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Cosmologia & Relatividade Geral COSMOLOGIA Sérgio Mittmann dos Santos Astronomia Licenciatura em Ciências da Natureza IFRS Câmpus Porto Alegre 2021/1 Expansão do Universo 1912 Vesto Melvin Slipher (1875‑1969) descobre que as linhas espectrais das estrelas da galáxia de Andrômeda mostram um enorme deslocamento para o azul [efeito Doppler relativístico, para a luz] Indicam que essa galáxia está se aproximando do Sol a uma velocidade de 300 km/s 1912-Início da década de 1930 Slipher demonstra que, de 41 galáxias, a maioria apresenta deslocamento espectral para o vermelho redshift Galáxias afastam-se de nós Luminosidade fraca mais distante redshift maior Lei de Hubble 1929 Edwin Powell Hubble (1889-1953) Mede o deslocamento para o vermelho z = / 0 nas linhas espectrais das galáxias observadas por Milton La Salle Humason (1891-1972) Mede as distâncias das galáxias Descobre que as galáxias estão se afastando, com velocidades proporcionais às suas distâncias Lei de Hubble v = H·r, sendo H 17·103 m/(s·ano-luz) Modelo do bolo de passas Expansão não indica que estamos no centro do Universo PARADOXO DE OLBERS O enigma da escuridão da noite 1610 Johannes Kepler (1571-1630) Céu escuro à noite prova que o Universo é finito Encerrado por uma parede cósmica escura Séc. 18 Edmund Halley (1656-1742) + 1826 Heinrich Wilhelm Mattäus Olbers (1758‑1840) Brilho das estrelas 1/distância2 Número de estrelas distância2 Linha de visada sempre intercepta uma estrela Brilho do céu Brilho da superfícieEstrela_média PARADOXO DE OLBERS Propostas de solução Olbers Poeira interestelar absorve a luz das estrelas PROBLEMA Poeira entra em equilíbrio térmico com as estrelas e passa a brilhar tanto quanto elas Expansão do Universo degrada a energia Luz de objetos muito distantes chega muito desviada para o vermelho, muito fraca PROBLEMA Cálculos mostram que não é suficiente para solucionar o paradoxo SOLUÇÃO Universo não existiu por todo o sempre Universo tem uma idade finita Luz tem uma velocidade finita Luz das estrelas mais distantes ainda não teve tempo de chegar até nós Universo que enxergamos é limitado no espaço, por ser finito no tempo Escuridão da noite é uma prova de que o Universo teve um início Big Bang Herman Bondi (1919-2005)+Thomas Gold (1920-2004)+Fred Hoyle (1915-2001) TEORIA DO ESTADO ESTACIONÁRIO Universo similar em todas as direções Imutável no tempo Produção contínua de matéria para contrabalançar a expansão Densidade média constante 1950 Fred Hoyle Sugestão pejorativa de um Big BangGrande Expansão para o início do Universo Big Bang (cont.) (definição) 1929 Hubble Galáxias estão se afastando umas das outras No passado, deveriam estar cada vez mais próximas Há cerca de 13,8 bilhões de anos, deveriam estar todas num mesmo ponto muito quente singularidade no espaço‑ tempo Início do Universo coincide com o início da expansão Criação matéria+radiação+espaço+tempo Início do nosso universo Big Bang (cont.) (indicação de que a teoria está correta) Década de 1920 Georges-Henri Édouard Lemaître (1894-1966)+Alexander Friedmann (1888-1925) Família de soluções das equações da Teoria da Relatividade Geral Prevêem EXPANSÃO eterna ou novo COLAPSO 1973 Edward P. Tryon Big Bang ocorreu por uma flutuação quântica do vácuo (radiação de Hawking) Big Bang (cont.) (indicação de que a teoria está correta) 1948 Ralph Asher Alpher (1921-)+Robert Herman (1922-1997) [associados de George Gamow (1904-1968)] Preveem uma radiação remanescente do estado quente do Universo, quando ficou transparente, há 380 mil anos depois do Big Bang T < 5 K 1964 Arno Allan Penzias (1933-)+Robert Woodrow Wilson (1936-) RADIAÇÃO CÓSMICA DO FUNDO DO UNIVERSO Descoberta ACIDENTAL de uma radiação vinda de todas as direções Proveniente das regiões mais distantes do Universo, a 13,8 bilhões de anos-luz Radiação remanescente do Big Bang T = 2,7 K 1978 Prêmio Nobel 1989 COBE (Cosmic Background Explorer) T = 2,735 K (<1%) Big Bang (cont.) (indicação de que a teoria está correta) 2001 WMAP (Wilkinson Microwave Anisotropy Probe) Confirma as predições do Big Bang 2010 Idade do Universo 13,78 ± 0,11 bilhões de anos Formação das primeiras estrelas 377±3 milhões de anos após o Big Bang Maior parte do Universo é ENERGIA ESCURA=constante cosmológica de Einstein=energia do vácuo=quintessência [Aristóteles] Tipo Porcentagem da densidade crítica Energia escura 72,1% Matéria escura 23,3% Matéria normal 4,6% Radiação 0,005% Modelo do Big Bang Destino do Universo Expansão