On the Curvature of Space

Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data.The model simultaneously describes the Big Bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Fridemann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time, rather it oscillates around the potential minimum while settling down, unlike the slow roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations. 98.80.Cq,

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“…(47), corresponding to all possible solutions of the Einstein equations (19)(20)(21) in the Einstein frame Table 2 -Solutions for b = 0.…”

Section: Relating the Einstein And Flat Gaugesmentioning

confidence: 99%

The big bang and inflation united by an analytic solution

Bars

Chen

2011

Phys. Rev. D

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“…By solving the Einstein equations for this system one obtains the Friedmann equations [26] (also knows as FLRW metric), which arė…”

Section: A Expansion Of Flat Universementioning

confidence: 99%

Lattice Boltzmann model for numerical relativity

Ilseven

Mendoza

2016

Phys. Rev. E

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In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for Numerical Relativity. Our model is validated with wellestablished tests, showing good agreement with analytical solutions. Furthermore, we show that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improves. Finally, in order to show the potential of our approach a linear scaling law for parallelisation with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

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“…Caso a(t) diminua com o tempo, a distância física também diminui e a galáxia se aproxima de nós. Se derivarmos a expressão (1.5) com relação ao tempo obtemoṡ 6) lembrando que f (r) não depende da coordenada t e que f (r) = d a…”

Section: Capítulo 1 Cosmologiaunclassified

“…Na contramão do pensamento vigente, Alexander Friedmann publicou em 1922 uma série de equações baseadas nas equações de Einstein que previam a expansão do Universo com curvatura positiva [6]. Em 1924, Friedmann obteve soluções expansionistas com curvatura negativa [7].…”

Section: Introductionunclassified

Formulação cinética para cosmologias com criação de matéria e aplicações

Raymundo¹

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Sílvio e Vinícius. Em especial ao professor GarySteigman pelas ricas discussões.A todos funcionários do IFUSP e do IAG. Ao Departamento de Física Geral do IFUSP pela infra-estrutura concedida.Agradeçoà minha mãe Tamara e ao meu pai Paulo, pela dedicação, apoio e incentivo incondicionais. Ao meu irmão Carlos eà minha sobrinha Larissa, que são fonte de inspiração e grande influência.A minha namorada Claire, pela companhia.A CAPES e CNPq pelo suporte financeiro.i Resumo Nesta tese, estudamos cosmologias com criação de matéria como alternativa ao modelo ΛCDM. Generalizamos a equação de Boltzmann relativística com um termo de produção de partículas fenomenológico, de tal forma que a equação resultante seja capaz de reobter os resultados da termodinâmica de não-equilíbrio das equações de balanço e evolução de temperatura.Após obter o termo correto para a equação generalizada de Boltzmann, investigamos como o formalismo proposto altera a equação de evolução de relíquias cósmicas na presença de criação gravitacional de partículas.ii AbstractIn this thesis, we study matter creation cosmologies as an alternative to the ΛCDM model. We generalize the relativistic Boltzmann equation with a phenomenological particle production term, in such a way that the resulting equation will be able to reproduce the non-equilibrium thermodynamics results of the balance equations and temperature evolution law.After obtaining the correct term to the generalized Boltzmann equation, we investigate how the proposed formalism changes the cosmic relic evolution equation in the presence of gravitational particle creation.iii Convenções• Adotaremos o sistema de unidades naturais em que c = k = h = 1. Quando for conveniente, reescreveremos as constantes explicitamente.

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On the Curvature of Space

Cited by 146 publications

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The big bang and inflation united by an analytic solution

The big bang and inflation united by an analytic solution

Lattice Boltzmann model for numerical relativity

Formulação cinética para cosmologias com criação de matéria e aplicações

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