arXiv subjects

Pierros Ntelis

Publications and source records attributed to Pierros Ntelis.

13 recordsLinked to original sources

arXiv2026

Advanced manifold-metric pairs

This article presents a novel mathematical formalism for advanced manifold--metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their associated metric spaces using functional methods, with a focus on integrating concepts from mathematical physics, field theory, topology, algebra, probability, and statistics. Our methodology employs rigorous mathematical construction proofs and logical foundations to develop generalized manifold--metric pairs, including homogeneous and isotropic expanding manifolds, as well as probabilistic and entropic variants. Key results include the establishment of metrizability for topological manifolds via the Urysohn Metrization Theorem, the formulation of higher-rank tensor metrics, and the exploration of complex and quaternionic codomains with applications to cosmological models like the expanding spacetime. By combining spacetime generalized sets with information-theoretic and probabilistic approaches, we achieve a unified framework that advances the understanding of manifold--metric interactions and their physical implications.

math.GN↗

arXiv2026

Analytical $poly\Lambda$CDM dynamics

We develop a novel analytical dynamical analysis to derive precise energy density ratio evolutions for the $\phi$CDM and $poly\Lambda$CDM models, comparing them to the standard $\Lambda$CDM model and validating against numerical solutions. Analytical solutions for the quintessence, i.e. $\phi$CDM, show sub percent agreement with $\Lambda$CDM with greater reliability than numerical integration of stiff systems. The $poly\Lambda$CDM model, a phenomenological modified gravity framework, captures radiation, matter, dark energy, and exotic epochs, offering a streamlined yet comprehensive alternative to existing studies. Its dynamics reveal a global transition from a dark energy-dark matter exchange reflector, through saddle points of matter, radiation, curvature, and modified gravity, to an SVT modified gravity attractor-saddle, and finally to a cosmological constant attractor in the far future, with saddle transitions between modified gravity components. The $poly\Lambda$CDM model integrates modified gravity models, using dynamical analysis to distinguish observationally viable critical points and differentiate gravity epochs. All three models align with observed cosmic evolution, but $poly\Lambda$CDM richer phenomenology provides deeper insights into modified gravity dynamics. Code available at GitHub.

gr-qc↗

arXiv2026

Chaotic motion and power spectral density in Schwarzschild Bertotti-Robinson black hole spacetime

In this paper, we show that in weak field limit Schwarzschild Bertotti-Robinson black hole (Schwarzschild-BR BH) turns into Schwarzschild black hole immersed in external uniform magnetic field which is given in 1. The dynamics of both magnetized and electrically charged particles in the vicinity of a Schwarzschild-BR black hole are investigated. The innermost stable circular orbits (ISCOs) for both magnetized and electrically charged particles are examined in detail, revealing that the magnetic field parameter B exerts a considerable influence, leading to an increase in the ISCO radius. The orbital and epicyclic motion of test particles in Schwarzschild-BR black hole spacetime was analyzed, including both circular orbits and their oscillatory perturbations. Additionally, the trajectories of both magnetized and electrically charged particles are analyzed for various configurations of the magnetic parameter B. We also demonstrate how the magnetic field B, electric charge q, and magnetic moment {\mu} influence the dynamics of charged particles, specifically affecting the chaotic behavior, Poincare' sections, oscillatory frequencies and power spectral density.

gr-qc↗

arXiv2025

Simple $\phi\Lambda$ CDM dynamics

In this paper, we introduce the $\phi\Lambda$CDM model and compare it to the concordance model. We present their respective epoch evolutions, perform a detailed dynamical analysis for each model, and conduct a comparative analysis between the two. This study revitalizes these models by considering systems with a higher number of variables. Additionally, the $\phi\Lambda$CDM model we present is both more comprehensive and simpler than those found in the literature, as it accounts for all known epochs, including the radiation, matter, and dark energy phases. Notably, existing studies on this model often omit the radiation epoch and focus on simpler dynamics. We find that both models, the $\phi\Lambda$CDM and the $\Lambda$CDM, can describe the generally accepted scenario of cosmic evolution, and current observations. Both models, describe qualitative and quantitative current observations about the epoch behaviour of the species of the universe. We find the $\phi\Lambda$CDM model has the following exotic transition from a \textit{dominant radiation energy density ratio} epoch, or a \textit{low scalar kinetic term energy density ratio} epoch, towards a \textit{dominant cosmological constant energy density ratio} epoch. This renders the $\phi\Lambda$CDM a richer phenomenologically model than the concordance cosmological model. The software of the study is publicly available online.

