BASICS OF COSMOLOGY Astro 2299

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1 BASICS OF COSMOLOGY Astro 2299 We live in a ΛCDM universe that began as a hot big bang (BB) and has flat geometry. It will expand forever. Its properties (laws of physics, fundamental constants) allow the formation of stars in galaxies organized into clusters of galaxies that comprise a cosmic web. The cosmic web represents structure that grew out of primordial fluctuations arising in the era of inflation occurring in the first fraction of a second after the big bang. Clusters and galaxies formed out of 3σ fluctuations of a random process mostly determined by dark matter that dominates gravity in the cosmic web. Cosmologically, dark matter is dominated by dark energy. Λ CDM = Cosmological constant = Cold Dark Matter Alternatives: the universe could have been one with hot dark matter, which would not have been as conducive to the formation of clusters of galaxies. It could have had curved space time and it could have been of a type that would recollapse into a big crunch. Overall, it could have had laws of physics that would not have allowed galaxies, stars, the elements and us to exist. Constituents: The three main constituents of the universe are: Baryonic matter: 4% familiar stuff: atoms (quarks) as we know them Dark matter: 23% stuff that has mass but is not baryonic (not made of quarks) Dark energy: 73% stuff that contributes to gravity and pressure of the universe, but otherwise does not interact with matter Matter/antimatter symmetry breaking: the laws of physics do not favor the existence of matter over antimatter. For example, electromagnetism works with positrons (e + ) as well as electrons (e ), which are a particle/antiparticle pair. Ditto for protons and antiprotons, Quarks and antiquarks. In the early universe, there were nearly equal numbers of particles and antiparticles. As the universe expanded and cooled, matter/antimatter pairs annhilated nearly completely, apart from a difference of approximately 1 part in one billion. What was left was matter. In our universe, anti-matter could have frozen out instead of matter. If we existed in such a universe, we would call the stuff we were made of matter, and the other stuff anti-matter, just as we do in our universe, but with the roles changed. The residual amount of matter has not really been explained. It may be related to deep questions about overall symmetries in particle physics. Elements were/are formed in two cosmological eras: 1. First 3 minutes: H, He, Li, Be 2. Later than 100 Myr after the BB: all elements heavier than H are formed in stars, supernovae, and mergers of neutron stars.

2 Two Principles: Copernican principle: We are not the central feature of any aspect of the universe. We are not at the center of the solar system. We are not at the center of the Galaxy. Our Galaxy is not at the center of the universe. What we are made of (baryons) is a minor constituent of the overall mass-energy of the universe. The universe evidently did not necessarily need to have properties to allow baryons to exist (i.e. the baryon fraction could have been zero!) Anthropic principle: The universe does allow the existence of elements whose properties allow the formation of complexity, including life. So what? If the universe can have an arbitrary set of laws of physics, is it not significant that it has those needed to allow the formation of life? Is this really a meaningful principle or just a cosmological selection effect? We wouldn t be here discussing this issue if the universe had other properties. Some argue theistically about this point. A natural explanation involves the recognition or statement that our universe is only one among many. So the selection effect is relevant. Our universe is not the central feature of the multiverse, it is just one where hominids can reflect on their own presence in their universe. Copernicanism wins.

3 How do we know these things? The observed universe (as seen in visual light, radio waves, infrared, X-rays, γ-rays) is hierarchical: planets orbit stars stars cluster in galaxies galaxies are bound in clusters of galaxies the visible universe consists of clusters of clusters of galaxies In addition, the cosmic microwave background (see below) traces structure in the universe as it was when the universe was about 300 kyr old. Galaxies were first seen in the 19th century. Their identity as objects external to the Milky Way Galaxy was not understood until the 1920 s (Shapley-Curtis debate in 1920; Hubble s discovery of expansion in 1929). Many millions of galaxies are now known and future surveys are expected to identify > 10 9 galaxies. Their placement in space-time has occupied the efforts of many astronomers for decades. Galaxies can be viewed as test particles for tracking flow patterns and potential wells of gravity. Their clustering then tells us about where there are enhancements or deficits over the mean matter density of the universe. We localize galaxies through measurement of their angular positions on the sky and through estimation of their distances. Distances are hard to measure because they involve assumptions about how bright various standard candles are. Indirect distances are calculated by making use of the redshift, which can then be related to distance through the Hubble law.

