The motivation of this thesis is to look for a signature of Lorentz violation, hopefully observable, in the gravitational waves emitted by cosmic strings. Aspects of cosmic strings are reviewed, in particular how focused bursts of gravitational radiation are emitted when a cusp forms on the string. The same phenomenon is then studied in an effective field theory with Lorentz violation called Einstein-aether theory. This is a simple theory with a dynamic preferred frame, but it retains rotational and diffeomorphism invariance. The linearized version of the theory produces five wave modes. We study the usual transverse traceless modes which now have a wave speed that can be lower or greater than the speed of light. This altered speed produces distinctive features in the waves. They depend on two free parameters: roughly the wave speed and the acceleration of the string cusp. The profile of the wave is analyzed in detail for different values of the parameters and explained by close comparison with the string motion.

The motivation of this thesis is to look for a signature of Lorentz violation, hopefully observable, in the gravitational waves emitted by cosmic strings. Aspects of cosmic strings are reviewed, in particular how focused bursts of gravitational radiation are emitted when a cusp forms on the string. The same phenomenon is then studied in an effective field theory with Lorentz violation called Einstein-aether theory. This is a simple theory with a dynamic preferred frame, but it retains rotational and diffeomorphism invariance. The linearized version of the theory produces five wave modes. We study the usual transverse traceless modes which now have a wave speed that can be lower or greater than the speed of light. This altered speed produces distinctive features in the waves. They depend on two free parameters: roughly the wave speed and the acceleration of the string cusp. The profile of the wave is analyzed in detail for different values of the parameters and explained by close comparison with the string motion.

The motivation of this thesis is to look for a signature of Lorentz violation, hopefully observable, in the gravitational waves emitted by cosmic strings. Aspects of cosmic strings are reviewed, in particular how focused bursts of gravitational radiation are emitted when a cusp forms on the string. The same phenomenon is then studied in an effective field theory with Lorentz violation called Einstein-aether theory. This is a simple theory with a dynamic preferred frame, but it retains rotational and diffeomorphism invariance. The linearized version of the theory produces five wave modes. We study the usual transverse traceless modes which now have a wave speed that can be lower or greater than the speed of light. This altered speed produces distinctive features in the waves. They depend on two free parameters: roughly the wave speed and the acceleration of the string cusp. The profile of the wave is analyzed in detail for different values of the parameters and explained by close comparison with the string motion. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-11-06T20:00:02Z No. of bitstreams: 1 Marcos Lima Dias.pdf: 1365744 bytes, checksum: 2aa8dc442d4e20438c570810fb9d2ab8 (MD5) / Made available in DSpace on 2017-11-06T20:00:02Z (GMT). No. of bitstreams: 1 Marcos Lima Dias.pdf: 1365744 bytes, checksum: 2aa8dc442d4e20438c570810fb9d2ab8 (MD5) Previous issue date: 2017-04-13 / CAPES / The theoretical study about the existence of magnetic monopole has begun by P. A. M. Dirac in 1931 and its main consequence has been the possibility of explaining the quantization of the electric charge. In Grand Uni cation Theories (GUT's), the magnetic monopole may appear as a topological defect by spontaneous symmetry break, in a process known as Higgs mechanism. The GUT's also predict the existence of a topological soliton which has both magnetic and electric charges: the so-called dyon. Theoretically, these particles are predicted very massive and abundant in the Universe. There are particular cases of monopole and dyon, called BPS's states, which have the smallest possible mass values, besides analytical solutions. In this work, we