This work explores the set of coupled partial differential equations of the Einstein equations yielding vacuum solutions in the original Alcubierre warp drive metric with the cosmological constant. It is shown that under an appropriate ansatz they reveal a Burgers-type equation and a heat-type equation. These results indicate that the spacetime distortion carrying a mass particle at superluminal speeds, the Alcubierre warp bubble, may be interpreted as a geometric analog of a propagating shock front, which suggests a possible novel theoretical framework to deal with superluminal warp speeds.

Fast Radio Bursts (FRBs) are millisecond-duration radio transients with an observed dispersion measure ($DM$) greater than the expected Milky Way contribution, which suggests that such events are of extragalactic origin. Although some models have been proposed to explain the physics of the pulse, the mechanism behind the FRBs emission is still unknown. From FRBs data with known host galaxies, the redshift is directly measured and can be combined with estimates of the $DM$ to constrain the cosmological parameters, such as the baryon number density and the Hubble constant. However, the poor knowledge of the fraction of baryonic mass in the intergalactic medium ($f_{IGM}$) and its degeneracy with the cosmological parameters impose limits on the cosmological application of FRBs. In this work we present a cosmological model-independent method to determine the evolution of $f_{IGM}$ combining the latest FRBs observations with localized host galaxy and current supernovae data. We consider constant and time-dependent $f_{IGM}$ parameterizations and show, through a Bayesian model selection analysis, that a conclusive answer about the time-evolution of $f_{IGM}$ depend strongly on the $DM$ fluctuations due to the spatial variation in cosmic electron density ($\delta$). In particular, our analysis show that the evidence varies from strong (in favor of a growing evolution of $f_{IGM}$ with redshift) to inconclusive, as larger values of $\delta$ are considered.

In 1994, Miguel Alcubierre proposed that the well-known special relativistic limitation that particles cannot travel with velocities higher than light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks, using a warped region of spacetime in the shape of a bubble that transports particles with mass traveling through spacetime with superluminal speed. Although initial results indicated this scenario as nonphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such a nonphysical situation may not always be true. This thesis presents newfound solutions for the Einstein field equations, considering the Alcubierre warp drive spacetime metrics. The central premise is to study the fluid matter as the gravity source, rather than the more common vacuum or negative energy sources, to explore the potential for generating superluminal velocities, or \textit{warp speeds}, through a warped region in the spacetime. Such solutions have various matter-energy sources: dust particles, perfect fluid, quasi-perfect fluid with anisotropic pressures, charged dust, and a perfect fluid within a cosmological constant spacetime. A connection between some of these solutions featuring shock waves described by a Burgers-type equation with a term on the right-hand side of the equation purely dependent on time is also shown. This could mean warp drives are closely related to vacuum energy and possibly have topological effects such as shock waves.

One of the most crucial tests of the standard cosmological model consists on testing possible variations on fundamental physical constants. In frameworks such as the minimally extended varying speed of light model (meVSL), the relationship between the luminosity distance ($D_{\text{L}}$) and the angular diameter distance ($D_{\text{A}}$), namely the cosmic distance duality relation (CDDR), is expected to deviate from $\eta(z) \equiv D_{\text{L}}(z)/D_{\text{A}}(z) = (1+z)^{2}$, making it a powerful probe of a potential variation of such a fundamental constant. Hence, we test the viability of the meVSL model through the CDDR by comparing $D_{\text{A}}$ measurements, provided by the transverse (2D) and anisotropic (3D) baryon acoustic oscillations (BAO) observations from different surveys, like SDSS, DES and DESI, in combination with $D_{\text{L}}$ measurements from Pantheon+ type Ia Supernova (SNe) compilation. The Gaussian Process reconstruction is employed on the SN data to match $D_{\text{A}}$ with $D_{\text{L}}$ at the same redshift. We find no deviation of the standard CDDR relation within 1-2$\sigma$ confidence level when considering SNe with 2D and 3D BAO samples combined together, as well as when considering SNe with 3D BAO only. However, when SNe and 2D BAO only are considered, the standard CDDR is only recovered at $\sim 4\sigma$ confidence level. However, such a result might be due to some recently discussed tensions between SN and BAO datasets, especially at low redshifts, in addition to possible inconsistencies between the BAO datasets individually. Therefore, our results show no significant evidence in favour of the meVSL model, once these potential systematics are taken into account.

