Tunneling probability for the birth of an asymptotically de Sitter universe

Barros, J. Acácio de; Silva, E. V. Corrêa; Monerat, G. A.; Oliveira‐Neto, G.; Filho, L. G. Ferreira; Romildo, P.

doi:10.1103/physrevd.75.104004

Cited by 22 publications

(68 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Here, we may see that, as was explained in Refs. [13] and [31], T P and T P W KB agree only for values of E ′ m s very close to the top of V ef f .…”

Section: Tunneling Probability As a Function Of E M And αmentioning

confidence: 96%

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

et al. 2007

Self Cite

View full text Add to dashboard Cite

The modeling of the early universe is done through the quantization of a Friedmann-Robertson-Walker model with positive curvature. The material content consists of two fluids: radiation and Chaplygin gas. The quantization of these models is made by following the Wheeler and DeWitt's prescriptions. Using the Schutz formalism, the time notion is recovered and the Wheeler-DeWitt equation transforms into a time dependent Schrödinger equation, which rules the dynamics of the early universe, under the action of an effective potential V ef . Using a finite differences method and the Crank-Nicholson scheme, in a code implemented in the program OCTAVE, we solve the corresponding time dependent Schrödinger equation and obtain the time evolution of a initial wave packet. This wave packet satisfies appropriate boundary conditions. The calculation of the tunneling probabilities shows that the universe may emerge from the Planck era to an inflationary phase. It also shows that, the tunneling probability is a function of the mean energy of the initial wave packet and of two parameters related to the Chaplygin gas. We also show a comparison between these results and those obtained by the WKB approximation.

show abstract

“…Here, we may see that, as was explained in Refs. [13] and [31], T P and T P W KB agree only for values of E ′ m s very close to the top of V ef f .…”

Section: Tunneling Probability As a Function Of E M And αmentioning

confidence: 96%

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

et al. 2007

Self Cite

View full text Add to dashboard Cite

show abstract

“…The mechanism of such transition is the quantum tunneling. It is striking that for the vacuum case the tunneling probability is very close to unity, much larger than the ones obtained in the literature for other cases [7,32].…”

Section: Discussionmentioning

confidence: 48%

Quantum Cosmology with Many Fluids and the Choice of Cosmological Time

Monerat¹,

Santos

Alvarenga

et al. 2019

Braz J Phys

Self Cite

View full text Add to dashboard Cite

In this work we propose the quantization of a cosmological model describing the primordial universe filled with five barotropic fluids, namely: radiation, dust, vacuum, cosmic strings and domain walls. We intend to identify which fluid is best suited to provide phenomenologically the temporal variable in accordance with the observable universe. Through the Galerkin spectral method and the finite difference method in the Crank-Nicolson scheme (vacuum case), the cosmological solutions are obtained and compared. The vacuum case is especially interesting because it provides a tunneling transition mechanism from the quantum to the classical phase and the possibility of calculating quantum tunneling probabilities. PACS number(s): 98

show abstract

“…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.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Tunneling probability for the birth of an asymptotically de Sitter universe

Cited by 22 publications

References 39 publications

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

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

Quantum Cosmology with Many Fluids and the Choice of Cosmological Time

Quantização de sistemas hamiltonianos via método de diferenças finitas

Contact Info

Product

Resources

About