present some basic ideas about topology and homotopy; we describe the main points that have led to the development of the theoretical study of monopole and dyon both as topological solitons; and nally we investigate the e ects of the Lorentz-violating CPTeven terms in the Gauge (in particular, non birefringent one) and Higgs sectors on the BPS's states of the 't Hooft-Polyakov magnetic monopole and of the Julia-Zee dyon, both given in the Georgi-Glashow SO(3) model. / O estudo teórico a respeito da existência do monopolo magnético foi iniciado por P. A. M. Dirac em 1931 e teve como principal consequência a possibilidade de explicar a quantização da carga elétrica. Em Teorias de Grande Unificação (GUT's), o monopolo magnético pode surgir como um defeito topológico por meio da quebra espontânea de simetria, em um processo conhecido como mecanismo de Higgs. As GUT's preveem também a existência de um sóliton topológico que possui tanto carga magnética quanto elétrica: o chamado dyon. Teoricamente, essas partículas se apresentam muito massivas e abundantes no Universo. Hé casos particulares do monopolo e do dyon, denominados estados BPS's, que têm os menores valores possíveis de massa, cujas soluções são analíticas. Neste trabalho, apresentamos algumas ideias básicas acerca de topologia e homotopia; descrevemos os principais pontos que levaram ao desenvolvimento do estudo teórico do monopolo e do dyon como sólitons topológicos; e investigamos finalmente os efeitos dos termos CPTpares de violação da simetria de Lorentz nos setores de Gauge (em especial, n~ao birrefrigente) e de Higgs sobre os estados BPS's do monopolo magnético de't Hooft-Polyakov e do dyon de Julia-Zee, ambos dados no modelo SO (3) de Georgi-Glashow.

Dans cette thèse, nous étudions plusieurs aspects de la radiation de Hawking en présence de violations de l'invariance locale de Lorentz. Ces violations sont introduites par une modification de la relation de dispersion, devenant non-linéaire aux courtes longueurs d’onde. Les principales motivations de ces travaux ont une double origine. Il y a d’une part le développement en matière condensée de trous noirs analogues, ou l’écoulement d’un fluide est perçu comme une métrique d’espace-temps pour les ondes de perturbations et ou la radiation de Hawking pourrait être détectée expérimentalement. D’autre part, il se pourrait que des effets de gravité quantique puissent être modélisés par une modification de la relation de dispersion. En premier lieu, nous avons obtenu des caractérisations précises des conditions nécessaires au maintien de l’effet Hawking en présence de violation de l’invariance de Lorentz. De plus, nous avons étudié l’apparition d’une onde macroscopique de fréquence nulle, dans des écoulements de type trous blancs et également pour des champs massifs. Une autre partie de ce travail a consisté à analyser une instabilité engendrée par les effets dispersifs, ou la radiation de Hawking est auto-amplifiée, générant ainsi un flux sortant exponentiellement croissant dans le temps. / In this thesis, we study several features of Hawking radiation in the presence of ultraviolet Lorentz violations. These violations are implemented by a modified dispersion relation that becomes nonlinear at short wavelengths. The motivations of this work arise on the one hand from the developing field of analog gravity, where we aim at measuring the Hawking effect in fluid flows that mimic black hole space-times, and on the other hand from the possibility that quantum gravity effects might be approximately modeled by a modified dispersion relation. We develop several studies on various aspects of the prob- lem. First we obtain precise characterizations about the deviations from the Hawking result of black hole radiation, which are induced by dispersion. Second, we study the emergence, both in white hole flows or for massive fields, of a macroscopic standing wave, spontaneously produced from the Hawking effect, and known as ‘undulation’. Third, we describe in detail an instability named black hole laser, which arises in the presence of two horizons, where Hawking radiation is self-amplified and induces an exponentially growing in time emitted flux.