para sempre ou Expansão parará e haverá novo colapso ao estado denso Para o colapso, atração gravitacional da matéria+energia deve ser suficiente para parar a expansão Não há como determinar se o Universo está se expandindo com velocidade maior do que a velocidade de escape, porque não há um pleno conhecimento sobre o comportamento das matéria+energia escuras, que parecem representar mais de 95% da matéria+energia total Destino do Universo Interrompe a expansão 5 átomos H/m3 Destino do Universo (cont.) 1998 Saul Perlmutter, Adam Riess e Brian Schmidt Detecção da aceleração do Universo, através da detecção das supernovas mais distantes Tamanho do Universo dobrou nos últimos 5 bilhões de anos 2011 Prêmio Nobel Referências K. S. Oliveira Fo. e M. F. O. Saraiva. Astronomia e astrofísica, 2a. ed. São Paulo: Livraria da Física, 2004 W. J. Maciel (ed.). Astronomia e astrofísica. São Paulo: EdUSP, 1991 D. Halliday, R. Resnick e J. Walker. Fundamentos de física, v. 4, 8a. ed. Rio de Janeiro: LTC, 2009 ADENDO TEORIA DA RELATIVIDADE Teoria da Relatividade ESPECIAL OU RESTRITA 1905 Albert Einstein (1879-1955) Propõe a Teoria da Relatividade Especial Velocidade da luz no vácuo é constante, independente da velocidade da fonte Contração do comprimento quando v c Dilatação do tempo quando v c Massa Velocidade Massa e energia são equivalentes E = mc2 Nenhuma informação ou matéria pode se mover mais rápido do que a luz no vácuo Restrita ao caso em que os campos gravitacionais são pequenos Teoria da Relatividade GERAL 1916 Einstein Propõe a Teoria da Relatividade Geral Válida mesmo nos casos em que os campos gravitacionais são grandes Teoria da gravidade Descreve a gravitação como a ação das massas nas propriedades do espaço e do tempo, que afetam o movimento dos corpos e outras propriedades físicas Espaçotempo é distorcido pela presença da matéria que ele contém 1917 Einstein Modelo esférico do Universo Introduziu a constante cosmológica, para obter um Universo estático Constante cosmológica Força repulsiva, que previne o colapso do Universo pela atração gravitacional 1917 Willem de Sitter (1872-1934) Constante cosmológica Permite um Universo em expansão, mesmo se ele não contivesse qualquer matéria Constante cosmológica Energia do vácuo Escalas pequenas Podemos ver estrelas, galáxias e aglomerados de galáxias Escalas acima de 10 milhões de anos-luz Observações indicam um universo homogêneo e isotrópico densidade média constante Princípio Cosmológico Universo homogêneo e isotrópico Teoria da Relatividade GERAL (cont.) Equações de Einstein Lentes gravitacionais Relatividade geral Raio de luz é desviado ao passar por um corpo massivo 1919 Expedição dupla chefiada por Arthur Stanley Eddington (1882-1944) a Sobral-CE e à Ilha de Príncipe-África Medição das posição das estrelas durante um eclipse total do Sol, em 29 de maio de 1919, na constelação do Touro Expedições de Eddington Cruz de Einstein Quasar a 8 bilhões de anos-luz Lente gravitacional Galáxia G2237+0305 a 400 milhões de anos-luz Número de imagens depende da distribuição de massa da galáxia e dos detalhes do alinhamento Deslocamentos dos periélios dos planetas terrestres Não pode ser explicado pela teoria newtoniana Somente a massa contribui para a gravidade Corretamente descrito pela teoria da relatividade Energia cinética do movimento dos planetas também contribui para a gravidade Espaçotempo é perturbado pela presença da massa do Sol Mercúrio 43"/séc. Vênus 8,6"/séc. Terra 3,8"/séc. Ondas gravitacionais Teoria da relatividade geral Massas aceleradas emitem ondas gravitacionais, como cargas elétricas aceleradas produzem ondas eletromagnéticas Ondas gravitacionais Perturbações na curvatura do espaçotempo Propagam-se à velocidade da luz 1974 Russell Alan Hulse (1950-) e Joseph Hooton Taylor Jr. (1941-) Medida da taxa de redução do período orbital do pulsar binário PSR 1913+16 (2 estrelas de nêutrons) Concorda com precisão melhor do que 1% com o cálculo de perda de energia devido à emissão de ondas gravitacionais 1993 Nobel de Física Ondas gravitacionais (cont.) LIGO (Laser Interferometer Gravitational-Wave Observatory) Louisianna & Washington Ambos detectores com braços de 4 km, distantes ≈ 3.000 km → ∆t ≈ 10 ms Virgo Itália KAGRA (Kamioka Gravitational-Wave Detector) Japão 2025 Índia 2015 Fusão de 2 buracos negros a ≈ 1 bilhão de anos-luz 2017 Nobel de Física para Rainer Weiss, Barry C. Barish & Kip S. Thorne Ondas gravitacionais (cont.).
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