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A. C. Amaro de Faria Jr

Publications and source records attributed to A. C. Amaro de Faria Jr.

11 recordsLinked to original sources
arXiv2024

Background gravitational waves as signature of the adiabatic expansion of a black body that represents the dark universe

We propose a toy model of a spherical universe made up of an exotic dark gas with temperature $T$ in thermal equilibrium with a black-body in adiabatic expansion. Each particle of this exotic gas mimics a kind of particle of dark energy represented by the vacuum energy, being quantized into virtual particles with extremely small masses that form such gas representng the own tissue of the expanding space-time governed by a negative pressure whose origin is the equation of state (EOS) of vacuum, i.e., $p=-ρ$, where $ρ$ is the vacuum energy density. So, each vacuum particle occupies a tiny area of space so-called Planck area $L_p^{2}$, which represents the minimum area of the whole space-time given by the spherical surface with area $4πR_H^2$, where $R_H$ is the Hubble radius. We realize that such spherical surface is the surface of the black-body for representing the dark universe as if it were the surface of an expanding balloon. Thus, we are able to derive the law of universal gravitation, thus leading us to understand the cosmological anti-gravity. We estimate the very small order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this toy model, as the dark universe can be thought of as a large black body, when we obtain its power and frequency of emission of radiation, we find very low values. We conclude that such radiation and frequency of the black body made up of dark energy is a background gravitational wave with very low frequency in the order of $10^{-17}$Hz due to the slight stretching of the fabric of space-time.

gr-qc↗
arXiv2023

A brief review of a modified relativity that explains cosmological constant

The present review aims to show that a modified space-time with an invariant minimum speed provides a relation with Weyl geometry in the Newtonian approximation of weak-field. The deformed Special Relativity so-called Symmetrical Special Relativity (SSR) has an invariant minimum speed $V$, which is associated with a preferred reference frame $S_V$ for representing the vacuum energy, thus leading to the cosmological constant ($Λ$). The equation of state (EOS) of vacuum energy for $Λ$, i.e., $ρ_Λ=ε=-p$ emerges naturally from such space-time, where $p$ is the pressure and $ρ_Λ=ε$ is the vacuum energy density. With the aim of establishing a relationship between $V$ and $Λ$ in the modified metric of the space-time, we should consider a dark spherical universe with Hubble radius $R_H$, having a very low value of $ε$ that governs the accelerated expansion of universe. In doing this, we aim to show that SSR-metric has an equivalence with a de-Sitter (dS)-metric ($Λ>0$). On the other hand, according to the Boomerang experiment that reveals a slightly accelerated expansion of the universe, SSR leads to a dS-metric with an approximation for $Λ<<1$ close to a flat space-time, which is in the $ΛCDM$ scenario where the space is quasi-flat, so that $Ω_{m}+Ω_Λ\approx 1$. We have $Ω{cdm}\approx 23\%$ by representing dark cold matter, $Ω_m\approx 27\%$ for matter and $Ω_Λ\approx 73\%$ for the vacuum energy. Thus, the theory is adjusted for the redshift $z=1$. This corresponds to the time $τ_0$ of transition between gravity and anti-gravity, leading to a slight acceleration of expansion related to a tiny value of $Λ$, i.e., we find $Λ_0=1.934\times 10^{-35}s^{-2}$. This result is in agreement with observations.

gr-qc↗
arXiv2023

The K-essence flow seen from the preferred frame $S_{V}$. A scalar field theory with Landau superfluid structure

We study the hypothesis of deformation of the invariance of Lorentz transformations produced by the introduction of a universal minimum velocity relative to a preferred frame. Our goal with this job is to apply this hypothesis to superfluids and study its consequences relating the minimum velocity to the idea of a fluid, with superfluid properties. In previous works we related the minimum velocity to the cosmological constant and even to cosmic inflation. Soon we could generate a hypothetical superfluid capable of modeling with characteristics of a cosmological fluid with dark energy properties. The first excited state of this universal superfluid would be a preferred frame from which all other excited states are observed and then we would have a preferred frame $S_{V}$ associated with the critical Landau velocity, thus implying that the universal minimum velocity coincides with the critical Landau velocity, and the objects observed by the preferred frame are excited states of the superfluid. This coincidence between the concepts of minimum velocity and Landau's critical velocity makes Landau's critical velocity a type of limit velocity, modifying the usual causal structure of restricted relativity. Formulating the phenomena in this preferred frame would have the advantage of providing a simple explanation for astrophysical and cosmological phenomena linked to a causal structure, which emerges from this construction and is very similar to causal structures linked to Gordon geometry and acoustic tachyons. We build a deformed relativistic Lagrangian, demonstrate its relation with a K-essence Lagrangian and calculate the quantities associated with that Lagrangian. We also studied an irrotational fluid and verified the role of enthalpy associated with the minimum velocity structure.

