arXiv subjects

Genly Leon

Publications and source records attributed to Genly Leon.

At least 37 records · Page 2Linked to original sources

arXiv2025

Cosmological phase-space analysis of $f(G)$-theories of gravity

The impact of topological terms that modify the Hilbert-Einstein action is here explored by virtue of a further $f(G)$ contribution. In particular, we investigate the phase-space stability and critical points of an equivalent scalar field representation that makes use of a massive field, whose potential is function of the topological correction. To do so, we introduce to the gravitational Action Integral a Lagrange multiplier and model the modified Friedmann equations by virtue of new non-dimensional variables. We single out dimensionless variables that permit \emph{a priori} the Hubble rate change of sign, enabling regions in which the Hubble parameter either vanishes or becomes negative. In this respect, we thus analyze the various possibilities associated with a universe characterized by such topological contributions and find the attractors, saddle points and regions of stability, in general. The overall analysis is carried out considering the exponential potential first and then shifting to more complicated cases, where the underlying variables do not simplify. We compute the eigenvalues of our coupled differential equations and, accordingly, the stability of the system, in both a spatially-flat and non-flat universe. Quite remarkably, regardless of the spatial curvature, we show that a stable de Sitter-like phase that can model current time appears only a small fraction of the entire phase-space, suggesting that the model under exam is unlikely in describing the whole universe dynamics, i.e., the topological terms appear disfavored in framing the entire evolution of the universe.

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arXiv2025

Noether Symmetries in $f(Q)-$Cosmology

We apply the Noether symmetry analysis in $f\left( Q\right)$-Cosmology to determine invariant functions and conservation laws for the cosmological field equations. For the FLRW background and the four families of connections, it is found that only power-law $f\left( Q\right)$ functions admit point Noether symmetries. Finally, exact and analytic solutions are derived using the invariant functions.

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arXiv2025

Cosmological Interactions with Phantom Scalar Field: Revisiting Background Phase-Space Analysis with Compactified Variables

Energy transfer in the dark sector of the universe gives rise to new phenomena of special interest in modern cosmology. When dark energy is modeled as a phantom scalar field, interactions become crucial to avoid Big Rip singularities. In this work, we revisit the phase-space analysis of the field equations by introducing a new set of dimensionless variables distinct from the traditional Hubble normalization approach. These new variables define a compactified phase space for the evolution of physical parameters. We demonstrate that these compactified variables offer fresh insights into the phase-space analysis in gravitational theories, particularly when the dark energy fluid is allowed to possess a negative kinetic energy density.

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arXiv2024

Fractional Einstein-Gauss-Bonnet scalar field cosmology

Our paper introduces a new theoretical framework called the Fractional Einstein--Gauss--Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein--Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss--Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, $m$ and $α_{0}=t_{0}H_{0}$ and the fractional derivative order $μ$. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss--Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss--Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of $m$ and $α_{0}$, indicating that the solution is consistent with an accelerated expansion at late times with the values $α_0=1.38\pm 0.05$, $m=1.44\pm 0.05$, and $μ=1.48 \pm 0.17$ (consistent with $Ω_{m,0}=0.311\pm 0.016$ and $h=0.712\pm 0.007$), resulting in an age of the Universe $t_{0}=19.0\pm 0.7$ [Gyr] at 1$σ$ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than $Λ$CDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology.

astro-ph.CO↗

arXiv2024

Revise the Dark Matter-Phantom Scalar Field Interaction

The cosmological history and evolution are examined for gravitational models with interaction in the dark sector of the universe. In particular, we consider the dark energy to be described by a phantom scalar field and the dark matter $ρ_{m}$ as a pressureless ideal gas. We introduce the interacting function $Q=β\left( t\right) ρ_{m}$, where the function $% β\left( t\right) $ is considered to be proportional to $\dotϕ, \dotϕ^{2}H^{-1},~H$, or a constant parameter with dimensions of $\left[H_{0}\right] $. For the four interacting models, we study in details the phase space by calculating the stationary points. The latter are applied to reconstruct the cosmological evolution. Compactified variables are essential to understand the complete picture of the phase space and to conclude about the cosmological viability of these interacting models. The detailed analysis is performed for the exponential potential $V\left( ϕ\right) =V_{0}e^{λϕ}$. The effects of other scalar field potential functions on the cosmological dynamics are examined.