4 Spectral lines from elements provide the means for measuring apparent motions of galaxies relative to us (Similar to Doppler shift). Redshift: motion away from us Blue shift: motion toward us Definition of redshift: z = λ λ = λ λ 0 V (for z 1) λ 0 c λ = rest wavelength of the light λ = λ λ 0 change in wavelength c = speed of light = km s 1. V = velocity of recession In these expressions, λ is the measured wavelength of a spectral line of some element, say, while λ 0 is the wavelength that would be measured in a laboratory where there is no motion. In the expression for the redshift z that has an approximate equality with V/c, the velocity V is only an effective velocity. For galaxies near to each other, the peculiar motions of the galaxies contribute to V. For very distant galaxies at high redshifts z > 1, the apparent velocity is larger than the speed of light! Hubble showed (1920 s) that galaxies tend to move away from us according to a law where more distant galaxies move away from us faster: cz = V = H 0 D (V=velocity, D = distance, H 0 = Hubble constant. ). To the present, many careers have been devoted to determining H 0 (V is easy, D is hard). Best value to date: H 0 70 km s 1 Mpc 1 Important note: In reality, the redshift is caused by both the expansion of the universe and by the gravitational redshift of light as it propagates to us and is influenced by the gravity of the universe. When we talk about the expansion of the universe, we mean that space-time is expanding. The apparent motion of galaxies away from each other is really due to the expansion of space-time, not kinetic motion of galaxies in some kind of fixed space-time. Therefore when we talk about recession velocity, we must think of the velocity as figurative, not actual. Units we like to use: Planck length = m corresponding to a Planck time = Planck scale / c = s. 10 km radius of a neutron star

5 6300 km radius of the Earth 1 AU = 1 astronomical unit = Earth-Sun distance 150 million km. 1 LY = distance traveled by light in one year km 60, 000 times the Earth-Sun distance. 1 parsec = 1 parallax arc second 3.27 light years (LY). 1 kpc = 1000 pc distance to next spiral arm in the MW 20 kpc diameter of the MW 1 Mpc = 1 Megaparsec (1 million parsec) distance to nearest large galaxy like the MW (Andromeda = M31) 3 Gpc scale length of the present day universe What does the Hubble expansion mean? Big Bang = event 13.7 Gyr ago = onset of expansion. The Hubble law is consistent with expansion of space time; this is analogous to expansion of a balloon in 3D if we view the 2D surface of the balloon as the allowed space. There is no favored position. All observers at all locations see the same expansion (statistically); all observers see galaxies moving away. All locations are centers or, equivalently, the center is everywhere. We say that space is homogeneous and isotropic (The Cosmological Principle). Matter and energy were somehow created in the instant of the big bang. The universe therefore evolves in time. In Big Bang cosmologies, the age of the universe is t H 1 0 (t = 2 3 H 1 0 for an Einstein de Sitter Universe). Steady State Theory: (Bondi, Gold, Hoyle): The expansion continues forever, there was no beginning. Space and time are both uniform (The Perfect Cosmological Principle). The SS theory requires the continuous creation of matter. Confirmation of the Big Bang model (in addition to Hubble expansion): Discovery of the Cosmic Microwave Background (CMB) in The CMB is the remnant radiation of a much hotter universe that cools as it expands. The CMB is, at present, blackbody radiation with a temperature of 2.7 degrees Kelvin. The CMB was predicted in the late 1940 s and again, independently, in the 1960 s. It was discovered accidently by two engineers at Bell Telephone Labs (Penzias & Wilson 1965; awarded Nobel prize in physics).