Fast Radio Bursts (FRBs) are millisecond transient radio events with a high energy. By identifying the origin of the \textbf{burst}, it is possible to measure the redshift of the host galaxy, which can be used to constrain cosmological and astrophysical parameters and test aspects of fundamental physics when combined with the dispersion measure ($DM$). However, some factors limit the cosmological application of FRBs: (i) the poor modelling of the fluctuations in the $DM$ due to spatial variation in the cosmic electrons density; (ii) the fact that the fraction of baryon mass in the intergalactic medium ($f_{IGM}$) is degenerated with some cosmological parameters; (iii) the limited knowledge about host galaxy contribution ($DM_{host}$). In this work, we investigate the impact of different redshift distribution models of FRBs to constrain the baryon fraction in the IGM and host galaxy contribution. We use a cosmological model-independent method developed in previous work \cite{Lemos2023} to perform the analysis and combine simulated FRB data from Monte Carlo simulation and supernovae data. We assume four distribution models for the FRBs: gamma-ray bursts (GRB), star formation rate (SFR), uniform and equidistant (ED). Also, we consider samples with $N = 15, 30, 100$ and $500$ points and different values of the fluctuations of electron density in the $DM$, $\delta = 0, 100, 200, 400, 230\sqrt{z}$ pc/cm$^{3}$. Our analysis shows that all the distribution models present consistent results within $2\sigma$ for the free parameters $f_{IGM}$ and $DM_{host,0}$ and highlights the crucial role of $DM$ fluctuations in obtaining more precise measurements.

We present a minimal extension of the left-right symmetric model based on the gauge group $SU(3)_{c} \times SU(2)_{L} \times SU(2)_{R} \times U(1)_{B-L} \times U(1)_{X}$, in which a vector-like fermion pair ($\zeta_L$ and $\zeta_R$) charged under the $U(1)_{B-L} \times U(1)_X$ symmetry is introduced. Associated with the symmetry breaking of the gauge group $SU(2)_{R} \times U(1)_{B-L} \times U(1)_{X}$ down to the Standard Model (SM) hypercharge $U(1)_Y$, Majorana masses for $\zeta_{L, R}$ are generated and the lightest mass eigenstate plays a role of the dark matter (DM) in our universe by its communication with the SM particles through a new neutral gauge boson "$X$". We consider various phenomenological constraints of this DM scenario, such as the observed DM relic density, the LHC Run-2 constraints from the search for a narrow resonance, and the perturbativity of the gauge couplings below the Planck scale. Combining all constraints, we identify the allowed parameter region which turns out to be very narrow. A significant portion of the currently allowed parameter region will be tested by the High-Luminosity LHC experiments.

The linear response of a Schwarzschild black hole to an external quadrupolar perturbation is studied in analogy to a mechanical electrodynamical system, with the goal to describe the gravitational polarizability. Its causality properties imply dispersion relations that relate fluctuation and dissipative properties. We review and combine results obtained via the Regge-Wheeler equation on one side and a perturbative, worldline effective field theory description on the other, obtaining a consistent description of the dispersion relations for the gravitational polarizability of a Schwarzschild black hole. We find that the classical part of the 2-point correlation function of the black hole multipole depends on the boundary conditions of the space-time the black hole is immersed in, which is relevant for the dispersion relations considered.

In the understanding of the fundamental interactions, the origin of an arrow of time is viewed as problematic. However, quantum field theory has an arrow of causality, which tells us which time direction is the past lightcone and which is the future. This direction is tied to the conventions used in the quantization procedures. The different possible causal directions have related physics - in this sense they are covariant under time-reversal. However, only one causal direction emerges for a given set of conventions. This causal arrow tells us the direction that scattering reactions proceed. The time direction of scattering in turn tells us the time direction for which entropy increases - the so-called arrow of thermodynamics. This connection is overlooked in most discussions of the arrow of time.

