Cosmology & the CMB - Cosmology: Overview - Cosmic Microwave Background - Large Scale Structure (Wed) - CMB Fluctuations (Wed)

Transcription

1 Oct 16, 2017 Cosmology & the CMB - Cosmology: Overview - Cosmic Microwave Background - Large Scale Structure (Wed) - CMB Fluctuations (Wed) Wednesday: HW#5 due

2 History of the universe

3 Discovery of Quasars Broad optical emission lines at strange positions Marteen Schmidt realized that these are redshifted hydrogen lines Þ z=0.158 Marteen Schmidt

4 Quasars and Active Galactic Nuclei The most distant quasar known today has a redshift of (ULAS_J ) That redshift corresponds to a look back time of 12.9 Gyr (12.9 billion years), or an epoch of only 776 Myr) after the Big Bang occurred. In order to interpret distances, times, sizes, etc, we must understand the geometry of the universe. The SMBH in the MW (SgrA*) has a mass of 3 x 10 6 M ʘ Quasar SMBHs can be up to M ʘ

5 Looking out is looking back The time it takes light to travel from a distant object to us depends on the geometry of the universe longer path shorter path In order to know the light travel time, we must know the geometry The geometry depends on the amount of matter (baryonic and dark) and (as we will see ) dark energy

6 è What is the Geometry of cosmic space? It depends on the density of its matter+energy content A high density Universe has POSITIVE curvature A low density Universe has NEGATIVE curvature A Universe with zero curvature, said to be FLAT, has critical density

7 History and Fate of the Universe Hot Big Bang Model 13.7 billion years ago, the universe was much hotter and much denser than it is today. A tremendous release of energy took place: the Big Bang event. Since then, the universe has been expanding. Will the universe keep expanding? Or will the expansion halt? The attractive force of gravity of all the mass in the universe should be acting to slow the expansion or so we would expect

8 Evidence for the Big Bang Model Olber s paradox: (Heinrich Olbers: 1823) The sky is dark at night (=> universe is finite in space and/or age) Hubble s Law & the expansion of the Universe (Edwin Hubble: 1927) More distant galaxies receding faster If the universe is finite in space and time and is expanding, it must have been smaller in the past. Cosmic Microwave Background (CMB) Radiation (Penzias & Wilson 1965) Thermal spectrum with equivalent temperature of 3 degrees => 3 degree blackbody radiation = CMB Abundance of the elements via primordial nucleosynthesis The large scale structure of the universe: the way galaxies are seen today to cluster into groups, clusters and super-clusters. Any alternative theory of cosmology would have to explain these critical observational facts.

9 Evidence for the Big Bang Model Olber s paradox: (Heinrich Olbers: 1823) Why is the sky dark at night? If the universe were infinite, then every line of sight would eventually intercept a star (or galaxy) and hence the whole night sky should look like the surface of a star. Solution: universe must be finite in space, in age or both Remember: the concept of galaxy is < 100 years old.

10 Discovery of the Microwave Background

11 NASA Animation Cosmic Microwave Background Radiation If the universe was smaller in the past, it was denser and hotter in the past After the Big Bang, the universe cooled as it expanded. About 380,000 years after the Big Bang, protons and electrons could combine to form hydrogen Þ the cosmic background radiation photons were emitted This radiation is called the Cosmic Microwave Background Radiation or the 3-degree Background Radiation

12 Cosmic Microwave Background Radiation The Cosmic Microwave Background photons were emitted about 380,000 years after the Big Bang at z ~ 1090 Photons emitted when thermal plasma in universe was ~3000 K. Spectrum then redshifted by factor of 1090 Appears as spectrum with temp ~ 3 Kelvin A more perfect BB than we can make in the lab Þ thermal

13 A Serendipitous Discovery - noise feature all over the sky, like radio or TV station - First suspect: antenna issues - white dielectric substance? (pigeon-related) Winning a Nobel Prize may involve some dirty work!

14 NASA Animation Cosmic Microwave Background Radiation Planck? foreground subtracted

15 Cosmic Microwave Background Radiation Motion of our rest-frame relative to absolute v CMB Galactic foreground Intrinsic CMB fluctuations

16 Cosmic Microwave Background Radiation

17 Dipole => Motion of the Sun 30 km/s Earth s velocity around the Sun 220 km/s Sun s velocity around the center of the MW ~330 km/s Galaxy s motion towards the Virgo cluster ~300 km/s Virgo s motion towards Great Attractor The CMB provides a cosmic framework relative to which we can determine velocities in an absolute sense. A frame of absolute rest exists in each place in the universe.