The thesis concerns the measurement of the neutrino velocity with the OPERA experiment in the CNGS beam. There are different theoretical models that allow for Lorentz violating effects which can be investigated with measurements on terrestrial neutrino beams. The MINOS experiment published in 2007 a measure on the muon neutrinos over a distance of 730 km finding a deviation with respect to the expected time of flight of 126 ns with a statistical error of 32 ns and a systematic error of 64 ns. The OPERA experiment observes as well muon neutrinos 730 km away from the source, with a sensitivity significantly better than MINOS thanks to the higher number of interactions in the detector due to the higher energy beam and the much more sophisticated timing system explicitly upgraded in view of the neutrino velocity measurement. This system is composed by atomic cesium clocks and GPS receivers operating in "common view mode". Thanks to this system a time-transfer between the two sites with a precision at the level of 1 ns is possible. Moreover, a Fast Waveform Digitizer was installed along the proton beam line at CERN in order to measure the internal time structure of the proton pulses that are sent to the CNGS target. The result on the neutrino velocity is the most precise measurement so far with terrestrial neutrino beams: the neutrino time of flight was determined with a statistical uncertainty of about 10 ns and a systematic uncertainty smaller than 20 ns.

Orientador: Prof. Dr. Alysson Fábio Ferrari / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2016. / Operadores contendo derivadas superiores não estão incluídos no Modelo Padrão Estendido (SME) e podem ter relevância na busca por uma teoria que opere na escala de Planck. Nessa tese de doutorado investigamos algumas consequências físicas no regime de baixas energias devido a violação de Lorentz (Lorentz violation, ou LV) gerada por operadores desse tipo. Começamos com um modelo constituído pelo campo fermiônico carregado e massivo , pelo campo do fóton A e pelo campo do tipo áxion (ALP ou axion-like-particle) . A LV aparece através dos acoplamentos não mínimos Fd e 5=b , onde d e b são os vetores constantes responsáveis pela introdução da LV. Assumimos que o campo fermiônico tem massa muito grande, e integramos a ação efetiva no campo do férmion, obtendo então como correção quântica de uma laço uma interação efetiva a baixa energia entre o campo do fóton e o campo do ALP, que resulta ser do mesmo tipo de interação que tem sido investigado em pesquisas experimentais atuais. Em seguida, estudamos outras consequências da interação Fd por meio correções quânticas de um laço, agora exclusivamente no setor de fóton. Mostramos que tal interação LV é responsável por gerar na ação efetiva operadores LV com derivadas superiores. Dentre as correções quânticas geradas consideramos a correção até primeira ordem no parâmetro LV d, juntamente com as correções não lineares de mais baixa ordem, e investigamos efeitos da LV na propagação de ondas eletromagnéticas em uma região contendo um campo magnético forte e constante. Por fim investigamos consequências físicas adicionais da interação Fd por meio das interações entre fontes externas intermediadas pelo campo eletromagnético, onde discutimos os principais fenômenos físicos que emergem dessa teoria e que não são contemplados na teoria de Maxwell usual. / Higher derivatives operators are not included in the Standard Model Extension (SME) and they can have relevance in the search by a theory which operates in the Planck energy scale. In this PhD thesis we investigate some physical consequences in the low energy regime due to LV which was generated by this kind of operators. We start with a model in the high energy regime that is constituted by the charged massive fermionic field , by the photon field A and by the axion-like-particle (ALP) field . The LV appear in our model due to the two couplings Fd and 5=b , where d and b are the constant vectors responsible for introducing the LV. We assume the fermion mass to be very high and we integrate the effective action in the fermion field, obtaining as one-loop quantum correction an effective interaction in the low energy regime between the photon field and ALP field, which we show to be of the same form as the one studied in current experimental searches. Then, we study other physical consequences of the interaction Fd through one-loop quantum corrections in the pure photon sector. We show that such LV interaction generates in the effective action Lorentz violating higher derivatives operators. Among the generated quantum corrections we consider the ones of the first order in the LV parameter d; together with the lowest order non-linear corrections, and we investigate the effects of the LV in the electromagnetic wave propagation in a region with a strong, constant magnetic field. To finish, we investigate additional physical consequences of the interaction Fd through interactions between external sources intermediated by the electromagnetic field, where we discuss the main physical phenomena that emerge of this theory which have no counterpart in Maxwell theory.