A minimal extension of the left-right symmetric model for neutrino masses that includes a vector-like singlet fermion dark matter (DM) is presented with the DM connected to the visible sector via a gauged U(1) portal. We discuss the symmetry breaking in this model and calculate the mass and mixings of the extra heavy neutral gauge boson at the TeV scale. The extra gauge boson can decay to both standard model particles as well to dark matter. We calculate the relic density of the singlet fermion dark matter and its direct detection cross section and use these constraints to obtain the allowed parameter range for the new gauge coupling and the dark matter mass.

Electromagnetic emissions from astrophysical sources at cosmological distances can be used to estimate the photon mass, $m_{\gamma}$. In this paper, we combine measurements of the dispersion measure ($\mathrm{DM}$) of fast radio bursts (FRB) with the luminosity distance from type Ia supernovae (SNe) to investigate update constraints on the photon rest mass. We derive the expression of $\mathrm{DM}$ dependence concerning a non-vanishing photon mass from a cosmological-model independent approach and constrain the parameter $m_{\gamma}$ from measurements of 68 well-localized FRBs and 1048 SNe data from the Pantheon compilation. We consider two scenarios for the baryon fraction in the intergalactic medium ($f_{\mathrm{IGM}}$): one where the value is fixed according to recent reports and another where it is treated as a free parameter, $f_{\mathrm{IGM}} = f_{\mathrm{IGM,0}}$. In the latter case, we find $m_{\gamma} = (29.4_{-15.5}^{+5.80}) \times 10^{-51}$ kg, at $1\sigma$ level. Our results also demonstrate an anticorrelation between $f_{\mathrm{IGM}}$ and $m_{\gamma}$, which highlights the importance of analyzing a larger sample of FRBs for a more comprehensive understanding of their properties.

In this work we have investigated some properties of classical phase-space with symplectic structures consistent, at the classical level, with two noncommutative (NC) algebras: the Doplicher-Fredenhagen-Roberts algebraic relations and the NC approach which uses an extended Hilbert space with rotational symmetry. This extended Hilbert space includes the operators $\theta^{ij}$ and their conjugate momentum $\pi_{ij}$ operators. In this scenario, the equations of motion for all extended phase-space coordinates with their corresponding solutions were determined and a rotational invariant NC Newton's second law was written. As an application, we treated a NC harmonic oscillator constructed in this extended Hilbert space. We have showed precisely that its solution is still periodic if and only if the ratio between the frequencies of oscillation is a rational number. We investigated, analytically and numerically, the solutions of this NC oscillator in a two-dimensional phase-space. The result led us to conclude that noncommutativity induces a stable perturbation into the commutative standard oscillator and that the rotational symmetry is not broken. Besides, we have demonstrated through the equations of motion that a zero momentum $\pi_{ij}$ originated a constant NC parameter, namely, $\theta^{ij}=const.$, which changes the original variable characteristic of $\theta^{ij}$ and reduces the phase-space of the system. This result shows that the momentum $\pi_{ij}$ is relevant and cannot be neglected when we have that $\theta^{ij}$ is a coordinate of the system.

Nowadays, technology has become dominant in the daily lives of most people around the world. From children to older people, technology is present, helping in the most diverse daily tasks and allowing accessibility. However, many times these people are just end-users, without any incentive to the development of computational thinking (CT). With advances in technologies, the abstraction of coding, programming languages, and the hardware resources involved will become a reality. However, while we have not progressed to this stage, it is necessary to encourage the development of CT teaching from an early age. This work will present state of the art concerning teaching initiatives and tools on programming (e.g., ScratchJr), robotics (e.g., KIBO), and other playful tools (e.g., Happy Maps) for the development of CT in the early ages, specifically filling the gap of CT at the kindergarten level. This survey presents a systematic review of the literature, emphasizing computational and robotic tools used in preschool classes to develop the CT. The systematic review evaluated more than 60 papers from 2010 to December 2020, electing 31 papers and adding three papers from the qualitative stage. The paper's amount was classified in taxonomy to show CT's principal tools and initiates applied to children early. To conclude this survey, an extensive discussion about the terms and authors related to this research area is present.