18 Foreground Subtraction

19 Large Scale Structure Our cosmological model must explain how the structure developed to look this way (and not something else) and it has to do it in 13.8 billion years (not earlier, not later) Planck Smoother earlier on Time => Galaxies, clusters, superclusters and voids today CMB

20 Why is the CMB so smooth? CMB is 2.725K, with variations only on hundreds of microk scales CMB fills the whole sky, yet is very smooth at such precision How does structure on such large scales know of each other? Þ Structure was imprinted when everything was much more compact Þ Strong support for a Hot Big Bang, but there is more to it Þ Also: distant galaxies are distributed nearly isotropically (around us) Þ Simple world models are a good starting point for cosmology dt ~10-5 x T CMB

21 Cosmology: Simple World Models The Universe is governed by gravity General Relativity (GR) is the theory of gravity Gravity is related to the geometry of spacetime, i.e., distances, sizes, timescales Cosmological Principle: (1) Averaged over large scales, the Universe is isotropic around us the universe appears the same in every direction (2) Our position in the Universe is not special => Universe is isotropic around every point => Universe is homogeneous every region in the same as every other region GR permits world models with these properties Þall free-falling ( fundamental ) observers see the universe isotropic and experience the same cosmic history Newtonian picture: homogenous, expanding sphere Þsimple, self-similar properties of Hubble flow

22 Properties of the Hubble Flow As the universe expands, relative distances galaxies stay the same Þ Define a coordinate system that accounts for this, in which coordinates stay the same with time x: co-moving coordinate, for all fundamental observers, x=const. => gives relative positions of galaxies for all times => Define a (barring peculiar motions etc.) a(t): cosmological scale factor, normalized such that a(t 0 ) = 1. between At time t 1, observer has position r(t 1 ) relative to center of Newtonian, expanding sphere At time t 2, observer has position r(t 2 ) = a(t 1,t 2 ) r(t 1 ) Today, t=t 0 ; define x=r(t 0 ): Þr(t) = a(t) x = a(t) r(t 0 ) To determine a(t) is a key subject of cosmology

23 The Hubble parameter: H(t) Velocity of a fundamental observer relative to center of sphere : x: co-moving coordinate a(t): cosmological scale factor where Relative velocity of two objects at r and r+dr: Every fundamental observer sees an isotropic velocity field around them, according to Hubble s law today: H 0-1 is the characteristic time (age of universe if expansion has been constant at the present rate). Þ Our location in the Universe is not special, other observers will also observe Hubble s law (when accounting for peculiar motion)

24 Friedmann s Equation Aim: to solve Einstein s equations for a homogenous and isotropic universe à exact solution originally developed by 4 people independently: Friedmann, Lemaitre, Robertson, Walker hence sometimes called FLRW universe/metric We here derive Friedmann s equation using a Newtonian approximation. Consider an expanding sphere of mass M and radius a(t), on the surface of which is a small particle of mass m. The particle is moving as a result of the expansion with speed v = da/dt. à kinetic energy of the particle: KE = ½ mv 2 à gravitational potential energy: PE = -GMm/a

25 Friedmann s Equation KE = ½ mv 2 PE = -GMm/a mass of the sphere: M = 4/3 pra 3 à Total energy of the particle (energy conservation equation): E tot = ½ mv 2 GMm/a = ½ mv 2-4/3 pgra 2 m = ½ m (da/dt) 2-4/3 pgra 2 m Þ [(da/dt)/a] 2 = 8/3 pgr + 2E tot /m a -2 Define: K = -2E tot /m note the minus sign!! # " a a $ & % 2 = 8πG 3 ρ K a 2 Friedmann s equation

26 Friedmann s Equation & Spatial Curvature Friedmann s equation This can be considered an equation of state (energy conservation) for the universe. It is a first order differential equation with a unique solution. Its known boundary condition is, by definition, a(t 0 ) = 1 today. The density scales as (1/volume), thus: r(t)/r(t 0 ) = [a 3 (t)/a 3 (t 0 )] -1 = a -3 (t) Þ! # " a a $ & % 2 a 2 8πG 3 = 8πG 3 ρ K a 2 ρ 0 a = K K is the spatial curvature term in general relativity. Three cases: K < 0 a K = 0 a 0 K K > 0 a max = 8πGρ 0 3K à eternal expansion as a à à eternal, but slowing expansion as a à à eventual contraction after a maximum at a = 0

27 Friedmann s Equation & Critical Density! # " a a $ & % 2 = 8πG 3 ρ K a 2 H 2 (t) = 8πG 3 ρ K a 2 Friedmann s equation today: H(t) = H 0 ( Hubble constant ), r = r 0. for a flat universe (K=0) at present day: H 0 2 = 8πG 3 ρ 0 with definition of the Hubble parameter ρ crit ρ 0 (K = 0) = 3H 0 2 8πG =1.88h g / cm 3 h = H 0 /100 km/s Mpc -1 where r crit is defined as the critical density of the universe. [~6 protons per m 3 ] r crit is a natural scale to measure densities in the universe: dividing line between eternally expanding and collapsing universes Then define W = r/r crit as a dimensionless, normalized density parameter.