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-06-06T20:31:13Z No. of bitstreams: 1 CarlosSantos.pdf: 658387 bytes, checksum: 1df4b4e3039b37f11e39d47fde182d45 (MD5) / Made available in DSpace on 2017-06-06T20:31:13Z (GMT). No. of bitstreams: 1 CarlosSantos.pdf: 658387 bytes, checksum: 1df4b4e3039b37f11e39d47fde182d45 (MD5) Previous issue date: 2008-08-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA) / In this work, we investigate some significant aspects of the Maxwell-Carroll-Field- Jackiw-Proca (MCFJP) electrodynamics. This electrodynamics is built through the im- plementation of the Carroll-Field-Jackiw(CFJ) term on the Proca Lagrangian. The CFJ term is the CPT odd term of the gauge sector of the Standard Model Extension. First, we verify under which circumstances this model yields a consistent Quantum Field The- ory (QFT) capable of describing the interactions mediated by photons. In this sense, the propagator ‹Aα(k)Av (k)› is carried out, with the dispersion relations and associated propagation modes being determined. Then, we verify which of these modes are stable, causal and unitary. Only when the theory is causal, stable and unitary, we can say that it can be consistently quantized. It follows that the MCFJP electrodynamics is consistent only for a purely space-like background field, Vα = (0; v). A posteriori, we investigate the classical solutions (static and stationary) of MCFJP electrodynamics. The starting point is the wave equation for the gauge field A (r), which through the use of Green Method, yields explicit expressions for A (k). For a purely time-like background field, Vα= (v0; 0), an exponentially decreasing solution for the electric sector is obtained, equal to the Maxwell-Proca solution. Therefore, the background does not promote any change in electric sectors of the MCFJP and MCFJ electrodynamics. On the other hand, the magnetic sector is changed: for stationary currents, it displays an oscillating behavior [in Maxwell-Proca (MP) electrodynamics, these solutions have an exponentially decreasing behavior]. In the limitMA!0, we obtain the stationary field B(r) ofMCFJ electrodynam- ics (oscillating behavior), which is compatible with the emission of Cerenkov radiation. For a purely space-like background, V = (0; v), we obtain stationary solutions at second order in v, assuming v2 M2 A ; and v jj r. It appears that both magnetic and electric sectors display exponentially decreasing solutions, which recover those ones of the MP electrodynamics in the limit v → 0. / Neste trabalho, objetiva-se investigar significativos aspectos da eletrodinâmica de Maxwell-Carroll-Field-Jackiw-Proca (MCFJP). Esta eletrodinâmica é construída via a implementação de campos de fundo (backgrounds), responsáveis pela violação da invariância de Lorentz, no setor de gauge puro do Modelo Padrão usual. Primeiramente, averigua-se sob quais circunstâncias é possível a definição de uma Teoria Quântica de Campo (TQC) consistente, ou seja, capaz de descrever as interações mediadas por fótons. Neste ínterim, calcula-se o propagador ‹Aα(k)Av (k)›, relações de dispersão e modos de propagação associados. Em seguida, identifica-se quais destes modos são estáveis, cau- sais e unitários. Apenas quando a teoria é causal, estável e unitária, pode-se dizer que a mesma pode ser consistentemente quantizada. Conclui-se que a eletrodinâmica deMCFJP é consistente apenas apenas para o caso de um background tipo-espaço, Vα = (0; v). Na sequência, investiga-se as soluções clássicas (estáticas e estacionárias) para a eletrodinâmica de MCFJP. Calcula-se a equação de onda para o setor Av(r) e, via a implementação do Método de Green, expressões explícitas para Av(k). Para um background tipo-tempo, Vα= (v0; 0), resulta um setor elétrico exponencialmente decrescente. No limite MA!0, conclui-se que o background não promove alteração nos setores elétricos das eletrodinâmicas de MCFJP e MCFJ. Já o setor magnético é alterado: quando gerado por cargas em movimento estacionário, este exibe um comportamento oscilante [na eletrodinâmica de Maxwell-Proca (MP), as soluções são exponencialmente decrescentes]. No limite MA→0, obtém-se o campo B(r) estacionário de MCFJ (comportamento oscilante), o qual é compatível com a emissão de radiação Cerenkov. Para um background tipo-espaço, Vα = (0; v), obtém-se soluções estacionárias em segunda ordem em v, e supondo v / r, v2≪ M2 A. Verifia-se que ambos os setores elétrico e magnético exibem soluções exponencialmente decrescentes, as quais, no limite v → 0, reproduzem aquelas da eletrodinâmica de MP.

