--- title: "On the bouncing completion of eternal inflation • CBPF Index" description: "O CBPF INDEX é o sistema de acompanhamento da produção científica e tecnológica do CBPF. Nele é possível obter a lista de publicações de artigos, livros, relatórios técnicos, etc de toda a comunidade do CBPF." canonical_url: "https://index.cbpf.br/publicacoes/6ad2a767639f62b11adbdaa8" locale: pt meta: "og:description": "O CBPF INDEX é o sistema de acompanhamento da produção científica e tecnológica do CBPF. Nele é possível obter a lista de publicações de artigos, livros, relatórios técnicos, etc de toda a comunidade do CBPF." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_On%2Bthe%2Bbouncing%2Bcompletion%2Bof%2Beternal%2Binflation%2Ctipo_~RGlzc2VydGHDp8OjbyBkZSBtZXN0cmFkbw%2Ccor_~IzdhM2E5OQ%2Cautores_~WGF2aWVyLCBWLiBOLg%2Cdetalhe_~MzAvMDUvMjAyNQ%2Csecao_~UHVibGljYcOnw7Vlcw%2Cp_Ii9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmRhYTgi%2Cs_3CpngfCV2I6eTO5z.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "On the bouncing completion of eternal inflation • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_On%2Bthe%2Bbouncing%2Bcompletion%2Bof%2Beternal%2Binflation%2Ctipo_~RGlzc2VydGHDp8OjbyBkZSBtZXN0cmFkbw%2Ccor_~IzdhM2E5OQ%2Cautores_~WGF2aWVyLCBWLiBOLg%2Cdetalhe_~MzAvMDUvMjAyNQ%2Csecao_~UHVibGljYcOnw7Vlcw%2Cp_Ii9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmRhYTgi%2Cs_3CpngfCV2I6eTO5z.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Dissertação de mestrado****Defendida** # **On the bouncing completion of eternal inflation** **Xavier, V. N.** 30/05/2025 [**Baixar PDF **1 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbdaa8/pdf) [**Contatar responsável**](mailto:denise@cbpf.br?subject=On%20the%20bouncing%20completion%20of%20eternal%20inflation) ## **Resumo** The duration of our Universe, all of its content, and whether it had a beginning or has always existed has long been the subject of intense investigation. As free particles trajectories are given by geodesics, the inquisition of godesic completeness and extensions become crucial for the investigation of possible eternal Universes. Nevertheless, General Relativity’s invariance under diffeomorphisms imposes an additional difficulty to realize whether the incompleteness has physical significance or if it is merely an inappropriate coordinate choice. In this context, the singularity theorems provide sufficient conditions for geodesic incompleteness without recurring to coordinate charts. However, kinematic alternatives for classifying incomplete space-times that are expanding have been proposed, leading to the Borde-Guth-Vilenkin (BGV) theorem, where no restriction on the matter fields are necessary, such as energy conditions. Notwithstanding, whether the space time admits a metric extension that is compatible with General Relativity, i.e, a 𝒞2 extension, needs to be addressed. In this dissertation, using the pivotal example of the flat patch of the de Sitter space, we manage to find a new global chart for this space - which without considerations of extensibility would be diagnosed as geodesically incomplete. Furthermore, we developed a general protocol for a 𝐶2 extension of a flat Friedmann-Lemaître-Robertson-Walker metric, and the necessary conditions for its application by exhausting all the possible cases in the asymptotic limit, finding necessary and sufficient conditions for extensibility. The incomplete spaces that violate the assumptions have either a scalar curvature singularity or a parallelly propagated singularity, in which cases no 𝒞2 extension is allowed. Moreover, we discuss results for possible cyclic scenarios proposed in the literature. The results obtained in this work were published in Phys. Rev. D 111, 123531 (2025). ## **Dados da publicação**
Autores
Xavier, V. N.
Tipo
Dissertação de mestrado
Status
Defendida
Data de publicação
30/05/2025
Instituição
CBPF
Data de defesa
30/05/2025
```json {"@context":"https://schema.org","@graph":[{"@id":"https://index.cbpf.br/#website","@type":"WebSite","description":"O CBPF INDEX é o sistema de acompanhamento da produção científica e tecnológica do CBPF. Nele é possível obter a lista de publicações de artigos, livros, relatórios técnicos, etc de toda a comunidade do CBPF.","inLanguage":"pt-BR","name":"CBPF Index","url":"https://index.cbpf.br/","publisher":{"@id":"https://index.cbpf.br/#identity"},"workTranslation":[{"@id":"https://index.cbpf.br/en#website"},{"@id":"https://index.cbpf.br/es#website"}]},{"@id":"https://index.cbpf.br/publicacoes/6ad2a767639f62b11adbdaa8#webpage","@type":"WebPage","description":"O CBPF INDEX é o sistema de acompanhamento da produção científica e tecnológica do CBPF. Nele é possível obter a lista de publicações de artigos, livros, relatórios técnicos, etc de toda a comunidade do CBPF.","name":"On the bouncing completion of eternal inflation","url":"https://index.cbpf.br/publicacoes/6ad2a767639f62b11adbdaa8","isPartOf":{"@id":"https://index.cbpf.br/#website"},"potentialAction":[{"@type":"ReadAction","target":["https://index.cbpf.br/publicacoes/6ad2a767639f62b11adbdaa8"]}],"primaryImageOfPage":{"@id":"https://index.cbpf.br/#logo"}},{"@id":"https://index.cbpf.br/#identity","@type":"Organization","alternateName":"CBPF","description":"Unidade de pesquisa do Ministério da Ciência, Tecnologia e Inovação dedicada à pesquisa básica em Física, suas aplicações e à formação científica.","email":"web@cbpf.br","legalName":"Centro Brasileiro de Pesquisas Físicas/CBPF","name":"Centro Brasileiro de Pesquisas Físicas","taxID":"04.044.443/0001-35","telephone":"+55-21-2141-7100","url":"https://cbpf.br","address":{"@type":"PostalAddress","streetAddress":"Rua Dr. Xavier Sigaud, 150","addressLocality":"Rio de Janeiro","addressRegion":"RJ","postalCode":"22290-180","addressCountry":"BR"},"logo":{"@id":"https://index.cbpf.br/#logo"},"sameAs":["https://twitter.com/cbpf_mcti"]},{"@id":"https://index.cbpf.br/#logo","@type":"ImageObject","caption":"Centro Brasileiro de Pesquisas Físicas","contentUrl":"https://index.cbpf.br/icon-512x512-light.png","inLanguage":"pt-BR","url":"https://index.cbpf.br/icon-512x512-light.png"}]} ``` ## Sitemap See the full [sitemap](https://index.cbpf.br/sitemap.md) for all pages.