Rodrigo Nemmen
October 09, 2017
110

# Universos de múltiplas componentes

Aula do curso de "Introdução à cosmologia" para graduação, Prof. Rodrigo Nemmen, IAG USP.

• universos de duas componentes: "densidade é destino"
• solução completa numérica da equação de Friedmann para um universo com três componentes
• propriedades do universo ΛCDM: idade, distâncias próprias, lookback time, tempo de emissão, distância de horizonte

https://rodrigonemmen.com/teaching/introducao-a-cosmologia/

October 09, 2017

## Transcript

1. ### Rodrigo Nemmen Dinâmica cósmica: Universos de múltiplas componentes Introdução à

Cosmologia  AGA0416
2. ### MATTER + CURVATURE 107 0 20 40 60 80 100

0 10 20 30 40 H 0 (t−t 0 ) a Ω 0 =1.1 Ω 0 =1.0 Ω 0 =0.9 2.5 Ryden Universo curvo, somente matéria k = 0 k = -1 k = +1 a(t) / t 2/3 a(t) / t2/3 a(t) / t ~

4. ### Resolvendo numericamente a equação de Friedmann, com todas as componentes

ce of “quintessence”, I will only consider the contributions = 0), radiation (w = 1/3), and the cosmological constant Λ erse, we expect the Friedmann equation (6.4) to take the form H2 H2 0 = Ωr,0 a4 + Ωm,0 a3 + ΩΛ,0 + 1 − Ω0 a2 , (6.6) εr,0 /εc,0 , Ωm,0 = εm,0 /εc,0 , ΩΛ,0 = εΛ,0 /εc,0 , and Ω0 = Ωr,0 + he Benchmark Model, introduced in the previous chapter as a nt with all available data, has Ω0 = 1, and hence is spatially although a perfectly ﬂat universe is consistent with the data, ded by the data. Thus, prudence dictates that we should keep ssibility that the curvature term, (1−Ω0 )/a2 in equation (6.6), ero. ˙ a/a, multiplying equation (6.6) by a2, then taking the square −1 0 ˙ a = [Ωr,0 /a2 + Ωm,0 /a + ΩΛ,0 a2 + (1 − Ω0 )]1/2 . (6.7) 0 Ω0 = 1, k = 0 he properties of “quintessence”, a component of the universe n-of-state parameter can lie in the range −1 < w < −1/3, rse with ¨ a > 0. However, in the absence of strong evidence ce of “quintessence”, I will only consider the contributions = 0), radiation (w = 1/3), and the cosmological constant Λ erse, we expect the Friedmann equation (6.4) to take the form H2 H2 0 = Ωr,0 a4 + Ωm,0 a3 + ΩΛ,0 + 1 − Ω0 a2 , (6.6) εr,0 /εc,0 , Ωm,0 = εm,0 /εc,0 , ΩΛ,0 = εΛ,0 /εc,0 , and Ω0 = Ωr,0 + he Benchmark Model, introduced in the previous chapter as a nt with all available data, has Ω0 = 1, and hence is spatially although a perfectly ﬂat universe is consistent with the data, ded by the data. Thus, prudence dictates that we should keep ssibility that the curvature term, (1−Ω0 )/a2 in equation (6.6), ero. ˙ a/a, multiplying equation (6.6) by a2, then taking the square
5. ### NCHMARK MODEL 119 −10 −8 −6 −4 −2 0 −6

