The expanding universe Lecture 2

Expanding universe : content part 1 : ΛCDM model ingredients: Hubble flow, cosmological principle, geometry of universe part 2 : ΛCDM model ingredients: dynamics of expansion, energy density components in universe Part 3 : observation data – redshifts, SN Ia, CMB, LSS, light element abundances - ΛCDM parameter fits Part 4: radiation density, CMB Part 5: Particle physics in the early universe, neutrino density Part 6: matter-radiation decoupling Part 7: Big Bang Nucleosynthesis Part 8: Matter - antimatter asymmetry 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Last lecture Universe is flat k=0 Expansion dynamics is described by Friedman-Lemaître equation Cosmological redshift Closure parameter Expansion rate as function of redshift 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 © Rubakov ΩCDM Part 5 Todays lecture > TeV 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 © Rubakov ΩCDM Part 5 Todays lecture > TeV 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 © Rubakov Ωneutrino Part 5 Todays lecture ΩCDM Part 5 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 © Rubakov Ωbaryons Part 7 Todays lecture Ωneutrino Part 5 ΩCDM Part 5 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 © Rubakov Ωbaryons Part 7 Ωrad Part 4&6 Todays lecture Ωneutrino Part 5 ΩCDM Part 5 2014-15 Expanding Universe lect 2

Part 4 radiation component - CMB Physics of the Cosmic Microwave Background Present day photon density

Expanding Universe lect 2 CMB in Big Bang model © Univ Oregon Matter photons are released Baryons/nuclei and photons in thermal equilibrium Photons decouple/freeze-out During expansion they cool down Expect to see today a uniform γ radiation which behaves like a black body radiation 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 CMB discovery in 1965 discovered in 1965 by Penzias and Wilson (Bell labs) when searching for radio emission from Milky Way Observed a uniform radio noise from outside the Milky Way This could not be explained by stars, radio galaxies etc Use Earth based observatory: limited to cm wavelengths due to absorption of mm waves in atmosphere Observed spectrum was compatible with black body radiation with T = (3.5 ±1) K Obtained the Nobel Prize in 1978 (http://nobelprize.org/) 2014-15 Expanding Universe lect 2

COBE : black body spectrum To go down to mm wavelengths : put instruments on satellites COBE = COsmic Background Explorer (NASA) satellite observations in 1990s: mm wavelengths Large scale dipole anisotropy due to motion of solar system in universe, with respect to CMB rest frame Strong radio emission in galactic plane After subtraction of dipole and away from galactic centre: radiation was uniform up to 0.005% Has perfect black body spectrum with T = 2.735±0.06 K (COBE 1990) Discovered small anisotropies/ripples over angular ranges Δθ=7° 2006 Nobel prize to Smoot and Mather for discovery of anisotropies 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 CMB temperature map small ripples on top of Black Body radiation: 2014-15 Expanding Universe lect 2

COBE measures black body spectrum Plancks radiation law for relativistic photon gas Black body with temperature T emits radiation with power Q at frequencies  Intensity Q Frequency ν (cm-1) λ=2mm 0.5mm 2014-15 Expanding Universe lect 2

COBE measures black body spectrum CMB has ‘perfect’ black body spectrum Fit of data of different observatoria to black body spectrum gives (pdg.lbl.gov, CMB, 2013) Or Intensity Q Frequency ν (cm-1) λ=2mm 0.5mm 2014-15 Expanding Universe lect 2

CMB number density today 1 CMB photons have black body spectrum today They also had black body spectrum when CMB was created But ! Temperature T in past was higher than today CMB = photon gas in thermal equilibrium → Bose-Einstein distribution : number of photons per unit volume in momentum interval [p,p+dp] gγ = number of photon substates Black body 2014-15 Expanding Universe lect 2

CMB number density today 2 gγ=2 T=2.725K 2014-15 Expanding Universe lect 2

CMB energy density today T=2.725K 2014-15 Expanding Universe lect 2

radiation energy density vs time In our model the early universe is radiation dominated For flat universe → Friedmann equation energy density of radiation during expansion Integration yields 2014-15 Expanding Universe lect 2

CMB temperature vs time for t0 = 14Gyr expect TCMB (today) ≈ 10K !!! BUT! COBE measures T = 2.7K Explanation??? 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Summary 2014-15 Expanding Universe lect 2

Questions?

Part 5 particle physics in the early universe Radiation dominated universe From end of inflation to matter-radiation decoupling From ~ 107 GeV to eV Physics beyond the Standard Model, SM, nuclear physics

Radiation domination era Planck era GUT era At end of inflation phase there is a reheating phase Relativistic particles are created Expansion is radiation dominated Hot Big Bang evolution starts kT TeV t 2014-15 Expanding Universe lect 2

Radiation domination era At end of inflation phase there is a reheating phase Relativistic particles are created Expansion is radiation dominated Hot Big Bang evolution starts R t Planck era GUT era 2014-15 Expanding Universe lect 2

Radiation domination era Planck era GUT era kT Today’s lecture TeV t 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Planck mass ~ 1019 GeV Grand Unification ~ 1015 GeV Inflation period 10 TeV-100 GeV LHC-LEP 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Today’s lecture Planck mass ~ 1019 GeV Grand Unification ~ 1015 GeV Inflation period 10 TeV-100 GeV LHC-LEP 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Relativistic particles Radiation dominated kT >> 100 GeV 2014-15 Expanding Universe lect 2

relativistic particles in early universe In the early hot universe relativistic fermions and bosons contribute to the energy density They are in thermal equilibrium at mean temperature T Fermion gas = quarks, leptons Fermi-Dirac statistics (gf = nb of substates) boson gas = photons, W and Z bosons … Bose Einstein statistics (gb = nb of substates) 2014-15 Expanding Universe lect 2

relativistic particles in early universe Bosons and fermions contribute to energy density with 2014-15 Expanding Universe lect 2

