_E) as a manifestation of DE, interpreted through the lens of Reparametrization Invariant Scaling Symmetry (RISS). Within this paradigm, Λ_E emerges as a “kinetic energy” term, derived from relative temporal motion, setting it apart from the conventional kinetic energy based on spatial relative motion.

Central to this exploration is the scale factor λ(t), representing a reparametrization capable of rendering Λ_E dynamically within the extended equations of Einstein’s General Relativity (EGR) as Λ = Λ_E λ² . Through meticulous derivations, the governing equations of λ(t) and its interplay with Λ_E are articulated. Imposing reparametrization symmetry on the equations of motion reveals a new avenue for addressing the missing mass problem evident at galactic and extragalactic scales. Here, improper/non-affine (non-co-moving) temporal parameterizations introduce fictitious forces, whose presence is reconciled through the symmetry framework.

This symmetry-based approach naturally yields the MOND-like relationship g² ∼ (a₀g_N), where g denotes gravitational acceleration, a₀ represents the fundamental MOND acceleration, and g_N is the Newtonian acceleration. The theoretical predictions for Λ_E and a₀ demonstrate remarkable alignment with their observed magnitudes, lending credence to this interpretation. This synthesis underscores a potential unifying principle in our understanding of dark energy and dark matter phenomena.

We present an extensive and systematic investigation of the semileptonic B_c → V decays within the self-consistent Covariant Light-Front Quark Model (CLFQM), a framework that provides a covariant and internally consistent description of hadronic transition dynamics in heavy–heavy meson systems. Traditional light-front approaches often suffer from ambiguities associated with spurious ω-dependence and zero-mode contributions, which can distort the extraction of physical form factors. The self-consistent CLFQM addresses these challenges by imposing explicit self-consistency conditions on the light-front vertex functions, thereby eliminating spurious contributions and ensuring that the resulting hadronic matrix elements are covariant and free from model artifacts. Within this refined theoretical framework, we compute the complete set of vector and axial-vector form factors for the B_c → V transitions and examine their behavior across the entire kinematic range. To achieve a stable and reliable representation of their q²-dependence, we employ a model-independent z-series expansion. Using these form factors, we present numerical predictions for a variety of physical observables, including branching fractions, forward–backward asymmetry, lepton-polarization fractions, etc. The results highlight the improved internal consistency and predictive capability of the self-consistent CLFQM and offer updated Standard Model benchmarks for B_c semileptonic channels. This study contributes to a deeper understanding of nonperturbative QCD effects in heavy meson systems and supports ongoing experimental and theoretical efforts aimed at probing heavy-quark dynamics and testing lepton-flavor universality.

This study examines how inflationary dynamics are affected by f(R)-theories with a non-minimal coupling between matter and curvature. Both positive and negative corrections to the minimal coupling of General Relativity are considered, and a robust numerical method is developed that evolves the metric and the inflaton field in this modified theory beyond slow-roll. Through a stability analysis, we find that positive models are inherently unstable during slow-roll, whereas negative ones can accommodate a stable attractor de Sitter solution. Using the amplitude of the scalar power spectrum from the latest data releases, we constrain the scale of the non-minimal coupling to be above 10¹³ GeV. In light of the 2018 Planck, BICEP/Keck and the recent Atacama Cosmology Telescope data for the scalar spectral index and tensor-to-scalar ratio, strong constraints on the coupling strength force the effects of these modified theories to be, at most, slightly above the perturbative level. Furthermore, we determine that the choice of the perfect fluid matter Lagrangian does not impact the inflationary observables at the pivot scale. Finally, we present the predicted observables for different inflationary potentials and show that even though classical gravity is still preferred by the data, there are areas of the parameter space that are viable for non-minimally coupled inflationary models.

Chiral cosmological models (CCM) can be used to describe not only inflation, but also the formation of primordial black holes (PBH) in the early Universe, because these models can produce large amplitude peaks at small scales. CCMs are related to modified gravity models through a conformal transformation of the metric. Two-field CCMs are actively studied. One of the most well-known modified gravity models that leads to such a CCM is the Higgs-$R^2$ inflationary model, which reproduces the Planck/BICEP observational data, but deviates from more recent data of the Atacama Cosmological Telescope (ACT).
In two-field CCMs with PBH formation, inflation includes two stages. In the first stage, one scalar field evolves, while the second one remains almost constant. This stage satisfies the slow-roll conditions, which allows us to calculate the inflationary parameters using the slow-roll approximation. The second stage of inflation corresponds to the evolution of the second scalar field. The slow-roll regime is violated during a few e-folds after the end of the first stage of inflation. After that, the slow-roll approximation is restored. This breaking of the slow-roll approximation is a necessary condition for PBH formation. The duration of the second inflationary stage affects the mass of these PBHs.
We have constructed new two-field CCMs that are connected with induced and F(R) gravity models. At certain values of the model parameters, these models are in good agreement with ACT observation data and are suitable to describe the formation of primordial black holes with masses similar to those of dark matter candidates. This talk is based on the papers by E.O. Pozdeeva and S.Yu. Vernov (Phys. Part. Nucl. 56 (2025) 542 [arXiv:2407.00999] and arXiv:2509.21220) as well as recent investigations.

