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Home , Vera Rubin

XVI Escola de Verão Jorge André Swieca Partículas e Campos 31 de janeiro a 11 de fevereiro de 2011, Campos do Jordão, SP Introduction to “I shall speak of the theoretical work of Einstein of Germany, de Sitter of Holland and Lemaître of Belgium. For observational data I turn to the americans Slipher, Hubble, Humason, recalling however that the vitally important datum of distance is found by a method which we owe to Hertzsprung of Denmark. ...

My subject disperses the , but it unites the earth. May no "cosmical repulsion" intervene to sunder us"

Arthur Eddington in a public lecture delivered at the meeting of the “International Astronomical Union" at Cambridge (Massachusetts) in September 1932.

Instituto de Física Universidade Federal do Rio de Janeiro Ioav Waga Introduction to Cosmology

I – Overview

II – Cosmic Dynamics

III – The Early

IV –

V – Cosmic Acceleration Bibliography

• E. Harrisson – Cosmology: The Science of the Universe, Cambridge University Press, (2000).

• A. Liddle – An Introduction to Cosmology, John Wiley & Sons, (1999)

• J. Berenstein – An Introduction to Cosmology, Prentice Hall, (1985).

• J. V. Narlikar – Introduction to Cosmology, Cambridge University Press, (2002).

• J. Rich – Fundamentals of Cosmology, Springer, (2001).

• B. Ryden - Introduction to Cosmology, Addison Wesley, (2003).

• P. Schneider - Extragalactic and Cosmology - An Introduction, Springer (2006).

• T. Padmanabhan - Theoretical Astrophysics - Volume III: Galaxies and Cosmology. I- Overview The Universe 100 years ago !

Composition: stars Solar System

30,000 light years

William Herschel (1738-1822) The key question 100 years ago !

What is the nature of spiral nebulae?

• Objects in our own ? • Distant objects similar to the Milky Way?

Andromeda Great Debate (1920) Heber D. Curtis x Harlow Shapley

H. D. Curtis H. Shapley The discovery of galaxies.

• 1923 - Hubble observed a Cepheid in Andromeda.

Andromeda Edwin Powel Hubble: 20/11/1889 - 28/9/1953 • 1912 - Henrietta Leavit, Henrietta Leavit from Harward, observed a correlation between the mean absolute luminosity of Cepheid stars and their pulsation period. •Higher the period, higher the luminosity. Standard candles How Hubble contributed to the discovery of galaxies.

19 February 1924.

To: A. H. Shapley, director of Harvard Observatory, Cambridge, Massachusets.

“You will be interested to hear that I have found a Cepheid in Andromeda nebula (M31). … . Enclosed is a copy of normal light curve, which, rough as it is, shows the Cepheid characteristics in an unmistakable fashion. … . With Seares´s value, the median pv magnitude is 17.6 and the distance comes out something over 300 000 parsecs" Hubble

1 parsec = 3,26 ly = 3,09 x 1013 Km Hubble ANDRÔMEDA

Age

• Universe – ~ 14 Gyr • Earth – ~4,5 Gyr (45 years) • First forms of life in Earth (35 yr ago) • Life in the oceans flourish abundantly (6 yr ago) • Flora and animals in Earth (4 yr ago) • Dinosaurs dominated the Earth 1 yr ago and disappeared 4 months ago. • The first humanoids appeared in the last week. • Our specie (homo sapiens) appeared only 4 hours ago. • Agriculture was invented one hour ago. • Brasil was discovered 3 minutes ago. The expansion of the Universe and the Hubble law.

• In 1912 Slipher observed that the spectra lines of Andromeda were in the wrong place, they were blue- shifted. • The velocity of Andromeda estimated by Slipher was, ~ 300 km/seg. • In 1915 he had spectra for 40 nebulae with 15 estimated velocities. This number incresed to 25 in 1917. • Unlike the result he obtained for Andromeda, most of the nebulae presented . For instance, from the 41 nebulae with measured redshift in 1923, only 5 (including Andromeda) were not receding V. M. Slipher from us. The expansion of the Universe and the Hubble law.

• 1842 - Doppler Effect

v ν − ν z = redshift = = source obs c νobs

Christian Doppler NGC 2276

http://www.astro.washington.edu/labs/hubble/

Δλ

Hidrogênio β Intensidade relativa Intensidade

Comprimento de onda (Angström) Cosmology Early Days

• 1917 - Einstein Cosmological Model

• Main characteristics of Einstein´s cosmological model: homogeneity, isotropy, positive space curvature and .

• Einstein introduces the cosmological term (Λ) in his GR field equations.

“The most important fact that we draw from experience is that the relative velocities of the stars are very small as compared with the velocity of light”. A. Einstein Repulsive term

The most general covariant action , constructed out of the metric and its first and second derivatives. By extremizing the action (including the matter terms) leads to the above equation.

