arXiv subjects

Alfredo D. Millano

Publications and source records attributed to Alfredo D. Millano.

18 recordsLinked to original sources

arXiv2025

Averaging Dynamics of Scalar Field-Matter Interacting Models in Anisotropic Universes: The Locally Rotationally Symmetric Bianchi I Spacetime

We consider an anisotropic cosmological model based on the locally rotational Bianchi I spacetime, incorporating a scalar field and a non-zero cosmological interaction term. The framework of averaging theory is employed to study the associated non-linear differential equations. Through a qualitative analysis of the gravitational field equations, we obtain valuable insights into the structure of the solution space for the anisotropic scalar field model with a generalized harmonic potential. The interaction between the scalar field and matter is described by a general expression that depends on the Hubble parameter, the time derivative of the scalar field, and the energy densities of cold dark matter and dark energy. This formulation involves real parameters that modulate the interaction, as well as a coupling constant with the dimensions of the Hubble parameter. We show that the Hubble parameter serves as a time-dependent perturbation parameter, controlling the discrepancy between the full system and its time-averaged counterpart. As this parameter decreases, both systems converge to the same asymptotic behaviour. This enables the suppression of oscillatory effects, significantly simplifying the dynamical analysis. Finally, we identify conditions on the interaction parameters that ensure the regularity of the system's evolution by preventing the emergence of singularities.

gr-qc↗

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

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

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

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.

gr-qc↗

arXiv2024

Kantowski-Sachs and Bianchi III dynamics in $f\left(Q\right)$-gravity

We explore the phase-space of homogeneous and anisotropic spacetimes within symmetric teleparallel $f(Q)$-gravity. Specifically, we consider the Kantowski-Sachs and locally rotational Bianchi III geometries to describe the physical space. By analyzing the phase-space, we reconstruct the cosmological history dictated by $f(Q)$-gravity and comment about the theory's viability. Our findings suggest that the free parameters of the connection must be constrained to eliminate nonlinear terms in the field equations. Consequently, new stationary points emerge, rendering the theory cosmologically viable. We identify the existence of anisotropic accelerated universes, which may correspond to the pre-inflationary epoch.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

arXiv2023

Global dynamics in Einstein-Gauss-Bonnet scalar field cosmology with matter

We study the dynamics of the field equations in a four-dimensional isotropic and homogeneous spatially flat Friedmann--Lema\^ıtre--Robertson--Walker geometry in the context of Einstein-Gauss-Bonnet theory with a matter source and a scalar field coupled to the Gauss-Bonnet scalar. In this theory, the Gauss-Bonnet term contributes to the field equations. The mass of the scalar field depends on the potential function and the Gauss-Bonnet term. For the scalar field potential, we consider the exponential function and the coupling function between the scalar field and the Gauss-Bonnet scalar is considered to be the linear function. Moreover, the scalar field can have a phantom behaviour. We consider a set of dimensionless variables and write the field equations into a system or algebraic-differential equations. For the latter, we investigate the equilibrium points and their stability properties. In order to perform a global analysis of the asymptotic dynamics, we use compactified variables. This gravitational theory can explain the Universe's recent and past acceleration phases. Therefore, it can be used as a toy model for studying inflation or as a dark energy candidate.

gr-qc↗

arXiv2023

Phase-space analysis of an Einstein-Gauss-Bonnet scalar field cosmology

We perform a detailed study of the phase-space of the field equations of an Einstein-Gauss-Bonnet scalar field cosmology for a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker spacetime. For the scalar field potential, we consider the exponential function. In contrast, for the coupling function of the scalar field with the Gauss-Bonnet term, we assume two cases, the exponential function and the power-law function. We write the field equations in dimensionless variables and study the equilibrium points using Poincare variables. For the exponential coupling function, the asymptotic solutions describe de Sitter universes or spacetimes where the Gauss-Bonnet term dominates. We recovered previous results but found new asymptotic solutions not previously studied. For the power-law coupling function, equilibrium points which describe the scaling solution appear. Finally, the power-law coupling provides a rich cosmological phenomenology.

