Non-Gaussianity in the primordial curvature perturbation is a crucial element of the early universe due to its significant impact on the primordial black hole (PBH) production. In this work, we focus on the effects of negative non-Gaussianity on PBH abundance through the lens of the compaction function criterion for PBH formation. Our setup utilizes an effective field theory of non-singular bounce, including the standard slow-roll inflation with an ultra-slow roll phase for amplifying the curvature perturbations to form PBHs. We investigate with two separate values of the non-Gaussianity parameter, $$f_\textrm{NL}=(-\,39.95,-\,35/8)$$ f NL = ( - 39.95 , - 35 / 8 ) , found within the ekpyrotic contraction and the matter bounce scenarios, respectively, and show that a negatively large amount of $$f_\textrm{NL}$$ f NL can provide sizeable abundance, $$10^{-3}\leqslant f_\textrm{PBH}\leqslant 1$$ 10 - 3 ⩽ f PBH ⩽ 1 , and completely mitigates the PBH overproduction issue. We also highlight that the case with the effective sound speed $$c_{s}=1$$ c s = 1 , coupled with $$f_\textrm{NL}=-\,39.95$$ f NL = - 39.95 , provides an agreement under $$1\sigma $$ 1 σ for the scalar-induced gravitational wave explanation of the latest PTA (NANOGrav15 and EPTA) signal. Lastly, we extract an upper bound on the most negative value of, $$f_\textrm{NL}\sim -60$$ f NL ∼ - 60 , below which we show breaching of the underlying perturbativity constraints on the power spectrum amplitude.

This paper investigates the implications of effective Quantum Chromodynamics (QCD) models for dark matter phenomenology, with a particular focus on the role of QCD phase transitions, topological defects, and low-energy effective models in understanding dark matter's nature and behavior. We begin by analyzing the formation and thermodynamic properties of the quark-gluon plasma (QGP) in the early Universe, emphasizing the speed of sound \( c_s^2 \) and its effects on primordial density fluctuations, which are crucial for the formation of large-scale structures. The thermodynamic relation \( c_s^2 = \frac{\partial p}{\partial \epsilon} \) is used to model the impact of these fluctuations on the evolution of the Universe. Topological structures arising from scale symmetry breaking during the rapid cooling phase of the early Universe, are explored as potential candidates for dark matter. These structures are shown to bridge the gap between QCD and cosmology, providing insights into the dark matter sector and predicting the presence of axions or other relic particles that could contribute to dark matter's observed properties. The paper also presents an in-depth study of Skyrme solitons and their potential to act as dark matter analogues. We examine the clustering dynamics of Skyrme solitons within dark matter halos, revealing a significant dependence of the soliton's energy density and stability on soliton number \( N \) and dark matter density \( \rho_{\text{DM}} \). Numerical simulations show a strong increase in system energy as both \( N \) and \( \rho_{\text{DM}} \) are increased, highlighting the role of solitons in dark matter clustering and the formation of cosmological structures. The dynamical mass \( M(T) \) of scalar fields in the presence of gravitational couplings and chemical potentials is analyzed, showing clear dependencies on the scalar field mass \( m_0 \), temperature \( T \), and gravitational coupling \( G \). The findings indicate that variations in the chemical potential \( \mu \) lead to significant changes in mass distribution, corroborating predictions from quantum field theory (QFT) and cosmological models. Further, Chiral Perturbation Theory (ChPT) is extended to the dark sector, where SU(N) symmetries govern dark matter interactions. This extension reveals new annihilation channels for dark matter and links dark sector dynamics with cosmological observables, such as the cosmic microwave background (CMB) and dark matter relic abundance. The effect of ChPT on dark matter perturbations and large-scale structure formation is analyzed, emphasizing the role of higher-order corrections to scattering amplitudes and cross-sections in shaping the evolution of dark matter.