According to the Bodmer–Witten hypothesis, ordinary nuclear matter is just a metastable state of the so-called strange quark matter. If it already exists in the universe, it can manifest as quark stars. Since this type of compact star has properties somewhat similar to neutron stars, one might think of them as potential candidates satisfying modern pulsar measurements. In this work, we study the radial and non-radial oscillations of hot and lepton-rich quark stars, i.e., instants after their potential birth in supernovae events. In order to calculate their fundamental-mode frequencies, we use a density-dependent quark mass framework for microphysics to build the equation of state, solve the eigenvalue problem to determine their radial stability, and use the full general-relativistic perturbative framework of non-radial oscillations. We found that their dependencies on the gravitational masses, compactness, and energy densities display remarkable differences compared to widely studied protoneutron stars. In order to quantify these differences, we build and propose some universal relations correlating all these stellar parameters. As expected, similar hadronic universal relations depart from our results. In this sense, our findings may serve as a smoking gun to distinguish strange quark stars from ordinary nuclear neutron stars using upcoming gravitational-wave data in the multimessenger astronomy era.

Models with nonminimally coupled scalar fields and F(R) gravity models are some of the most popular modified gravity models of cosmological inflation. Using the conformal transformation of the metric, one can transform the original modified gravity models to the General Relativity models with minimally coupled scalar fields; in other words, using the Einstein frame. The standard way to construct such modified gravity models is to consider them in the Einstein frame using slow-roll approximation. For the simplest inflationary F(R) gravity models, including the Starobinsky R+R² inflationary model, this method gives precise results, but F(R) gravity models with more complicated functions F(R) usually correspond to the inflaton potential given in the parametric form. Such F(R) functions usually appear in the models that describe not only inflation, but also primordial black hole formation.

The slow-roll approximation is a method used to analyse the dynamical properties of the early universe during inflation. We propose new versions of the slow-roll approximation for inflationary models with nonminimally coupled scalar fields and F(R) gravity models. We investigate the inflationary dynamics in the initial (Jordan) frame without the use of the conformal transformation and rewrite evolution equations in the Jordan frame in a form that is similar to the Friedmann equations in the Einstein frame. The proposed slow-roll approximations are described in the papers by E.O. Pozdeeva, M.A. Skugoreva, A.V. Toporensky, and S.Yu. Vernov, JCAP 05 (2025) 081 and S.V. Ketov, E.O. Pozdeeva, and S.Yu. Vernov, JCAP 12 (2025) 40. This approximation allows us to construct a new inflationary model with the fifth-order polynomial F(R) function. This model is in good agreement with the recent observations of the cosmic microwave background radiation obtained by the Atacama Cosmology Telescope. The presentation is based on these papers and recent results.

We investigate the generation of the matter–antimatter asymmetry in the early universe, prior to the electroweak phase transition, by extending the Standard Model with three right-handed neutrinos that complete Dirac mass terms and two heavy scalar fields. This constitutes a minimal and well-motivated Beyond-the-Standard-Model framework, since the Standard Model alone cannot account for neutrino masses or produce the observed baryon asymmetry due to insufficient CP violation. Using the Closed Time Path (CTP) formalism, we analyze-2-by 2 scattering processes mediated by heavy off-shell scalars. Since these scalars remain off-shell throughout, the post-inflationary temperature of the universe does not need to be high enough to produce them on-shell.

In this setup, right-handed neutrinos depart from thermal equilibrium, generating a lepton asymmetry that is subsequently converted into the observed baryon asymmetry via sphaleron processes. We compute the resulting baryon-to-photon ratio and compare it with the observational value reported by the Planck mission. We also compare the predicted contribution of the right-handed neutrinos to the effective number of relativistic species N_{eff}​ with current cosmological bounds, confirming the model’s consistency with observations.

The use of the CTP formalism eliminates the need for Real Intermediate State (RIS) subtraction, leading to a more consistent and elegant treatment. Furthermore, by incorporating quantum statistical factors, we demonstrate that viable asymmetry generation is achievable even with only two right-handed neutrino flavours. Consequently, the mechanism is generic and does not rely on specific particle species such as leptoquarks or other particular Standard Model extensions.