gr-qc↗

arXiv2023

Revisiting Fractional Cosmology

Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting theory is compared against observational data. In this context, dynamical systems can be used along with an analysis the phase spaces for different values of the fractional order of the derivative and their different matter contents. The equilibrium points are classified, providing a range for the order of the fractional derivative in order to investigate whether the cosmological history can be reconstructed and a late-time accelerating power-law solution obtained for the scale factor. In this paper, we discuss the physical interpretation of the corresponding cosmological solutions with particular emphasis on the influence of the fractional order of the derivative in a theory of gravity that includes a scalar field minimally coupled to gravity. The presented results improve and extend those obtained previously, further demonstrating that fractional calculus can play a relevant role in cosmology.

gr-qc↗

arXiv2023

Phase space analysis of the bouncing universe with stringy effects

We use the recently modified Friedmann equations obtained from string T-duality effects that encode the zero-point length (Phys. Lett. B 836 (2023), 137621) to study the phase space analyses of a bouncing early universe. An important implication of such stringy effects is that they can alleviate the initial singularity since the Raychaudhuri equation is modified. We investigate if the Universe can undergo an accelerated expansion phase for a specific domain of the equation of state parameter. The stringy effects are encoded in the parameter $Γ$, which depends not only on the zero-point length but also on the state parameter $ω$. We construct two dynamical systems depending on whether $-1 < ω\leq -1/3$ and $ω\geq -1/3$, and we classify the equilibrium points of each system. Exact solutions and cosmological implications are discussed.

gr-qc↗

arXiv2022

Scalar Field cosmology from a Modified Poisson Algebra

We investigate the phase space of a scalar field theory obtained by minisuperspace deformation. We consider quintessence or phantom scalar fields in the action which arise from minisuperspace deformation on the Einstein-Hilbert action. We use a modified Poisson Algebra where Poisson brackets are the $α$-deformed ones and are related to the Moyal-Weyl star product. We discuss early and late-time attractors, and we reconstruct the cosmological evolution. We show that the model can have $Λ$CDM model as a future attractor if we initially consider a massless scalar field without a cosmological constant term.

gr-qc↗

arXiv2022

Observational constraints and dynamical analysis of Kaniadakis horizon-entropy cosmology

We study the scenario of Kanadiakis horizon entropy cosmology which arises from the application of the gravity-thermodynamics conjecture using the Kaniadakis modified entropy. The resulting modified Friedmann equations contain extra terms that constitute an effective dark energy sector. We use data from Cosmic chronometers, Supernova Type Ia, HII galaxies, Strong lensing systems, and Baryon acoustic oscillations observations and we apply a Bayesian Markov Chain Monte Carlo analysis to construct the likelihood contours for the model parameters. We find that the Kaniadakis parameter is constrained around 0, namely, around the value where the standard Bekenstein-Hawking is recovered. Concerning the normalized Hubble parameter, we find $h=0.708^{+0.012}_{-0.011}$, a result that is independently verified by applying the $\mathbf{\mathbb{H}}0(z)$ diagnostic and, thus, we conclude that the scenario at hand can alleviate the $H_0$ tension problem. Regarding the transition redshift, the reconstruction of the cosmographic parameters gives $z_T=0.715^{+0.042}_{-0.041}$. Furthermore, we apply the AICc, BIC and DIC information criteria and we find that in most datasets the scenario is statistical equivalent to $Λ$CDM one. Moreover, we examine the Big Bang Nucleosynthesis (BBN) and we show that the scenario satisfies the corresponding requirements. Additionally, we perform a phase-space analysis, and we show that the Universe past attractor is the matter-dominated epoch, while at late times the Universe results in the dark-energy-dominated solution. Finally, we show that Kanadiakis horizon entropy cosmology accepts heteroclinic sequences, but it cannot exhibit bounce and turnaround solutions.