gr-qc↗

arXiv2022

Optimal 1D Ly$α$ Forest Power Spectrum Estimation -- II. KODIAQ, SQUAD & XQ-100

We measure the 1D Ly$\,α$ power spectrum $P_\mathrm{1D}$ from Keck Observatory Database of Ionized Absorption toward Quasars (KODIAQ), The Spectral Quasar Absorption Database (SQUAD) and XQ-100 quasars using the optimal quadratic estimator. We combine KODIAQ and SQUAD at the spectrum level, but perform a separate XQ-100 estimation to control its large resolution corrections in check. Our final analysis measures $P_\mathrm{1D}$ at scales $k<0.1\,$s$\,$km$^{-1}$ between redshifts $z=$ 2.0 -- 4.6 using 538 quasars. This sample provides the largest number of high-resolution, high-S/N observations; and combined with the power of optimal estimator it provides exceptional precision at small scales. These small-scale modes ($k\gtrsim 0.02\,$s$\,$km$^{-1}$), unavailable in Sloan Digital Sky Survey (SDSS) and Dark Energy Spectroscopic Instrument (DESI) analyses, are sensitive to the thermal state and reionization history of the intergalactic medium, as well as the nature of dark matter. As an example, a simple Fisher forecast analysis estimates that our results can improve small-scale cut off sensitivity by more than a factor of 2.

astro-ph.CO↗

arXiv2022

A $(D_\tau,D_x)$-manifold with $N$-correlators of $N_t$-objects

In this paper, we describe a mathematical formalism for a $(D_\tau,D_x)$-dimensional manifold with $N$-correlators of $N_t$ types of objects, with cross correlations and contaminants. In particular, we build this formalism using simple notions of mathematical physics, field theory, topology, algebra, statistics n-correlators and Fourier transform. We discuss the applicability of this formalism in the context of cosmological scales, i.e. from astronomical scales to quantum scales, for which we give some intuitive examples.

physics.gen-ph↗

arXiv2021

Testing the theory of gravity with DESI: estimators, predictions and simulation requirements

Shortly after its discovery, General Relativity (GR) was applied to predict the behavior of our Universe on the largest scales, and later became the foundation of modern cosmology. Its validity has been verified on a range of scales and environments from the Solar system to merging black holes. However, experimental confirmations of GR on cosmological scales have so far lacked the accuracy one would hope for -- its applications on those scales being largely based on extrapolation and its validity sometimes questioned in the shadow of the unexpected cosmic acceleration. Future astronomical instruments surveying the distribution and evolution of galaxies over substantial portions of the observable Universe, such as the Dark Energy Spectroscopic Instrument (DESI), will be able to measure the fingerprints of gravity and their statistical power will allow strong constraints on alternatives to GR. In this paper, based on a set of $N$-body simulations and mock galaxy catalogs, we study the predictions of a number of traditional and novel estimators beyond linear redshift distortions in two well-studied modified gravity models, chameleon $f(R)$ gravity and a braneworld model, and the potential of testing these deviations from GR using DESI. These estimators employ a wide array of statistical properties of the galaxy and the underlying dark matter field, including two-point and higher-order statistics, environmental dependence, redshift space distortions and weak lensing. We find that they hold promising power for testing GR to unprecedented precision. The major future challenge is to make realistic, simulation-based mock galaxy catalogs for both GR and alternative models to fully exploit the statistic power of the DESI survey and to better understand the impact of key systematic effects. Using these, we identify future simulation and analysis needs for gravity tests using DESI.

astro-ph.CO↗

arXiv2021

Cosmological constraints from cosmic homogeneity

In this paper, we study the normalised characteristic scale of transition to cosmic homogeneity, $\mathcal{R}_H/d_V$, as a cosmological probe. We use a compilation of SDSS galaxy samples, comprising more than $10^6$ galaxies in the redshift range $0.17 \leq z \leq 2.2$ within the largest comoving volume to date, $\sim 8 h^{-3}\mathrm{Gpc}^3$. We show that these samples can be described by a single bias model as a function of redshift. By combining our measurements with prior Cosmic Microwave Background and Lensing information from the Planck satellite, we constrain the total matter density ratio of the universe, $Ω_m = 0.363 \pm 0.025$, and the Dark Energy density ratio, $Ω_Λ = 0.649 \pm 0.021$, improving the values from Planck alone by 31% and 28%, respectively. Our results are compatible with a flat $Λ$CDM model. These results show the complementarity of the normalised homogeneity scale with other cosmological probes and open new roads to cosmometry.