We present a comprehensive study of gravitational exciton dynamics arising from higher-dimensional theories, with a focus on establishing a robust effective framework that incorporates self-interactions, higher-derivative corrections, and quantum effects. Starting from a \( D \)-dimensional Einstein--Hilbert action on a warped product manifold, we perform a systematic dimensional reduction to obtain a four-dimensional effective action in the Einstein frame. Our formulation extends the classical potential by including self-interacting moduli fields and RG-improved parameters via the Coleman--Weinberg mechanism, thereby accounting for both matter and graviton loop corrections. The resulting renormalization group flow modifies the effective mass and coupling constants, which in turn plays a critical role in moduli stabilization and the low-energy phenomenology.Taking the non-relativistic limit, we derive a Gross--Pitaevskii equation that governs the dynamics of the gravitational exciton condensate, and couple it self-consistently with Poisson’s equation to capture gravitational backreaction. Through both variational and numerical analyses, we obtain stationary solutions in spherically symmetric, rotating, and anisotropic configurations, and perform a linear stability analysis using the Bogoliubov--de Gennes formalism. Our results reveal a Bogoliubov dispersion relation that exhibits a phonon-like linear regime at low momenta, transitioning to quadratic free-particle behavior at high momenta.

The black hole entropy problem, often framed through the semi-classical relation between horizon area and entropy, challenges the consistency of quantum gravity and thermodynamic principles. Within the framework of string theory, Fuzzball solutions offer a nontrivial resolution by positing that black holes are ensembles of horizonless microstates, whose degeneracy matches the leading-order entropy scaling predicted by $S \sim A$. This paper conducts a comparative analysis of Fuzzball microstate geometries against other competing proposals, such as holographic dualities, where $S_{\text{CFT}}$ asymptotically approaches black hole entropy and approaches derived from loop quantum gravity, which quantize spacetime at the Planck scale. Recent advancements in the moduli space of supersymmetric and near-extremal Fuzzball solutions have pushed forward our understanding of microstate counting, though extending these solutions to nonextremal configurations remains a formidable challenge. Moreover, the emergence of Hawking radiation as a coherent quantum process, while preserving unitarity, raises new questions about the completeness of the Fuzzball paradigm in resolving the information paradox. In this work, we explore the complex interplay between gravitational entropy, quantum information, and the non-local structure of spacetime, ultimately confronting the limitations and future directions of Fuzzball theory in addressing the full range of gravitational entropy phenomena.

We study the three-loop gauge \(\beta\)-functions in general \(\mathcal N=1\) supersymmetric gauge theories regularized by higher-covariant-derivatives (HCD) supplemented with Pauli–Villars subtraction. The all-structure three-loop form of the \(\beta\)-functions in the HCD framework is known and involves regulator-dependent parameters. Here we evaluate these parameters explicitly for the exponential regulators \(R(x)=e^{x^n}\) and \(F(x)=e^{x^m}\). We obtain the constants \(A(n)\) and \(B(m)\) in closed form, together with their large-\(n,m\) asymptotics, and substitute them into the general three-loop expressions. This yields fully explicit, regulator-parameterized \(\beta\)-functions and a systematic expansion in \(1/n\) and \(1/m\) that organizes finite, scheme-dependent terms. We then introduce finite coupling redefinitions that map the renormalized \(\overline{\mathrm{DR}}\) result to a scheme compatible with the Novikov–Shifman–Vainshtein–Zakharov relation. Our analysis clarifies how exponential higher-derivative regulators preserve this relation at the bare level and illustrates the regulator-driven structure of supersymmetric renormalization group flows.

We study a generalized holographic dark energy model in which the infrared cutoff depends on the Hubble parameter and its first two time derivatives. The inclusion of the $\ddot H$ term introduces a finite relaxation timescale for the horizon degrees of freedom, which can be interpreted as an effective entropic inertia of the holographic vacuum energy. The resulting background dynamics admit late--time solutions in which the cosmic expansion gradually halts. In the underdamped regime, the Hubble parameter undergoes exponentially damped oscillations and asymptotically approaches $H\to0$. The scale factor grows monotonically but by a finite amount, while curvature invariants decay exponentially, leading to an asymptotically Minkowski spacetime without future singularities. We confront the full nonlinear background evolution with cosmic chronometer measurements of the Hubble parameter and find good agreement with current late--time expansion data, with a reduced chi--squared $χ^2/ν\simeq0.52$. At observable redshifts, oscillatory features are strongly suppressed and remain consistent with existing constraints.