In this paper, we obtain new measurements of the angular homogeneity scale ($\theta_H$) from the BOSS DR12 and eBOSS DR16 catalogs of Luminous Red Galaxies of the Sloan Digital Sky Survey. Considering the flat $\Lambda$CDM model, we use the $\theta_H(z)$ data to constrain the matter density parameter ($\Omega_{m0}$) and the Hubble constant ($H_{0}$). We find $H_0 = 65^{+10}_{-7}$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_{m0}>0.296$. By combining the $\theta_H$ measurements with current Baryon Acoustic Oscillations (BAO) and Type Ia Supernova (SN) data, we obtain $H_{0}= 66.8 \pm 5.0$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_{m0} = 0.292^{+0.013}_{-0.015}$ ($\theta_H$ + BAO) and $H_{0}=66.8 \pm 5.4$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_{m0}=0.331 \pm 0.018$ ($\theta_H$ + SN). We show that $\theta_H$ measurements help break the BAO and SN degeneracies concerning $H_0$, as they do not depend on the sound horizon scale at the drag epoch or the SN absolute magnitude value obtained from the distance ladder method. Hence, despite those constraints are less stringent compared to other probes, $\theta_H$ data may provide an independent cosmological probe of $H_0$ in light of the Hubble tension. For completeness, we also forecast the constraining power of future $\theta_H$ data via Monte Carlo simulations. Considering a relative error of the order of 1$\%$, we obtain competitive constraints on $\Omega_{m0}$ and $H_0$ ($\approx 5\%$ error) from the joint analysis with current SN and BAO measurements.

We derive the formula of the entanglement entropy between the left and right oscillating modes of the $\sigma$-model with the de Sitter target space. To this end, we study the theory in the \emph{cosmological gauge} in which the non-vanishing components of the metric on the two-dimensional base space are functions of the expansion parameter of the de Sitter space. The model is embedded in the causal north pole diamond of the Penrose diagram. We argue that the cosmological gauge is natural to the $\sigma$-model as it is compatible with the canonical quantization relations. In this gauge, we obtain a new general solution to the equations of motion in terms of time-independent oscillating modes. The constraint structure is adequate for quantization in the Gupta-Bleuler formalism. We construct the space of states as a one-parameter family of Hilbert spaces and give the Bargmann-Fock and Jordan-Schwinger representations of it. Also, we give a simple description of the physical subspace as an infinite product of $\mathcal{D}^{+}_{\frac{1}{2}}$ in the positive discreet series irreducible representations of the $SU(1,1)$ group. We construct the map generated by the Hamiltonian between states at two different values of time and show how it produces the entanglement of left and right excitations. Next, we derive the formula of the entanglement entropy of the reduced density matrix for the ground state acted upon by the Hamiltonian map. Finally, we determine the asymptotic form of the entanglement entropy of a single mode bi-oscillator in the limit of large values of time.

The quantum scenario concerning Hawking radiation, gives us a precious clue that a black hole has its temperature directly connected to its area gravity and that its entropy is proportional to the horizon area. These results have shown that there exist a deep association between thermodynamics and gravity. The recently introduced Barrow formulation of back holes entropy, influenced by the spacetime geometry, shows the quantum fluctuations effects through Barrow exponent, $\Delta$, where $\Delta=0$ represents the usual spacetime and its maximum value, $\Delta=1$, characterizes a fractal spacetime. The quantum fluctuations are responsible for such fractality. Loop quantum gravity approach provided the logarithmic corrections to the entropy. This correction arises from quantum and thermal equilibrium fluctuations. In this paper we have analyzed the nonextensive thermodynamical effects of the quantum fluctuations upon the geometry of a Barrow black hole. We discussed the Tsallis' formulation of this logarithmically corrected Barrow entropy to construct the equipartition law. Besides, we obtained a master equation that provides the equipartition law for any value of the Tsallis $q$-parameter and we analyzed several different scenarios. After that, the heat capacity were calculated and the thermal stability analysis was carried out as a function of the main parameters, namely, one of the so-called pre-factors, $q$ and $\Delta$.