Einstein considered that his model has 3 important merits:

1. Λ could be related to the mean density of matter; it realizes Mach´s expectation relating local physics and the content of the .

2. Einstein´s model appeared to be the unique model admitted by GRT that was static and in accordance with Mach principle.

3. With GRT it was possible to construct a wholly consistent model for the entire universe. de Sitter effect

• However, in the same year (1917) de Sitter obtained solutions for the EFE with Λ, that were stationary but with ρ = 0.

• de Sitter effect: the recessional velocity of two proof objects in a increase with distance. Friedmann (Lemaître) models • 1922 - Aleksander Aleksandrovich Friedmann obtained expansionist solutions of the E.E., with matter and Λ.

• Main characteristics of Friedmann ´s model: homogeneity, isotropy and expansion.

• 1927 - Lemaître showed that Einstein model is unstable. As we shall see, Einstein and de Sitter models are, in fact, extreme states of expanding .

A. A.G. FriedmannLemaître The Hubble Law

• In 1929 Hubble announces the discovery that the real Universe is expanding.

• In the following years, he and Milton Humanson put on a firm basis what is now known as the Hubble law.

Recessional velocity Hubble constant Milton Humason and Hubble Proper distance 20000

15000

10000

5000

0 0 10 20 30

distance (Mpc)

[Hubble & Humason (1931)]

[Hubble (1929)] Kolb A lei de Hubble

There is no center in the Universe The Hubble Law Where are the galaxies expanding to?

No

Yes Dunkle Materie “If it is not DARK, it doesn´t MATTER” Anonymous

– , in 1933, showed that visible matter constitutes only a small fraction of all the mass in the Universe.

– He measured the radial velocities of 8 galaxies in the Coma cluster and, by estimating the velocity dispersion obtained that the mean matter density was 400 times (50) the density estimated from observations of luminous matter. This discrepancy has become known as the “missing matter problem.”

– In 1936, Sinclair Smith confirmed Zwicky results analyzing the Virgo cluster.

Fritz Zwicky Flat Rotation Curves In Spiral Galaxies

v2 GM = ∝ ρr r r2 v = const ⇒ M ∝ r or ρ ∝ r−2

Vera Rubin Primordial Nucleosynthesis

• “Gamow was fantastics in his ideas. He was right, he was wrong. More often wrong than right. Always interesting; … and when his idea was not wrong it was not only right, it was new.”

Edward Teller, about George Gamow Primordial Nucleosynthesis

Alpher Bethe Gamow Herman “Delter” In the 1940’s, Gamow and collaborators suggested the possibility that all the chemical elements we see today had been generated trough a long chain of neutron capture in a primordial Universe that was cooling due to the expansion. This scheme did not work because there are no stable isotopes with mass number 5 and 8. Primordial Nucleosynthesis

• Predictions of theory:

– Forms mostly Hydrogen & 4Helium p – Results depend on the ratio of 2H n protons and neutron at Tf & on neutron decay rate p 3He

• Ratio (p:n) at TN= 7:1 n 4He – So…. Abundance (by mass) of helium = of total. 25% +2He – Also produces small amounts of (Rare) 9Be 2 3 7 7Li H, He and Li 6Li 4He 3He 2H 1 H A=8 Predictions based on well A=5 understood physics Sean Paling Primordial Nucleosynthesis

• Predictions: Observed value Predicted values – Current abundances depend 1

on, essentially, only one He ~25% parameter, the baryon photon ‘Allowed’ density ratio or, equivalently, the baryon -3 density at nucleosynthesis. (& 10 therefore density now). D Relative Abundance

10-6

– Observations agree very Li well with predictions 10-9

0.005 0.01 0.02

2 Current Baryon Density ΩB0h

Sean Paling , G. Burbidge, W. Fowler and F. Hoyle Cosmic Microwave Background Radiation

• "Arno and I of course were happy to have any sort of answer to our dilemma. Any reasonable explanation would have probably made us happy. In fact, I do not think that either of us took the cosmology very seriously at first. ... So I thought that we should report our result as a simple measurement: the measurement might be true after the cosmology was no longer true"

A. A. Penzias & R. W. Wilson, Robert W. Wilson in "Discovery of the cosmic 1964, Bell Laboratory microwave background" Inflation – 1980’s

The ‘Flatness Problem' –Why the energy density was so close to the critical density (ρc) at early times? The ‘Horizon Problem’ –Why is the CMB so uniform?’ Ioav Waga PECACG 1-5 September 2003

1998 Major advances and theoretical successes in Cosmology in the XX century General Relativity as a theory of gravitation; existence of a self consistent framework. Universe expansion and the Hubble law (Hubble – 1929). Gamow, his group and others developed the theory of primordial nucleosynthesis. Concordance of theory and observations. Gamov and his group predicted the existence of the CMBR. Discovery of the CMBR by Penzias e Wilson (1964). Existence of dark matter (non baryonic) and its role in . and the problem of initial conditions in the Universe. Possible explanation for the origin of density fluctuations necessary to form large-scale structures. and matter anti-matter asymmetry. Observational evidence for and the accelerated expansion of the Universe.