−4 −2 0 2 log(H 0 t) log(a) t rm t mΛ t 0 a∝t1/2 a∝t2/3 a∝eKt Expansão do universo, todas as componentes Ryden dominado por radiação dominado por matéria dominado por Λ CHAPTER 6. MULTIPLE-COMPONENT UNIVERSES Table 6.2: Properties of the Benchmark Model List of Ingredients Ωγ,0 = 5.0 × 10−5 Ων,0 = 3.4 × 10−5 ation: Ωr,0 = 8.4 × 10−5 atter: Ωbary,0 = 0.04 c dark matter: Ωdm,0 = 0.26 ter: Ωm,0 = 0.30 cal constant: ΩΛ,0 ≈ 0.70 Important Epochs atter equality: arm = 2.8 × 10−4 trm = 4.7 × 104 yr bda equality: amΛ = 0.75 tmΛ = 9.8 Gyr a0 = 1 t0 = 13.5 Gyr chmark Model 118 CHAPTER 6. MULTIPLE-COMPONENT UNIVERSES Table 6.2: Properties of the Benchmark Model List of Ingredients photons: Ωγ,0 = 5.0 × 10−5 neutrinos: Ων,0 = 3.4 × 10−5 total radiation: Ωr,0 = 8.4 × 10−5 baryonic matter: Ωbary,0 = 0.04 nonbaryonic dark matter: Ωdm,0 = 0.26 total matter: Ωm,0 = 0.30 cosmological constant: ΩΛ,0 ≈ 0.70 Important Epochs radiation-matter equality: arm = 2.8 × 10−4 trm = 4.7 × 104 yr matter-lambda equality: amΛ = 0.75 tmΛ = 9.8 Gyr Now: a0 = 1 t0 = 13.5 Gyr 6.5 Benchmark Model The Benchmark Model, which I have adopted as the best ﬁt to the currently
6. ### 118 CHAPTER 6. MULTIPLE-COMPONENT UNIVERSES Table 6.2: Properties of the

Benchmark Model List of Ingredients photons: Ωγ,0 = 5.0 × 10−5 neutrinos: Ων,0 = 3.4 × 10−5 total radiation: Ωr,0 = 8.4 × 10−5 baryonic matter: Ωbary,0 = 0.04 nonbaryonic dark matter: Ωdm,0 = 0.26 total matter: Ωm,0 = 0.30 cosmological constant: ΩΛ,0 ≈ 0.70 Important Epochs radiation-matter equality: arm = 2.8 × 10−4 trm = 4.7 × 104 yr matter-lambda equality: amΛ = 0.75 tmΛ = 9.8 Gyr Now: a0 = 1 t0 = 13.5 Gyr 6.5 Benchmark Model The Benchmark Model, which I have adopted as the best ﬁt to the currently
7. ### Ryden Distâncias próprias, modelo padrão .01 .1 1 10 100

1000 .01 .1 1 10 100 Observation z (H 0 /c) d p (t 0 ) matter−only Benchmark Λ−only
8. ### Ryden Distâncias próprias, modelo padrão .01 .1 1 10 100

1000 .01 .1 1 10 100 Observation z (H 0 /c) d p (t 0 ) matter−only Benchmark Λ−only dp (t0) [Gpc] 4.3 0.43 0.04 43. 430.
9. ### Ryden “Lookback time”, modelo padrão 0 2 4 6 0

5 10 15 z t 0 −t e (Gyr) matter−only Benchmark Λ−only

11. ### Tamanho do universo [a(t)dhor] vs idade (t) log (tamanho do

universo, anos-luz) 10-8 10-5 0.01 10 104 106 108 1010 1012 1014 log (idade do universo, anos)
12. ### https://medium.com/starts-with-a-bang/throwback-thursday-how-big-is-our-observable-universe-2c7f59cf1fc8 Tamanho do universo [a(t)dhor] vs idade (t) log (tamanho

do universo, anos-luz) log (idade do universo, anos) universo hoje
13. ### https://medium.com/starts-with-a-bang/throwback-thursday-how-big-is-our-observable-universe-2c7f59cf1fc8 Tamanho do universo [a(t)dhor] vs idade (t) log (tamanho

do universo, anos-luz) log (idade do universo, anos) universo hoje energia escura começa a dominar sobre matéria matéria começa a dominar sobre radiação 1 aninho de idade tamanho da Via Láctea 1 segundo de idade distância Terra-Sol 1 ano-luz
14. ### Universo tinha o tamanho do Sistema Solar quando t =