astro-ph.CO↗

arXiv2022

A Perturbative Analysis of Interacting Scalar Field Cosmologies

Scalar field cosmologies with a generalized harmonic potential are investigated in flat and negatively curved Friedmann-Lemaître-Robertson-Walker and Bianchi I metrics. An interaction between the scalar field and matter is considered. Asymptotic methods and averaging theory are used to obtain relevant information about the solution space. In this approach, the Hubble parameter plays the role of a time-dependent perturbation parameter which controls the magnitude of the error between full-system and time-averaged solutions as it decreases. Our approach is used to show that full and time-averaged systems have the same asymptotic behavior. Numerical simulations are presented as evidence of such behavior. Moreover, the asymptotic behavior of the solutions is independent of the coupling function.

gr-qc↗

arXiv2021

Averaging generalized scalar field cosmologies III: Kantowski--Sachs and closed Friedmann--Lemaître--Robertson--Walker models

Scalar field cosmologies with a generalized harmonic potential and matter with energy density $ρ_m$, pressure $p_m$, and barotropic equation of state (EoS) $p_m=(γ-1)ρ_m, \; γ\in[0,2]$ in Kantowski-Sachs (KS) and closed Friedmann--Lemaître--Robertson--Walker (FLRW) metrics are investigated. We use methods from non--linear dynamical systems theory and averaging theory considering a time--dependent perturbation function $D$. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late--time attractors of full and time--averaged systems are two anisotropic contracting solutions, which are non--flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for $0\leq γ\leq 2$, and flat FLRW matter--dominated universe if $0\leq γ\leq \frac{2}{3}$. For closed FLRW metric late--time attractors of full and averaged systems are a flat matter--dominated FLRW universe for $0\leq γ\leq \frac{2}{3}$ as in KS and Einstein-de Sitter solution for $0\leqγ<1$. Therefore, time--averaged system determines future asymptotics of full system. Also, oscillations entering the system through Klein-Gordon (KG) equation can be controlled and smoothed out when $D$ goes monotonically to zero, and incidentally for the whole $D$-range for KS and for closed FLRW (if $0\leq γ< 1$) too. However, for $γ\geq 1$ closed FLRW solutions of the full system depart from the solutions of the averaged system as $D$ is large. Our results are supported by numerical simulations.

gr-qc↗

arXiv2021

Averaging Generalized Scalar Field Cosmologies II: Locally Rotationally Symmetric Bianchi I and flat Friedmann-Lemaître-Robertson-Walker models

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lemaître-Robertson-Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $γ$, the late-time attractors of physical interests are flat quintessence dominated FLRW universe and Einstein-de Sitter solution. With this approach, the oscillations entering the system through the Klein-Gordon (KG) equation can be controlled and smoothed out as the Hubble parameter $H$ - acting as time-dependent perturbation parameter - tends monotonically to zero. Numerical simulations are presented as evidence of such behavior.

gr-qc↗

arXiv2021

Averaging Generalized Scalar Field Cosmologies I: Locally Rotationally Symmetric Bianchi III and open Friedmann-Lemaître-Robertson-Walker models

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lemaître-Robertson-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic index $γ$ late-time attractors of physical interests for LRS Bianchi III metric are Bianchi III flat spacetime, matter dominated FLRW universe (mimicking de Sitter, quintessence or zero acceleration solutions) and matter-curvature scaling solution. For open FLRW metric late-time attractors are a matter dominated FLRW universe and Milne solution. With this approach, oscillations entering nonlinear system through Klein-Gordon (KG) equation can be controlled and smoothed out as the Hubble factor $H$ - acting as a time-dependent perturbation parameter - tends monotonically to zero. Numerical simulations are presented as evidence of such behaviour.

gr-qc↗