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arXiv2024

Dark Universe Phenomenology from Yukawa Potential?

We argue that the effect of cold dark matter in the cosmological setup can be explained by the coupling between the baryonic matter particles in terms of the long-range force having a graviton mass $m_g$ via the Yukawa gravitational potential. Such a quantum-corrected Yukawa-like gravitational potential is characterized by the coupling parameter $α$, the wavelength parameter $λ$, which is related to the graviton mass via $m_g=\hbar/(λc)$, that determines the range of the force and, finally, a Planck length quantity $l_0$ that makes the potential regular at the centre. The corrected Friedmann equations are obtained using Verlinde's entropic force interpretation of gravity based on the holographic scenario and the equipartition law of energy. The parameter $α$ modifies Newton's constant as $G_{\rm eff}\rightarrow G(1+α)$. We argue that dark matter is an apparent effect as no dark matter particle exists in this picture. Furthermore, the dark energy is also related to graviton mass and $α$; in particular, we point out that the cosmological constant can be viewed as a self-interaction effect between gravitons. We further show that there exists a precise correspondence with Verlinde's emergent gravity theory, and due to the long-range force, the theory can be viewed as a non-local gravity theory. To this end, we performed the phase space analyses and estimated $λ\simeq 10^3 $[Mpc] and $α\in (0.0385,0.0450)$, respectively. Finally, from these values, for the graviton mass, we get $m_g\simeq 10^{-68}$ kg, and cosmological constant $Λ\simeq 10^{-52}\rm m^{-2}$. Further, we argue how this theory reproduces the MOND phenomenology on galactic scales via the acceleration of Milgrom $a_0 \simeq 10^{-10}\rm m/s^2$.

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arXiv2024

Addressing the Hubble tension in Yukawa cosmology?

In Yukawa cosmology, a recent discovery revealed a relationship between baryonic matter and the dark sector. The relation is described by the parameter α and the long-range interaction parameter λ - an intrinsic property of the graviton. Applying the uncertainty relation to the graviton raises a compelling question: Is there a quantum mechanical limit to the measurement precision of the Hubble constant (H0)? We argue that the uncertainty relation for the graviton wavelength λ can be used to explain a running of H0 with redshift. We show that the uncertainty in time has an inverse correlation with the value of the Hubble constant. That means that the measurement of the Hubble constant is intrinsically linked to length scales (redshift) and is connected to the uncertainty in time. On cosmological scales, we found that the uncertainty in time is related to the look-back time quantity. For measurements with a high redshift value, there is more uncertainty in time, which leads to a smaller value for the Hubble constant. Conversely, there is less uncertainty in time for local measurements with a smaller redshift value, resulting in a higher value for the Hubble constant. Therefore, due to the uncertainty relation, the Hubble tension is believed to arise from fundamental limitations inherent in cosmological measurements. Finally, our findings indicate that the mass of the graviton fluctuates with specific scales, suggesting a possible mass-varying mechanism for the graviton.

astro-ph.CO↗

arXiv2024

Dynamics of a higher-dimension Einstein-Scalar-Gauss-Bonnet cosmology

We study the dynamics of the field equations in a five-dimensional spatially flat Friedmann-Lemaître-Robertson-Walker metric in the context of a Gauss-Bonnet-Scalar field theory where the quintessence scalar field is coupled to the Gauss-Bonnet scalar. Contrary to the four-dimensional Gauss-Bonnet theory, where the Gauss-Bonnet term does not contribute to the field equations, in this five-dimensional Einstein-Scalar-Gauss-Bonnet model, the Gauss-Bonnet term contributes to the field equations even when the coupling function is a constant. Additionally, we consider a more general coupling described by a power-law function. For the scalar field potential, we consider the exponential function. For each choice of the coupling function, we define a set of dimensionless variables and write the field equations into a system of ordinary differential equations. We perform a detailed analysis of the dynamics for both systems and classify the stability of the equilibrium points. We determine the presence of scaling and super-collapsing solutions using the cosmological deceleration parameter. This means that our models can explain the Universe's early and late-time acceleration phases. Consequently, this model can be used to study inflation or as a dark energy candidate.