astro-ph.CO↗

arXiv2018

The scale of cosmic homogeneity as a standard ruler

In this paper, we study the characteristic scale of transition to cosmic homogeneity of the universe, $\mathcal{R}_H$, as a standard ruler, to constrain cosmological parameters on mock galaxy catalogues. We use mock galaxy catalogues that simulate the CMASS galaxy sample of the BOSS survey in the redshift range $0.43 \leq z \leq 0.7$. In each redshift bin we obtain the homogeneity scale, defined as the scale at which the universe becomes homogeneous to $1\%$, i.e. $D_2(\mathcal{R}_H) = 2.97$. With a simple Fisher analysis, we find that the performance of measuring the cosmological parameters with either the position of the BAO peak or the homogeneity scale is comparable. We show that $\mathcal{R}_H$ has a dependence on the galaxy bias. If the accuracy and precision of this bias is achieved to $1\%$, as expected for future surveys, then $\mathcal{R}_H$ is a competitive standard ruler.

astro-ph.CO↗

arXiv2018

Homogeneity in the search of the Dark Sector

In the era of precision cosmology, we investigate an novel method to probe the Dark Universe. By studying the fractality of the universe, we estimate a characteristic scale of homogeneity. Using a fisher analysis, we investigate the potential impact of this scale to the cosmological information we can gain from the Euclid satellite, and therefore understand the nature of Dark Energy and Dark matter of our universe.

astro-ph.CO↗

arXiv2017

Exploring cosmic homogeneity with the BOSS DR12 galaxy sample

In this study, we probe the transition to cosmic homogeneity in the Large Scale Structure (LSS) of the Universe using the CMASS galaxy sample of BOSS spectroscopic survey which covers the largest effective volume to date, $3\ h^{-3}\ \mathrm{Gpc}^3$ at $0.43 \leq z \leq 0.7$. We study the scaled counts-in-spheres, $\mathcal{N}( 2.97$ for $r>\mathcal{R}_H$, we find $\mathcal{R}_H = (63.3\pm0.7) \ h^{-1}\ \mathrm{Mpc}$, in agreement at the percentage level with the predictions of the $Λ$CDM model $\mathcal{R}_H=62.0\ h^{-1}\ \mathrm{Mpc}$. Thanks to the large cosmic depth of the survey, we investigate the redshift evolution of the transition to homogeneity scale and find agreement with the $Λ$CDM prediction. Finally, we find that $\mathcal{D}_2$ is compatible with $3$ at scales larger than $300\ h^{-1}\ $Mpc in all redshift bins. These results consolidate the Cosmological Principle and represent a precise consistency test of the $ΛCDM$ model.

astro-ph.CO↗

arXiv2016

A 14 $h^{-3}$ Gpc$^3$ study of cosmic homogeneity using BOSS DR12 quasar sample

The BOSS quasar sample is used to study cosmic homogeneity with a 3D survey in the redshift range $2.2<z<2.8$. We measure the count-in-sphere, $N(<\! r)$, i.e. the average number of objects around a given object, and its logarithmic derivative, the fractal correlation dimension, $D_2(r)$. For a homogeneous distribution $N(<\! r) \propto r^3$ and $D_2(r)=3$. Due to the uncertainty on tracer density evolution, 3D surveys can only probe homogeneity up to a redshift dependence, i.e. they probe so-called "spatial isotropy". Our data demonstrate spatial isotropy of the quasar distribution in the redshift range $2.2<z<2.8$ in a model-independent way, independent of any FLRW fiducial cosmology, resulting in $3-\langle D_2 \rangle < 1.7 \times 10^{-3}$ (2 $σ$) over the range $250<r<1200 \, h^{-1}$Mpc for the quasar distribution. If we assume that quasars do not have a bias much less than unity, this implies spatial isotropy of the matter distribution on large scales. Then, combining with the Copernican principle, we finally get homogeneity of the matter distribution on large scales. Alternatively, using a flat $Λ$CDM fiducial cosmology with CMB-derived parameters, and measuring the quasar bias relative to this $Λ$CDM model, our data provide a consistency check of the model, in terms of how homogeneous the Universe is on different scales. $D_2(r)$ is found to be compatible with our $Λ$CDM model on the whole $10<r<1200 \, h^{-1}$Mpc range. For the matter distribution we obtain $3-\langle D_2 \rangle < 5 \times 10^{-5}$ (2 $σ$) over the range $250<r<1200 \, h^{-1}$Mpc, consistent with homogeneity on large scales.

astro-ph.CO↗

arXiv2016

The Homogeneity Scale of the universe

In this study, we probe the cosmic homogeneity with the BOSS CMASS galaxy sample in the redshift region of $0.43 < z < 0.7$. We use the normalised counts-in-spheres estimator $\mathcal{N}(<r)$ and the fractal correlation dimension $\mathcal{D}_{2}(r)$ to assess the homogeneity scale of the universe. We verify that the universe becomes homogenous on scales greater than $\mathcal{R}_{H} \simeq 64.3\pm1.6\ h^{-1}Mpc$, consolidating the Cosmological Principle with a consistency test of $Λ$CDM model at the percentage level. Finally, we explore the evolution of the homogeneity scale in redshift.

astro-ph.CO↗