COSMOLOGY 101 2 Chris Pearson : RAL Space July 2015 COSMOLOGY 1 How did the Universe Begin ? 1 How old is the Universe ? 1 How big is the Universe ? 1 Where are we in the Universe ? 1 What is the Universe made of ? 1 Will the Universe end ? 2 COSMOLOGY 1 Our Universe is flat and infinite 1 The expansion of the Universe is expanding 1 The Universe began in a hot Big Bang Ho = 67.3 ± 0.012 km/s/Mpc τage = 13.81 ± 0.05 Gyr ΩΛ,o = 0.685 ± 0.017 Ωm,o = 0.315 ± 0.016 ΩDM,o = 0.2662 ± 0.016 Ωb,o = 0.0487 ± 0.00027 3 A Very Brief History of Time 4 The Redshift Frequency increasing Frequency decreasing Wavelength decreasing Wavelength increasing Wave crests get closer together Wave crests get further apart Colour gets BLUER = BLUESHIFT Colour gets REDDER = REDSHIFT 5 The Redshift ! Δν Δλ ν −ν λ − λ v z = = = e o = o e ≈ υ << c ν λ ν λ c ! o e o e for! λe λo ! νe λo -0.2 + z = ≡ The Redshift νo λe -0.4 ! 1 -0.6 )) ν ! (F -0.8 (Flux -1 lg -1.2 Cirrus Spectrum -1.4 -1.6 6 8 10 12 14 16 wavelength (µm) 6 The Redshift Δν Δλ ν ❍ Doppler Redshift z = = = e − ν λ ν ! o e o 1 ! ! ! ! ν + v c c + v v ❍ Special Relativistic Redshift + z = e = ! = ! ≈ υ << c ν − v c c − v c ! o 1 / 1 for! 1 / ! ! ❍ Cosmological Redshift Hubble’s Law v = cz = Hod ! §. Correct interpretation of Cosmological Redshift of galaxies is NOT a Doppler shift. §. Wave fronts expand with the expanding Universe, stretching the photon wavelength. 7 The Redshift Cosmological Redshift λ R t + z ≡ = ( o ) λ0 R t ! e ( e ) 1Cosmological explanation: Redshift - natural consequence since R(t) is an increasing function of time !Wavefronts expand with the expanding Universe, stretching the photon wavelength. R(to) λo λe R(te) 8 A Very Brief History of Time THE HOT BIG BANG: How does the temperature of the early Universe evolve ? Redshift Wiens Law λ o Ro λ R T = RT = = (1+ z) maxT = constant o o λ R Energy density of radiation 4 2 ε = aT = ρc 2 ρ Friedmann Equation R 8πG 2 = R 3 ! $ -1/4 32πGa -1/2 10 -1/2 T = # 2 & t ≈1.5x10 t " 3c % = Radiation constant a = Newton’s Gravitational Constant G = speed of light c Temperature evolution in early Universe depends ONLY on Nature’s fundamental constants! 9 A Very Brief History of Time t=0 10-43s 10-35s 10-12s 10-6s 10-4s 0.01s 1s 4s 3mins 3x105yrs 107yrs 109yrs 1010yrs T=∞ 1031K 1027K 1015K 1013K 1012K 1011K 1010K 5x109K 109K 3000K 300K 30K 2.73K Dark Ages q+ He W± µ+ ν ? o Z q- µ-­‐ ν ν Matter ν Atoms Clumping Initial Singularity + annihila�on µ -­‐ decouple μ e Planck Time Infla�on E-­‐W Phase Transi�on quark -­‐ an�quark annihila�on Hadron-­‐Lepton Reac�ons ν shi� -­‐> Proton n-­‐p ra�o freezes Primordial NucleosynthesisEpoch of Recombina�on First Stars and Galaxies Epoch (re-­‐ioniza�on) of Galaxy Forma�on Forma�on of Solar System and Birth of Life 10 It All Started with a Big Bang 11 It All Started with a Big Bang In the Beginning…… Planck Era = 10-43 s 1031 K # → ' % t 0 % % → % Running Time backwards $ R 0 ( Initial singularity - The Creation Event %T → ∞% % % &ρ → ∞) -43 O t < 10 s known as the Planck Era O Quantum Effects become important O Einstein’s Theory of gravity breaks