Physics in the year 2006 is tightly constrained by experiment, observation, and mathematical consistency. The Standard Model provides a remarkably precise de- scription of particle physics, and general relativity is quite successful in describing gravitational phenomena. At the same time, it is clear that a more fundamental theory is needed for several distinct reasons. Here we consider a new approach, which begins with the unusually ambitious point of view that a truly fundamental theory should aspire to explaining the origins of Lorentz invariance, gravity, gauge fields and their symmetry, supersymmetry, fermionic fields, bosonic fields, quantum mechanics and spacetime. The present dissertation is organized so that it starts with the most conventional ideas for extending the Standard Model and ends with a microscopic statistical picture, which is actually the logical starting point of the theory, but which is also the most remote excursion from conventional physics. One motivation for the present work is the fact that a Euclidean path integral in quantum physics is equivalent to a partition function in statistical physics. This suggests that the most fundamental description of nature may be statistical. This dissertation may be regarded as an attempt to see how far one can go with this premise in explaining the observed phenomena, starting with the simplest statistical picture imaginable. It may be that nature is richer than the model assumed here, but the present results are quite suggestive, because, with a set of assumptions that are not unreasonable, one recovers the phenomena listed above. At the end, the present theory leads back to conventional physics, except that Lorentz invariance and supersymmetry are violated at extremely high energy. To be more specific, one obtains local Lorentz invariance (at low energy compared to the Planck scale), an SO(N) unified gauge theory (with N = 10 as the simplest possibility), supersymmetry of Standard Model fermions and their sfermion partners, and other familiar features of standard physics. Like other attempts at superunification, the present theory involves higher dimensions and topological defects.

Observations from the 1930s until the present have established the existence of dark matter with an abundance that is much larger than that of luminous matter. Because none of the known particles of nature have the correct properties to be identified as the dark matter, various exotic candidates have been proposed. The neutralino of supersymmetric theories is the most promising example. Such cold dark matter candidates, however, lead to a conflict between the standard simulations of the evolution of cosmic structure and observations. Simulations predict excessive structure formation on small scales, including density cusps at the centers of galaxies, that is not observed. This conflict still persists in early 2007, and it has not yet been convincingly resolved by attempted explanations that invoke astrophysical phenomena, which would destroy or broaden all small scale structure. We have investigated another candidate that is perhaps more exotic: Lorentz-violating dark matter, which was originally motivated by an unconventional fundamental theory, but which in this dissertation is defined as matter which has a nonzero minimum velocity. Furthermore, the present investigation evolved into the broader goal of exploring the properties of Lorentz-violating matter and the astrophysical consequences – a subject which to our knowledge has not been previously studied. Our preliminary investigations indicated that this form of matter might have less tendency to form small-scale structure. These preliminary calculations certainly established that Lorentz-violating matter which always moves at an appreciable fraction of the speed of light will bind less strongly. However, the much more thorough set of studies reported here lead to the conclusion that, although the binding energy is reduced, the small-scale structure problem is not solved by Lorentz-violating dark matter. On the other hand, when we compare the predictions of Lorentz-violating dynamics with those of classical special relativity and general relativity, we find that differences might be observable in the orbital motions of galaxies in a cluster. For example, galaxies – which are composed almost entirely of dark matter – observed to have enlarged orbits about the cluster center of mass may be an indication of Lorentz violation.