Dynamics of the early universe and the initial conditions for inflation in a model with radiation and a Chaplygin gas

Monerat, G. A.; Oliveira‐Neto, G.; Silva, E. V. Corrêa; Filho, L. G. Ferreira; Romildo, P.; Fabris, J. C.; Fracalossi, R.; Gonçalves, S. V. B.; Alvarenga, F. G.

doi:10.1103/physrevd.76.024017

Cited by 48 publications

(44 citation statements)

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“…Del Campo and Herrera [25,26] studied warm-Chaplygin and tachyonChaplygin inflationary universe models. Monerat et al [27] explored the dynamics of the early universe and initial conditions for an inflationary model with radiation and CG.…”

Section: Introductionmentioning

confidence: 99%

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Study of inflationary generalized cosmic Chaplygin gas for standard and tachyon scalar fields

Sharif

Saleem

2014

Eur. Phys. J. C

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We consider an inflationary universe model in the context of the generalized cosmic Chaplygin gas by taking the matter field as standard and tachyon scalar fields. We evaluate the corresponding scalar fields and scalar potentials during the intermediate and logamediate inflationary regimes by modifying the first Friedmann equation. In each case, we evaluate the number of e-folds, scalar as well as tensor power spectra, scalar spectral index, and the important observational parameter, the tensor-scalar ratio in terms of inflation. The graphical behavior of this parameter shows that the model remains incompatible with WMAP7 and Planck observational data in each case.

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Section: Introductionmentioning

confidence: 99%

“…The corresponding scalar spectral index is (27) From P R and P g , we find the tensor-scalar ratio as…”

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confidence: 99%

Study of inflationary generalized cosmic Chaplygin gas for standard and tachyon scalar fields

Sharif

Saleem

2014

Eur. Phys. J. C

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“…Recentemente utilizamos o método de diferenças finitas no esquema de CrankNicolson [11] para obter a quantização de modelos cosmológicos homogêneos e isotrópicos com diferentes fontes de matéria [12][13][14][15]. Métodos espectrais [16] também têm se mostrado importantes ferramentas na determinação do espectro de energia de sistemas físicos com soluções analíticas desconhecidas.…”

Section: Introductionunclassified

Quantização de sistemas hamiltonianos via método de diferenças finitas

Monerat

Filho

Silva

et al. 2010

Rev. Bras. Ensino Fís.

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Propomos a introdução do método de diferenças finitas como tópico a ser abordado na disciplina de mecânica quântica de um curso de graduação em física. O métodoé suficientemente simples para ser introduzido e exemplificado em seis horas de aula, permitindo a obtenção de resultados tanto qualitativamente corretos como de alta precisão quantitativa. Devido a sua grande aplicabilidade, seu entendimento por parte dos alunos de graduação em física, futuros pesquisadores,é essencial para a formação acadêmica destes. No presente trabalho, apresentamos o método em detalhes. Sua precisãoé verificada calculando o espectro de energia para o oscilador harmônico e comparando-os com os resultados analíticos conhecidos. Em seguida aplicamos o método a dois outros sistemas, o oscilador anarmônico quártico e o potencial linear. Para cada um destes sistemas, calculamos os dez níveis de energia mais baixos, bem como seus respectivos auto-estados. Palavras-chave: quantização de sistemas hamiltonianos, diferenças finitas.We propose the introduction of the finite differences method as one topic to be inserted in the discipline of quantum mechanics in a physics undergraduate course. The method is simple enough to be introduced and exemplified in about six hours of class allowing both qualitatively correct and high-precision quantitative results. Due to the great applicability of the method, it is essential that the undergraduate students, future researchers, learn it. In the present work, we show the method in detail and verify its precision initially by calculating the energy spectrum of the harmonic oscillator and comparing it to its well-known analytical results. Then we apply it to two other systems, the anharmonic oscillator and the one with linear potential. For each of those systems We compute, for both systems, the ten lowest energy eigenvalues are calculated, as well as their corresponding eigenfunctions.

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“…Note that all these characteristics are solutions of stationary WDW equation, while non-stationary consideration of multiple packets moving along barrier gives clear understanding of the process. In order to give a basis to readers to estimate ability of the approach developed in this paper, let us consider results in (Monerat et al, 2007) (see eq. (19)).…”

Section: Passage To Non-stationary Wdw Equation: Motivationsmentioning

confidence: 99%

A Fully Quantum Model of Big Bang

Maydanyuk¹,

Popolo²,

Olkhovsky³

et al. 2012

Theoretical Concepts of Quantum Mechanics

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16www.intechopen.com 2 Will-be-set-by-IN-TECH (Vilenkin, 1994) could seem to be the most natural and clear description, where the wave function should represent an outgoing wave only in the enough large value of the scale factor a. However, is really such a wave free in the asymptotic region? In order to draw attention on the increase of the modulus of the potential with increasing value of the scale factor a and increasing magnitude of the gradient of such a potential, acting on this wave "through the barrier", then one come to a serious contradiction: the influence of the potential on this wave increases strongly with a! Now a new question has appeared: what should the wave represent in general in the cosmological problem? This problem connects with another and more general one in quantum physics -the real importance to define a "free" wave inside strong fields.T o this aim we need a mathematical stable tool to study it. It is unclear whether a connection between exact solutions for the wave function at turning point and "free" wave defined in the asymptotic region is correct. Note that the semiclassical formula of the penetrability of the barrier is constructed on the basis of wave which is defined concerning zero potential at infinity, i.e. this wave should be free outgoing in the asymptotic region. But in the cosmological problem we have opposite case, when the force acting on the wave increases up to infinity in the asymptotic region. At the same time, deformations of the shape of the potential outside the barrier cannot change the penetrability calculated in the framework of the semiclassical approach (up to the second order). An answer to such problem can be found in non-locality of definition of the penetrability in quantum mechanics, which is reduced to minimum in the semiclassical approach (i. e. this is so called "error" of the cosmological semiclassical approach). The problem of the correct definition of the wave in cosmology is reinforced else more, if one wants to calculate the incident and reflected waves in the internal region. Even with the known exact solution for the wave function there is uncertainty in determination of these waves! But, namely, the standard definition of the coefficients of penetrability and reflection is based on them. In particular, we have not found papers where the coefficient of reflection is defined and estimated in this problem (which differs essentially from unity at the energy of radiation close to the height of the barrier and, therefore, such a characteristics could be interesting from a physical point of view). Note that the semiclassical approximation put serious limits to the possibility of its definition at all (Landau & Lifshitz, 1989). Thus, in order to estimate probability of the formation of the Universe as accurately as possible, we need a fully quantum definition of the wave. Note that the non-semiclassical penetrability of the barrier in the cosmological problems has not been studied in detail and, therefore, a development of fully quantum methods for ...

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Dynamics of the early universe and the initial conditions for inflation in a model with radiation and a Chaplygin gas

Cited by 48 publications

References 35 publications

Study of inflationary generalized cosmic Chaplygin gas for standard and tachyon scalar fields

Study of inflationary generalized cosmic Chaplygin gas for standard and tachyon scalar fields

Quantização de sistemas hamiltonianos via método de diferenças finitas

A Fully Quantum Model of Big Bang

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