10-14 s Universo tinha o tamanho da Terra quando t = 10-20 s

16. ### LETTERS A c-ray burst at a redshift of z <

8.2 N. R. Tanvir1, D. B. Fox2, A. J. Levan3, E. Berger4, K. Wiersema1, J. P. U. Fynbo5, A. Cucchiara2, T. Kru ¨hler6,7, N. Gehrels8, J. S. Bloom9, J. Greiner6, P. A. Evans1, E. Rol10, F. Olivares6, J. Hjorth5, P. Jakobsson11, J. Farihi1, R. Willingale1, R. L. C. Starling1, S. B. Cenko9, D. Perley9, J. R. Maund5, J. Duke1, R. A. M. J. Wijers10, A. J. Adamson12, A. Allan13, M. N. Bremer14, D. N. Burrows2, A. J. Castro-Tirado15, B. Cavanagh12, A. de Ugarte Postigo16, M. A. Dopita17, T. A. Fatkhullin18, A. S. Fruchter19, R. J. Foley4, J. Gorosabel15, J. Kennea2, T. Kerr12, S. Klose20, H. A. Krimm21,22, V. N. Komarova18, S. R. Kulkarni23, A. S. Moskvitin18, C. G. Mundell24, T. Naylor13, K. Page1, B.E. Penprase25,M.Perri26,P.Podsiadlowski27,K. Roth28,R.E.Rutledge29,T. Sakamoto21,P.Schady30,B. P.Schmidt17, A. M. Soderberg4, J. Sollerman5,31, A. W. Stephens28, G. Stratta26, T. N. Ukwatta8,32, D. Watson5, E. Westra4, T. Wold12 & C. Wolf27 Long-duration c-ray bursts (GRBs) are thought to result from the explosions of certain massive stars1, and some are bright enough that they should be observable out to redshifts of z . 20 using current technology2–4. Hitherto, the highest redshift measured for any object was z 5 6.96, for a Lyman-a emitting galaxy5. Here we report that GRB 090423 lies at a redshift of z < 8.2, imply- ing that massive stars were being produced and dying as GRBs 630 Myr after the Big Bang. The burst also pinpoints the location of its host galaxy. GRB 090423 was detected by the Burst Alert Telescope (BAT) on NASA’s Swift satellite6 at 07:55:19 UT on 23 April 2009. Observations with Swift’s X-ray Telescope (XRT), which began 73 s after the trig- ger, revealed a variable X-ray counterpart and localized its position to textbook case of a short-wavelength ‘drop-out’ source. The full grizYJHK spectral energy distribution (SED) obtained ,17 h after burst gives a photometric redshift of z 5 8:06z0:21 {0:28 , assuming a simple intergalactic medium (IGM) absorption model. Complete details of our imaging campaign are given in Supplementary Table 1. Our first NIR spectroscopy was performed with the European Southern Observatory (ESO) 8.2-m VLT, starting about 17.5 h after the burst. These observations revealed a flat continuum that abruptly disappeared at wavelengths less than about 1.13 mm, confirming the origin of the break as being due to Lyman-a absorption by neutral Vol 461|29 October 2009|doi:10.1038/nature08459

18. None

21. ### THE COSMOLOGICAL CONSTANT Exponds forever Recollapses Ωm0 Liddle Classiﬁcação de

tipos de universo a(0) 6= 0 ¨ a > 0 ¨ a < 0 k = 0 k = 0 k = +1 k = -1 ΩΛ0 ⌦m 0 + ⌦⇤ 0 = 1 ⌦m0 + ⌦⇤0 > 1 ⌦m0 + ⌦⇤0 < 1
22. ### THE COSMOLOGICAL CONSTANT Exponds forever Recollapses Ωm0 ΩΛ0 Liddle ¨

a > 0 ¨ a < 0 a(t) 6= 0 8t Classiﬁcação de tipos de universo