gr-qc↗
arXiv2023

Deformed Special Relativity with a minimum speed as explanation of the tiny value of the cosmological constant based on the Boomerang experiment in the $ΛCDM$ scenario

In this paper we will show that a new structure of space-time with a minimum speed reveals a connection with Weyl geometry in the approximation of weak-field Newtonian limit. Symmetrical Special Relativity (SSR) has a minimum speed $V$ that plays the role of a preferred reference frame $S_V$ of vacuum that leads to the cosmological constant $Λ$. In order to realize such a connection between $V$ and $Λ$ within a scenario of space-time metric, we will use a model of spherical universe with Hubble radius $R_H$ filled by a low vacuum energy density $ρ_Λ$ that governs the accelerated expansion of the universe. In doing this, we will show that SSR-metric plays the role of a de-Sitter (dS)-metric with a positive cosmological constant ($Λ>0$). On the other hand, according to the Boomerang experiment as it is shown that the three-dimensional space of the universe is Euclidean and with a slightly accelerated expansion, SSR leads to a dS-metric with an approximation for $Λ<<1$ close to a flat space-time, which is in the $ΛCDM$ scenario where the space is quasi-flat, so that $Ω_{m}+Ω_Λ\approx 1$. We have $Ω{cdm}\approx 23\%$ by representing dark cold matter, $Ω_m\approx 27\%$ for matter and $Ω_Λ\approx 73\%$ for the vacuum energy. Thus, the theory is adjusted for redshift $z=1$, i.e., the time $τ_0$ at which the universe goes over from a decelerating to an accelerating expansion by obtaining the numerical value $Λ_0=1.934\times 10^{-35}s^{-2}$, being in good agreement with measurements.

physics.gen-ph↗
arXiv2021

Variation of the fundamental constants over the cosmological time: veracity of Dirac's intriguing hypothesis

We investigate how the universal constants, including the fine structure constant, have varied since the early universe close to the Planck energy scale ($E_P\sim 10^{19}$GeV) and, thus, how they have evoluted over the cosmological time related to the temperature of the expanding universe. We have already shown that the speed of light was much higher close to the Planck scale. In the present work, we will go further, first by showing that both the Planck constant and the electron charge were also too large in the early universe. However, we conclude that the fine structure constant ($α\cong 1/137$) has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data. Furthermore, we will obtain the divergence of the electron (or proton) mass and also the gravitational constant ($G$) at the Planck scale. Thus, we will be able to verify the veracity of Dirac's belief about the existence of "coincidences" between dimensionless ratios of sub-atomic and cosmological quantities, leading to a variation of $G$ with time, i.e., the ratio of the electrostatic to gravitational force between an electron and a proton ($\sim 10^{41}$) is roughly equal to the age of the universe divided by an elementary time constant, so that the strength of gravity, as determined by $G$, must vary inversely with time just in the approximation of lower temperature or for times very far from the early period, in order to compensate for the time-variation of the Hubble parameter ($H\sim t^{-1}$). In short, we will show the validity of Dirac's hypothesis only for times very far from the early period or $T\sim T_P\sim 10^{32}$K.

gr-qc↗
arXiv2020

Lorentz violation with an invariant minimum speed as foundation of the tachyonic inflation within a Machian scenario

We show the relationship between the scalar kinematics potential of Symmetrical Special Relativity (SSR) and the ultra-referential of vacuum connected to an invariant minimum speed postulated by SSR. The property of the conformal metric of SSR is showed, from where we deduce a kind of de Sitter metric. The negative curvature of spacetime is calculated from the conformal property of the metric. Einstein equation provides an energy-momentum tensor which is proportional to SSR-metric. We also realize that SSR leads to a deformed kinematics with quantum aspects directly related to the delocalization of the particle and thus being connected to the uncertainty principle. We finish this work by identifying the lagrangian of SSR with the so-called tachyonic models (slow-roll), where the tachyonic potential is a function depending on the conformal factor, thus allowing the SSR-lagrangian to be able to mimic a tachyonic lagrangian related to the so-called Dirac-Born-Infeld lagrangian, where the superluminal effects are interpreted as being a large stretching of spacetime due to new relativistic effects close to the invariant minimum speed as being the foundation of the inflationary vacuum connected to a variable cosmological parameter that recovers the cosmological constant for the current universe.