Based on the non-relativistic regime of the Dirac equation coupled to a torsion pseudo-vector, we study the dynamics of magnetization and how it is affected by the presence of torsion. We consider that torsion interacting terms in Dirac equation appear in two ways one of these is thhrough the covariant derivative considering the spin connection and gauge magnetic field and the other is through a non-minimal spin torsion coupling. We show within this framework, that it is possible to obtain the most general Landau, Lifshitz and Gilbert (LLG) equation including the torsion effects, where we refer to torsion as a geometric field playing an important role in the spin coupling process. We show that the torsion terms can give us two important landscapes in the magnetization dynamics: one of them related with damping and the other related with the screw dislocation that give us a global effect like a helix damping sharped. These terms are responsible for changes in the magnetization precession dynamics.

We report a measurement of the energy spectrum of cosmic rays above $2.5{\times} 10^{18}$ eV based on $215,030$ events. New results are presented: at about $1.3{\times} 10^{19}$ eV, the spectral index changes from $2.51 \pm 0.03 \textrm{ (stat.)} \pm 0.05 \textrm{ (sys.)}$ to $3.05 \pm 0.05 \textrm{ (stat.)}\pm 0.10\textrm{ (sys.)}$, evolving to $5.1\pm0.3\textrm{ (stat.)} \pm 0.1\textrm{ (sys.)}$ beyond $5{\times} 10^{19}$ eV, while no significant dependence of spectral features on the declination is seen in the accessible range. These features of the spectrum can be reproduced in models with energy-dependent mass composition. The energy density in cosmic rays above $5{\times} 10^{18}$ eV is $(5.66 \pm 0.03 \textrm{ (stat.)} \pm 1.40 \textrm{ (sys.)} ) {\times} 10^{53}~$erg Mpc$^{-3}$.

The search for a space-time variation of the fundamental constants has been explored over the years to test our physical theories. In this paper, we use the dispersion measure ($DM$) of fast radio bursts (FRB) combined with type Ia supernovae (SNe) data to investigate a possible redshift evolution of the fine-structure constant ($\alpha$), considering the runaway dilaton scenario, which predicts $\frac{\Delta \alpha}{\alpha} = - \gamma\ln{(1+z)}$, where $\gamma$ is a constant proportional to the current value of the coupling between the dilaton field and hadronic matter. We derive all the relevant expressions for the $DM$ dependence concerning the fine-structure constant and constrain the parameter $\gamma$ from measurements of 17 well-localized FRBs and 1048 SNe data from the Pantheon compilation. We also use Monte Carlo simulations to forecast the constraining power of larger samples of FRB measurements for data sets with $N = 500$ and $N = 1000$ points. We found that the uncertainty on $\gamma$ can be improved by one order of magnitude and that limits on $\frac{\Delta \alpha}{\alpha}$ beyond $\sigma \sim 10^{-2}$ will depend crucially on better control of statistical and systematic uncertainties of upcoming FRB data.

We consider the entanglement dynamics between two-level atoms in a rotating black hole background. In our model the two-atom system is envisaged as an open system coupled with a massless scalar field prepared in one of the physical vacuum states of interest. We employ the quantum master equation in the Born-Markov approximation in order to describe the time evolution of the atomic subsystem. We investigate two different states of motion for the atoms, namely static atoms and also stationary atoms with zero angular momentum. The purpose of this work is to expound the impact on the creation of entanglement coming from the combined action of the different physical processes underlying the Hawking effect and the Unruh-Starobinskii effect. We demonstrate that, in the scenario of rotating black holes, the degree of quantum entanglement is significantly modified due to the phenomenon of superradiance in comparison with the analogous cases in a Schwarzschild spacetime. In the perspective of a zero angular momentum observer (ZAMO), one is allowed to probe entanglement dynamics inside the ergosphere, since static observers cannot exist within such a region. On the other hand, the presence of superradiant modes could be a source for violation of complete positivity. This is verified when the quantum field is prepared in the Frolov-Thorne vacuum state. In this exceptional situation, we raise the possibility that the loss of complete positivity is due to the breakdown of the Markovian approximation, which means that any arbitrary physically admissible initial state of the two atoms would not be capable to hold, with time evolution, its interpretation as a physical state inasmuch as negative probabilities are generated by the dynamical map.