down 12 It All Started with a Big Bang In the Beginning…… Planck Era = 10-43 s 1031 K Quantum fluctuations of spacetime ~ Planck length, are of cosmic magnitude For a particle of mass, m, λ h Scale at which quantum effects become important : Compton Wavelength c = mc Scale at which self gravity becomes important : Schwarzchild Radius 2Gm RS = 2 c λC RS For a particle of mass, mP = the Planck mass λ c ≈RS Compton Wavelength & Schwarzchild Radius are comparable 13 It All Started with a Big Bang In the Beginning…… Planck Era = 10-43 s 1031 K Did the Big Bang …….. Bang?!? Or was it a Quantum Theory of Gravity ? 1. Quantum Gravity 2. Super Gravity 3. Superstrings 4. M-Theory 14 Problems with the Big Bang ? The Inflationary Era = 10-35 s 1027 K 1. THE HORIZON PROBLEM the isotropy of apparent causally disconnected regions of the CMB 2. THE FLATNESS PROBLEM the apparent remarkable closeness of Omega to 1 3. THE RELIC PROBLEM the apparent absence of relics from the Big Bang in our Universe 15 Problems with the Big Bang ? The Inflationary Era = 10-35 s 1027 K 1. THE HORIZON PROBLEM the isotropy of apparent causally disconnected regions of the CMB 2. THE FLATNESS PROBLEM the apparent remarkable closeness of Omega to 1 3. THE RELIC PROBLEM the apparent absence of relics from the Big Bang in our Universe 16 The Horizon Problem The Inflationary Era = 10-35 s 1027 K Cosmological Horizon: measure of distance at a given time from which information can be retrieved into the past: Defines the Observable Universe. t x y 17 The Horizon Problem The Inflationary Era = 10-35 s 1027 K Cosmological Horizon: measure of distance at a given time from which information can be retrieved into the past: Defines the Observable Universe. Cosmic distance from # 2 & 2 2 2 2 % dr 2 θ 2 2θ φ 2 ( Robertson Walker metric dS = c dt -R (t)% 2 + r (d +sin d )( $1-kr ' The Horizon Scale: ∫ tH c d H = R(tH)r = R(tH) 0 dt ≈ 3ctH R(t) Horizon size today: ~ 46 Billion light years 18 The Horizon Problem The Inflationary Era = 10-35 s 1027 K Horizon size today: ~ 46 Billion light years 5 13 Horizon on microwave background: t ~ 3x10 yrs 10 s : 1 million light years ~ 1.3 degrees on the sky 180 degrees O CMB isotropic To is identical to 1 part in 10,000 O Opposite regions appear never to have been in causal contact O But opposite points in CMB are ~ 90 horizon distances apart !! O So how do they know that they should be at the same temperature?? 19 Problems with the Big Bang ? The Inflationary Era = 10-35 s 1027 K 1. THE HORIZON PROBLEM the isotropy of apparent causally disconnected regions of the CMB 2. THE FLATNESS PROBLEM the apparent remarkable closeness of Omega to 1 3. THE RELIC PROBLEM the apparent absence of relics from the Big Bang in our Universe 20 The Flatness Problem The Inflationary Era = 10-35 s 1027 K Planck satellite Observations: The Universe is almost flat today: Ωo~1± 0.02 How about in the past ? 2 ! 2 ρ 2 2 k c R 2 8πG kc Ω 2 kc Ω 2 = H = - 2 = H - 2 -1 = 2 2 !R 3 R R ! R H 2 2 Ω -1 (R H ) t to Evolution of Ω with time = 2 2 Ω -1 (R H ) ! to t Matter dominated Era: 2/3 ∝ 2/3 ⇒ 2 2 ! 