Important Open Questions Nature of the dark matter and the dark energy. Quantum gravity and the origin of the Universe. A more complete theory of structure formation. II- Cosmic Dynamics Standard Cosmology Working Hypothesis - The physics laws, that are valid in the Solar system, can be extrapolated to the entire Universe. - The physics laws can also be extrapolated to the past. - Gravity is the dominant force on large scales. • Strong and weak force are short range forces ~ <10-13 cm. Although 2 2 e /GMp >>1, planets, stars, galaxies etc are neutral electrically. - Gravitation Theory: Einstein’s General Relativity (GRT) - : on large enough distance scales the Universe is spatially homogeneous and isotropic. • There are no preferred directions or preferred places in the Universe. - In constructing cosmological models the real Universe with galaxies, clusters of galaxies etc, is approximated by a continuous fluid caractherized by its density (ρ), pressure (p), temperature (T) etc. Olbers Paradox Why the night sky is dark? Olbers Paradox

dN = n4πr2dr ⇒ number of stars in the shell. L df = dN = nLdr 4πr2 ∞ f = ∫ nLdr =∞ !!!! 0 Why the night sky is dark?

The Olbers Paradox

1.The stars (galaxies) number density (n) and luminosity (L=energy/volume) are not space dependent.

2.L and n are not time dependent (no evolution, no beginning).

3.The Universe is not expanding.

4.Space is euclidean and f=L/4πr2. Olbers Paradox If we abandon hypothesis 2 (or 1) and, for instance, assume that the Universe had a beginning, let say, t0 years ago such that If nL falls of more L = 0 and/or n = 0 for r > ct0 1 rapidly than we have r ct f = 0 n L dr is finite ∫0 If we abandon hypothesis 3, the problem can also be solved if V  c. V V 1− 1− ν = ν c ⇒ L = L c obs emit V obs emit V 1+ 1+ c c Newtonian Cosmology

References: E. Harrison – Cosmology: The Science of the Universe A. Liddle – An Introduction to Modern Cosmology

Newtonian Cosmology, as we know it today, appeared in the 1930’s with Milne and MacCrea. It was developed after GTR.

It is not consistent. For instance i) Hubble law and v>c ; ii) in an infinite space filled with homogeneously distributed matter the potential is not well defined.

Main advantage: we can obtain using only newtonian theory the same equations we obtain using GTR. It is more intuitive.

Why the equations are the same? Newtonian Cosmology is a good approximation for d << c H-1 . Newtonian Cosmology

ρ here is the mass density

Co-moving coordinate

Physical coordinate r = a(t)x The Friedmann equation

Friedmann Equation

k does not depend on x ; U is proportional to x2 The fluid equation

Consider an isentropic expansion (dS=0) and we get The acceleration equation

By differentiating with respect to time the Friedmann equation we get:

2 ⎛a ⎞ 8πG kc2 ⎜ ⎟ = ρ − ⎝a ⎠ 3 a2 ⎛a ⎞⎛aa − a2 ⎞ 8πG kc2a 2⎜ ⎟⎜ ⎟ = ρ + 2 ⎝a ⎠⎝ a2 ⎠ 3 a2 a ⎛ p ⎞ By substituting the fluid equation, ρ=-3 ⎜ρ + ⎟ and dividing a ⎝ c2 ⎠ 2 a a ⎛a ⎞ ⎛ p ⎞ kc2 by 2 , we get ⇒ − ⎜ ⎟ = −4πG⎜ρ + 2 ⎟+ 2 a a ⎝a ⎠ ⎝ c ⎠ a

By using the Friedmann equation again we obtain the acceleration equation Summary 2 ⎛a ⎞ 8πG kc2 ⎜ ⎟ = ρ − ⎝a ⎠ 3 a2 a p ρ + 3 (ρ + ) = 0 a c2 a 4π G ⎛ 3p ⎞ = − ⎜ρ + ⎟ a 3 ⎝ c2 ⎠ p = p(ρ) Summary ε = ρ c2 2 ⎛ a ⎞ 8πG kc2 ⎜ ⎟ = ε − ⎝ a ⎠ 3c2 a2 a ε + 3 (ε + p) = 0 a a 4π G = − ε + 3p a 3c2 ( ) p p( ) = ε