physics.gen-ph↗
arXiv2020

Lorentz violation with an invariant minimum speed as foundation of the Gravitational Bose Einstein Condensate of a Dark Energy Star

We aim to search for the connection between the spacetime with an invariant minimum speed so-called Symmetrical Special Relativity (SSR) with Lorentz violation and the Gravitational Bose Einstein Condensate (GBEC) as the central core of a star of gravitational vacuum (gravastar), where one normally introduces a cosmological constant for representing an anti-gravity. This usual model of gravastar with an equation of state (EOS) for vacuum energy inside the core will be generalized for many modes of vacuum (dark energy star) in order to circumvent the embarrassment generated by the horizon singularity as the final stage of a gravitational collapse. In the place of the problem of a singularity of an event horizon, we introduce a phase transition between gravity and anti-gravity before reaching the Schwarzschild (divergent) radius $R_S$ for a given coexistence radius $R_{coexistence}$ slightly larger than $R_S$ and slightly smaller than the core radius $R_{core}$ of GBEC, where the metric of the repulsive sector (core of GBEC) would diverge for $r=R_{core}$, so that for such a given radius of phase coexistence $R_S<R_{coexistence} <R_{core}$, both divergences at $R_S$ of Schwarzschild metric and at $R_{core}$ of the repulsive core are eliminated, thus preventing the formation of the event horizon. So the causal structure of SSR helps us to elucidate such puzzle of singularity of event horizon by also providing a quantum interpretation for GBEC and thus by explaining the origin of a strong anisotropy due to the minimum speed that leads to the phase transition gravity/anti-gravity during the collapse of the star. Furthermore, due to the absence of an event horizon of black hole (BH) where any signal cannot propagate, the new collapsed structure presents a signal propagation in its region of coexistence of phases where the coexistence metric does not diverge.

physics.gen-ph↗
arXiv2017

Invariance of the fine structure constant with temperature of the expanding universe

Our goal is to interpret the energy equation from Doubly Special Relativity (DSR) of Magueijo-Smolin with an invariant Planck energy scale in order to obtain the speed of light with an explicit dependence on the background temperature of the expanding universe. We also investigate how other universal constants, including the fine structure constant, have varied since the early universe and, thus, how they have evoluted over the cosmological time related to the temperature of the expanding universe. For instance, we show that both the Planck constant and the electron charge were also too large in the early universe. However, we finally conclude that the fine structure constant has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data.

physics.gen-ph↗
arXiv2017

Lorentz violation with a universal minimum speed as foundation of de Sitter relativity

We aim to investigate the theory of Lorentz violation with an invariant minimum speed so-called Symmetrical Special Relativity (SSR) from the viewpoint of its metric. Thus we should explore the nature of SSR-metric in order to understand the origin of the conformal factor that appears in the metric by deforming Minkowski metric by means of an invariant minimum speed that breaks down Lorentz symmetry. So we are able to realize that there is a similarity between SSR and a new space with variable negative curvature ($-\infty<\mathcal R<0$) connected to a set of infinite cosmological constants ($0<Λ<\infty$), working like an extended de Sitter (dS) relativity, so that such extended dS-relativity has curvature and cosmological "constant" varying in the time. We obtain a scenario that is more similar to dS-relativity given in the approximation of a slightly negative curvature for representing the current universe having a tiny cosmological constant. Finally we show that the invariant minimum speed provides the foundation for understanding the kinematics origin of the extra dimension considered in dS-relativity in order to represent the dS-length.

physics.gen-ph↗
arXiv2016

Unruh effect as foundation of universal gravitation within the cosmological scenario

We aim to build a simple model of a gas with temperature ($T$) in thermal equilibrium with a black-body that plays the role of the adiabatically expanding universe, so that each particle of such a gas mimics a kind of "particle" (quantum) of dark energy, which is inside a very small area of space so-called Planck area ($l_p^{2}$), that is the minimum area of the whole space-time represented by a huge spherical surface with area $4πr_u^2$, $r_u$ being the Hubble radius. So we should realize that such spherical surface is the surface of the black-body for representing the universe, whose temperature ($T$) is related to an acceleration ($a$) of a proof particle that experiences the own black-body radiation according to the Unruh effect. Thus, by using this model, we derive the law of universal gravitation, which leads us to understand the anti-gravity in the cosmological scenario and also estimate the tiny order of magnitude of the cosmological constant in agreement with the observational data.

gr-qc↗