2 ∝ -2/3 Ω ! $ ! $ R t R H = R t -1 t t t = # & = # & Radiation dominated Era: Ω " % " % -1 to matter to radiation to 1/2 2 2 ! 2 -1 ! R∝t ⇒ R H = R ∝t 21 The Flatness Problem The Inflationary Era = 10-35 s 1027 K Planck satellite Observations: The Universe is almost flat today: Ωo~1± 0.02 How about in the past ? ! $2/3 ! $ Ω -1 t t t Evolution of Ω with time = # & = # & Ω " % " % -1 to matter to radiation ! to 6 13 ➠ -7 Ma�er Radia�on Equality teq~ 10 yr = 10 s |1-Ω| < 10 ➠ -18 Big Bang Nucleosynthesis tBBN~ 3mins = 180s |1-Ω| < 10 -43 ➠ -63 Planck Time tP ~ 10 s |1-Ω| < 10 Why is the Universe so FLAT ….. fine Tuning FLATNESSto > 1 part in 1060 Why did the Universe not expand - contract back to a big crunch very quickly Why did the Universe not expand so quickly that galaxies and life were unable to form PROBLEM22 Problems with the Big Bang ? The Inflationary Era = 10-35 s 1027 K 1. THE HORIZON PROBLEM the isotropy of apparent causally disconnected regions of the CMB 2. THE FLATNESS PROBLEM the apparent remarkable closeness of Omega to 1 3. THE RELIC PROBLEM the apparent absence of relics from the Big Bang in our Universe 23 The Relic Problem The Inflationary Era = 10-35 s 1027 K PHASE TRANSITION Strong Nuclear Electromagnetic GUT STRENGTH STRENGTH ELECTROWEAK t=10-­‐35s T=1027K TOE -­‐12 t=10 s E=1015GeV T=1015K Weak Nuclear E=102GeV t=10-­‐43s T=1031K E=1019GeV Gravity O At high energies the forces of nature unify O Symmetry ➡ Forces become indistinguishable from each other O Universe cools ➡ temperature drops ➡ symmetry breaks ➡ phase transition O Like water freezing into ice ➡ defects appear on cooling 24 The Relic Problem The Inflationary Era = 10-35 s 1027 K PHASE TRANSITION Strong Nuclear Electromagnetic GUT STRENGTH STRENGTH ELECTROWEAK t=10-­‐35s T=1027K TOE -­‐12 t=10 s E=1015GeV T=1015K Weak Nuclear E=102GeV t=10-­‐43s T=1031K E=1019GeV Gravity O Phase transition ➡ loss of symmetry ➡ topological defects O Predicted for GUT (strong/electroweak unification) t=10-35s, T=1027K, E=1015GeV O Compare with freezing water O different ice nucleation sites O different axes (domains) of symmetry ➡ topological defects 25 The Relic Problem The Inflationary Era = 10-35 s 1027 K PHASE TRANSITION Strong Nuclear Electromagnetic GUT STRENGTH STRENGTH ELECTROWEAK t=10-­‐35s T=1027K TOE -­‐12 t=10 s E=1015GeV T=1015K Weak Nuclear E=102GeV t=10-­‐43s T=1031K E=1019GeV Gravity O 0D point like defects = Magnetic Monopoles (isolated North/South poles) O 1D linear defects = Cosmic Strings O 2D sheet like defects = Textures 26 The Relic Problem The Inflationary Era = 10-35 s 1027 K Magnetic Monopole rest energy ~ 1015GeV ➡ E=mc2 ➡ mass ≡ bacterium O Phase Transition ➡ symmetry breaking ➡ topological defects O Expect one topological defect / horizon distance Horizon distance at tGUT d H = 2ctGUT Number density of Monopoles 1 146 -3 3 ≈10 Mpc d H 2 with energy density mc 161 -3 3 ≈10 GeVMpc d H Monopoles would dominate the energy density and close the Universe by 10-12 s However…… we are here …… so where are the monopoles ???? 27 Problems with the Big Bang ? The Inflationary Era = 10-35 s 1027 K 1.