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arXiv2024

Bianchi I spacetimes in $f\left(Q\right)$-gravity

The Kasner spacetimes are exact solutions that are self-similar and of significant interest because they can describe the dynamic evolution of kinematic variables near the singularity of the Mixmaster universe. The chaotic behavior of the Mixmaster universe is related to the Kasner relations. This study investigates Kasner and Kasner-like solutions in symmetric teleparallel $f\left( Q\right) $-gravity. We consider three families of connections for the spatially flat Friedmann-Lema\^ıtre-Robertson-Walker. We found that Kasner-like solutions are present in the theory when the nonmetricity scalar $Q$ vanishes. Kasner-like relations are introduced only for the field equations of the connection defined in the coincidence gauge. Finally, we perform a detailed phase-space analysis to understand the dynamics of $f\left( Q\right) $-gravity in the evolution of anisotropies and the effects of different connections on this evolution.

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arXiv2024

Dark matter signatures of black holes with Yukawa potential

This study uses a nonsingular Yukawa--modified potential to obtain a static and spherically symmetric black hole solution with a cosmological constant. Such Yukawa--like corrections are encoded in two parameters, $α$ and $λ$, that modify Newton's law of gravity in large distances, and a deformation parameter $\ell_0$, which plays an essential role in short distances. The most significant effect is encoded in $α$, which modifies the total black hole mass with an extra mass proportional to $αM$, mimicking the dark matter effects at large distances from the black hole. On the other hand, the effect due to $λ$ is small for astrophysical values. We scrutinize the \textit{quasinormal} frequencies and shadows associated with a spherically symmetric black hole and the thermodynamical behavior influenced by the Yukawa potential. In particular, the thermodynamics of this black hole displays a rich behavior, including possible phase transitions. We use the WKB method to probe the \textit{quasinormal} modes of massless scalar, electromagnetic, and gravitational field perturbations. In order to check the influence of the parameters on the shadow radius, we consider astrophysical data to determine their values, incorporating information on an optically thin radiating and infalling gas surrounding a black hole to model the black hole shadow image. In particular, we consider Sgr A* black hole as an example and we find that its shadow radius changes by order of $10^{-9}$, meaning that the shadow radius of a black hole with Yukawa potential practically gives rise to the same result encountered in the Schwarzschild black hole. Also, in the eikonal regime, using astrophysical data for Yukawa parameters, we show that the value of the real part of the QNMs frequencies changes by $10^{-18}$.

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arXiv2024

Conformal and Non-Minimal Couplings in Fractional Cosmology

Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases where the power law is observed accurately. Fractional calculus must reflect non-local, frequency- and history-dependent properties of power-law phenomena. This tool has various important applications, such as fractional mass conservation, electrochemical analysis, groundwater flow problems, and fractional spatiotemporal diffusion equations. It can also be used in cosmology to explain late-time cosmic acceleration without the need for dark energy. We review some models using fractional differential equations. We look at the Einstein--Hilbert action, which is based on a fractional derivative action, and add a scalar field, $ϕ$, to create a non-minimal interaction theory with the coupling, $ξR ϕ^2 $, between gravity and the scalar field, where $ξ$ is the interaction constant. By employing various mathematical approaches, we can offer precise schemes to find analytical and numerical approximations of the solutions. Moreover, we comprehensively study the modified cosmological equations and analyze the solution space using the theory of dynamical systems and asymptotic expansion methods. This enables us to provide a qualitative description of cosmologies with a scalar field based on fractional calculus formalism.

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arXiv2024

New analytic solutions in $f\left( R\right) $-Cosmology from Painlevé analysis

Using the singularity analysis, we investigate the integrability properties and existence of analytic solutions in $f\left( R\right)$-cosmology. Specifically, for some power-law $f\left( R\right) $-theories of particular interest, we apply the ARS algorithm to prove if the field equations possess the Painlevé property. Constraints for the free parameters of the power-law models are derived, and new analytic solutions are derived, expressed in terms of Laurent expansions.

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arXiv2024

Charged Black Holes with Yukawa Potential

This study derives a novel family of charged black hole solutions featuring short- and long-range modifications. These ones are achieved through a Yukawa-like gravitational potential modification and a nonsingular electric potential incorporation. The short-range corrections encode quantum gravity effects, while the long-range adjustments simulate gravitational effects akin to those attributed to dark matter. Our investigation reveals that the total mass of the black hole undergoes corrections owing to the apparent presence of dark matter mass and the self-adjusted electric charge mass. Two distinct solutions are discussed: a regular black hole solution characterizing small black holes, where quantum effects play a crucial role, and a second solution portraying large black holes at considerable distances, where the significance of Yukawa corrections comes into play. Notably, these long-range corrections contribute to an increase in the total mass and hold particular interest as they can emulate the role of dark matter. Finally, we explore the phenomenological aspects of the black hole. Specifically, we examine the influence of electric charge and Yukawa parameters on thermodynamic quantities, the quasinormal modes for the charged scalar perturbations as well as for the vector perturbations, analysis of the geodesics of light/massive particles, and the accretion of matter onto the charged black hole solution.