28 Friedmann s Equation & the Omegas scale factor a critical W = r/r crit is a dimensionless, normalized density parameter It can be understood in analogy to a ratio between potential and kinetic energy. High density/large W/positive curvature: gravity wins over kinetic energy from the Big Bang Critical density/flat: gravity slows down expansion, but is not sufficient to cause collapse Low density/small W/negative curvature: expansion due to the Big Bang wins à Big Chill

29 Friedmann s Equation & Densities! # " a a $ & % 2 = 8πG 3 ρ K a 2 W = r/r crit Friedmann s equation dimensionless, normalized density parameter The energy density r, and therefore W, has different components. r bary : density of baryonic (visible) matter light from galaxies, and density required to cause relative abundances in Big Bang nucleosynthesis (the larger r bary, the more efficiently 2 H is converted to 4 He à measure 2 H/ 1 H abundance to infer W b ) à only 15% - 25% of W b is seen as light in galaxies à many baryons in diffuse IGM r DM : density of dark matter can be measured from CMB + clustering at different times à local universe: W m = W b + W DM ~ >> W b (CMB: W m = 0.27; W b ~ 17% W m ) à evidence for DM from galaxy rotation profiles, from gravitational lensing masses, and from cosmology on many different scales! r rad : density of radiation measured, e.g., from the CMB; v. small today (W rad,0 < 10-4 )

30 Friedmann s Equation & Densities! # " a a $ & % 2 = 8πG 3 ρ K a 2 W = r/r crit Friedmann s equation dimensionless, normalized density parameter à W = W m + W rad ~ 0.27 What is measured for the total value? W obs = /- 0.02, i.e., consistent with 1 à r = r crit à some energy density appears to be missing dark energy! à W = W m + W rad + W L (~W m + W L ) & r = r m + r rad + r L à only 4.6% of the energy density of the universe are actually seen à L is also known as Einstein s cosmological constant

31 ! # " a a $ & % 2 Friedmann s Equation & Densities = 8πG 3 ρ K a 2 Friedmann s equation The Friedmann equation relates the expansion rate of the universe to the density of matter. However, to solve this equation, we need to know how the density evolves as a function of the scale parameter, a. à Heuristically, for simple types of matter (non-relativistic): - consider the universe as a box, and non-relativistic matter as particles in the box - if there is no net creation/destruction of particles, then the total number of particles N stays constant density = particle mass x number density number density = particle number / volume à The volume of the box increases as a 3, and the particle density scales as a -3. Þ r m = r m,0 /a 3, where r m,0 is the density today, when a(t 0 )=1

32 Friedmann s Equation & Densities For relativistic matter/radiation: - Evolution of radiation density has two components. 1) Energy density e rad = r rad c 2 photon energy density = photon energy x number density of photons à scales with a -3 as the universe expands, like non-relativistic matter 2) As the universe expands, light undergoes a cosmological redshift, which reduces the photon energy E: E/E emit = l emit /l = a emit /a à redshifting of photons reduces energy as E 1/a Taking both effects into account: Þ r rad = r rad,0 /a 4 Thus: cosmological constant

33 Mixture of Matter/Energy & Densities à at early times, radiation is the most prominent component à since the density of radiation falls off more quickly than that of matter, at some point later on matter will take over and start to dominate à this likely occurred around or at redshift z~20000 à at present day, we live in an universe in which the expansion is accelerated which implies that the energy density is dominated by the cosmological constant today! Reminder: the sum of all W is related to curvature as W = W m + W r + W L = 1 - K

34 Implications of Friedmann-Lemaitre Universe Þ a(t) à 0 at finite time in the past à Big Bang Þ The existence of a Big Bang is indicated by knowing W m,0 >0.1 today and the existence of galaxies at high redshift alone Þ Very close to Big Bang, our knowledge of the laws of physics is incomplete (e.g., quantum gravity) Reason: T(z)=(1+z)T 0 =a -1 T 0 where T 0 =2.73K (observed CMB constraint) Þ As a(t) à 0, T à infinity, i.e., very high median energy E=k B T Þ Universe both very dense and very hot early on; Energies become high enough that the conditions cannot be fully described with known physics (thermodynamics, atomic/nuclear physics, etc.)

35 Thermal History of the universe In the moments after the BB, the universe was much hotter and denser than conditions today (except near BHs and for brief moments at LHC) Planck scale: quantum gravity becomes strong GUT scale: strong, weak, EM forces become similar strength, unify to one force