6 Evolution of Galaxies and Quasars: Galaxies and quasars at high redshifts do not look the same as nearby galaxies. (But note that the atoms and molecules are the same as those inside us, based on spectra that show lines with the same pattern as produced by terrestrial particles.) This implies that structures in the universe have evolved, in contradiction to the steady state picture. Element formation in the early universe. The observed abundances of light elements (D, He, Li) depend on conditions at t 3 minutes. A hot, not-too-dense universe was required to produce these light elements. The night sky is dark. An infinite universe that is infinitely old would be infinitely bright (Olber s Paradox). Open or closed universe? 1. open = expansion forever (Kinetic Energy > Gravity) 2. closed = expansion stops, collapse begins (Gravity > Kinetic Energy) How do we tell? Do a census of matter in the universe. If there is enough, gravity will be strong enough to halt the expansion. Matter Census: count galaxies, estimate their masses, and calculate the total mass. Need a critical mass density = ρ crit to halt the expansions: mass density = mass volume ρ crit = 3H2 0 8πG ρ H2 O 1 gm cm 3 gm cm 3 Current status: 1. There are too few galaxies to give enough mass to close the universe. 2. Not all matter in the universe is visible. Matter can be dim or dark (planets, blackholes, exotic particles). It can be baryonic or non-baryonic.

7 3. Evidence for dark matter exists: we see the effects of gravity from material that does emit electromagnetic energy. (Examples: galaxy rotation curves; binary galaxies; clusters of galaxies.) 4. There is not enough dark matter to close the universe. 5. Recent work shows that not only is the universe expanding, but the rate of expansion is increasing (the accelerating universe). Evidence for expansion and for constraining the constituents of the universe come from (a) studies of the Hubble law for type Ia supernovae (one type of standard candle) and (b) studies of the CMB with the Wilkinson Microwave Anisotropy Probe (WMAP), the PLANCK satellite, and other radio telescopes that study the CMB. 6. The apparent acceleration may be associated with a non-zero cosmological constant, a term that Einstein included and then removed from his equation describing the evolution of the universe. Einstein may have been right in his original equation, which however predicted a static universe. When Hubble discovered expansion of the universe, Einstein self-assessed his orginal equation as his greatest blunder. Ω: Omega = actual mass-energy density / critical density: Ω = ρ ρ crit Ω > 1 closed universe Ω < 1 open universe Ω = 1 flat spacetime. General Relativity: Contributions to ρ (and Ω) are not only from mass but any form of energy (recall E = mc 2 ). Λ: Lambda = cosmological constant: represents a term in the equation of motion of the universe that contributes to the energy density Ω = ρ/ρ crit counteracts the attractive force of gravity: it can accelerate the universe because it exerts negative pressure. The total value of Ω may be written as the sum of contributions from matter (M), from the cosmological constant (Λ), and from space-time curvature (k): Ω = Ω M + Ω Λ + Ω k.

8 Evidence from the CMB and type Ia supernovae suggests that we live in flat space time for which Ω k = 0 and Ω = 1, so that Ω Λ = 1 Ω M. We have Ω M 0.27 and Ω Λ = The census of baryonic matter indicates that it is only about 4% of Ω M, indicating that most of the matter is dark and non-baryonic. We do not know yet what comprises this matter. Evidently it is not made up of neutrinos. Timeline for the Universe: Time Period Key Events Temperature Redshift 0 Big Bang 3 minutes Formation of light elements 10 9 K 1 month CMB spectrum fixed 10 7 K 10 4 yr Radiation = Matter K 2000 Recombination yr CMB last scattering 3000K 1000 (CMB fluctuations) yr First sources of light: 10 4 K (matter) 10-20? Pop III stars Black holes/quasars Reionization First galaxies

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