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arXiv2024

Dynamical system analysis in multiscalar-torsion cosmology

We explore the phase-space of a multiscalar-torsion gravitational theory within a cosmological framework characterized by a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker model. Our investigation focuses on teleparallelism and involves a gravitational model featuring two scalar fields, where one scalar field is coupled to the torsion scalar. We consider coupling in the two scalar fields' kinetic and potential components. We employ exponential functions for the scalar field potentials and analyze the field equations' equilibrium points to reconstruct the cosmological evolution. Remarkably, we discover many equilibrium points in this multiscalar field model, capable of describing various eras of cosmological evolution. Hence, this model can be used to describe the early and late time acceleration phases of the universe and as a unification model for the elements of the dark sector of the universe.

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arXiv2023

Mapping Solutions in Nonmetricity Gravity: Investigating Cosmological Dynamics in Conformal Equivalent Theories

We investigate the impact of conformal transformations on the physical properties of solution trajectories in nonmetricity gravity. Specifically, we explore the phase-space and reconstruct the cosmological history of a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker universe within scalar-nonmetricity theory in both the Jordan and Einstein frames. A detailed analysis is conducted for three different connections defined in both the coincident and non-coincident gauges. Our findings reveal the existence of a unique one-to-one correspondence for equilibrium points in the two frames. Furthermore, we demonstrate that solutions describing accelerated universes remain invariant under the transformation that relates these conformally equivalent theories.

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arXiv2023

Averaging generalized scalar field cosmologies IV: locally rotationally symmetric Bianchi V model

This research focuses on scalar field cosmologies with a generalized harmonic potential. Our attention is centred on the anisotropic LRS Bianchi I and III metrics, Bianchi V metrics, and their isotropic limits. We provide a comprehensive overview of the first two metrics classes and offer new findings for Bianchi V metrics. We show that the Hubble parameter is a time-dependent perturbation parameter that controls the magnitude of the error between full-system and time-averaged solutions as it decreases, such that those complete and time-averaged systems have the same asymptotic behaviour. Therefore, oscillations entering the system can be controlled and smoothed out, which simplifies the problem at hand.

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arXiv2023

Observational constraints on Yukawa cosmology and connection with black hole shadows

We confront Yukawa modified cosmology, proposed in arXiv:2304.11492 [Jusufi et al. arXiv:2304.11492], with data from Supernovae Type Ia (SNe Ia) and Hubble parameter (OHD) observations. Yukawa cosmology is obtained from a Yukawa-like gravitational potential, with coupling parameter $α$ and wavelength parameter $λ$, which gives rise to modified Friedmann equations. We show that the agreement with observations is very efficient, and within $1σ$ confidence level we find the best-fit parameters $λ=\left(2693_{-1262}^{+1191}\right)\, \rm Mpc$, $α=0.416_{-0.326}^{+1.137}$, and a graviton mass of $m_{g}=\left(2.374_{-0.728}^{+2.095}\right)\times 10^{-42}\, \text{GeV}$. Additionally, we establish a connection between the effective dark matter and dark energy density parameters and the angular radius of the black hole shadow of the SgrA and M87 black holes in the low-redshift limit, consistent with the Event Horizon Telescope findings.

astro-ph.CO↗

arXiv2023

Global dynamics of two models for Quintom Friedman-Lemaître-Robertson-Walker Universes

We comprehensively analyze the dynamics for the gravitational field equations for the Chiral-Quintom theory in a Friedman-Lemaître-Robertson-Walker cosmology with an additional matter source. We consider a new set of dimensionless variables and write the field equations in the equivalent form of an algebraic-differential system. Specifically, we consider two families of quintom models where the two scalar fields interact in the kinetic sector. We mathematically focus on the dynamical effect of spatial curvature. Physically, we find two periods of inflation related to the Universe's early and late-time acceleration phases.

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