Degrees of freedom for kT > 100 GeV bosons spin per particle total   W+ W- Z gluons photon H-boson total bosons 28 fermions quarks antiquarks e,µ,τ neutrinos anti-neutrinos total fermions 90 If we take only the known particles 2014-15 Expanding Universe lect 2

Degrees of freedom for kT > 100 GeV bosons spin per particle total   W+ W- 1 3 2 x 3 = 6 Z gluons 2 8 x 2 = 16 photon H-boson total bosons 28 fermions quarks ½ 3 (color) x 2 (spin) 6 x 3 x 2 = 36 antiquarks 36 e,µ,τ 6 x 2 = 12 neutrinos LH 3 x 1 = 3 anti-neutrinos RH total fermions 90 If we take only the known particles 2014-15 Expanding Universe lect 2

Degrees of freedom for kT > 100 GeV Assuming only particles from Standard Model of particle physics Energy density in hot universe what happens if there were particles from theories beyond the Standard Model? 2014-15 Expanding Universe lect 2

For instance : SuperSymmetry At LHC energies and higher : possibly SuperSymmetry Symmetry between fermions and bosons Consequence is a superpartner for every SM particle ~ Double degrees of freedom g* 2014-15 Expanding Universe lect 2

Neutralino = Dark Matter ? Neutral gaugino and higgsino fields mix to form 4 mass eigenstates → 4 neutralinos no charge, no colour, only weak and gravitational interactions is Lightest Supersymmetric Particle – LSP - in R-parity conserving scenarios → stable Massive : Searches at LEP and Tevatron colliders 2014-15 Expanding Universe lect 2

Neutralino = Dark Matter ? Lightest neutralino may have been created in the early hot universe when Equilibrium interactions When kT is too low, neutralinos freeze-out (decouple) → are non-relativistic at decoupling = ‘cold’ survive as independent population till today the observed dark matter abundance today puts an upper limit on the mass (chapter 7) 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Status around a few GeV 2014-15 Expanding Universe lect 2

Cool down from > TeV to kT ≈ GeV Start from hot plasma of leptons, quarks, gauge bosons, Higgs, exotic particles Temperature decreases with time Production of particles M stops when For example, some particles decay: W, Z, t .. Run out of heavy particles when kT<<100GeV when when 2014-15 Expanding Universe lect 2

Age of universe at kT ≈ few GeV Radiation dominated expansion since Big Bang Calculate time difference relative to Planck era Calculate age of universe at kT=100 GeV t= kT = 1 GeV t= kT = 200 MeV t= And compare to lifetimes of unstable particles 2014-15 Expanding Universe lect 2

Questions?

Expanding Universe lect 2 Free quarks form hadrons Cooldown to kT ≈ 200 MeV 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 A phase transition Quarks form hadrons Decay of particles with lifetime < µsec g* kT(GeV) 200 MeV 2014-15 Expanding Universe lect 2

Down to kT ≈ 200 MeV From fit to data αs confinement t Phase transition from Quark Gluon Plasma (QGP) to hadrons Ruled by Quantum Chromo Dynamics (QCD) describing strong interactions Strong coupling constant is ‘running’ : energy dependent From perturbative regime to non-perturbative regime around ΛQCD From fit to data When µ ≈ 200 MeV αs t confinement Quarks cannot be free at distances of more than 1fm = 10-15m 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Colour confinement large distances Expansion of universe Increases inter-quark distance Asymptotic freedom small distances 2014-15 Expanding Universe lect 2

around and below kT ≈ 200 MeV free quarks and gluons are gone and hadrons are formed Most hadrons are short lived and decay with Example Leptons : muon and tauon decay weakly << 1µs Stable or long lived 2014-15 Expanding Universe lect 2

pauze QUESTIONS?

Expanding Universe lect 2 Run out of unstable hadrons Neutrino decoupling/freeze-out Big bang nucleosynthesis Cooldown to a few MeV 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Cooldown to kT ≈ 10MeV After about 1ms all unstable particles have decayed Most, but not all, nucleons annihilate with anti-nucleons (chapter 6) expect g* kT(GeV) TeV GeV MeV 106.75 10 3.4 we are left with γ + e-, νe, νμ, ντ and their anti-particles 2014-15 Expanding Universe lect 2

Around kT ≈ MeV: Big Bang Nucleosynthesis around few MeV: mainly relativistic γ, e,νe, νμ, ντ + anti-particles in thermal equilibrium + few protons & neutrons weak interactions become very weak start primordial nucleosynthesis: formation of light nuclei (chapter 6) 2014-15 Expanding Universe lect 2

Around kT ≈ 3MeV : Neutrino freeze out Equilibrium between photons and leptons remaining photons today : CMB with T=2.75K What about remaining neutrinos? Weak interaction cross section decreases with energy Weak interaction 2014-15 Expanding Universe lect 2

Neutrino freeze-out weak collision rate interactions/sec relative During expansion T decreases As soon as W < H neutrinos stop interacting Weak interaction e+, e- number density (FD statistics) ~ T3 Weak Cross section ~ s ~ T2 Relative velocity of e+ and e- 2014-15 Expanding Universe lect 2

Cosmic Neutrino Background W << H when kT < 3MeV or t > 1s (problem 5.12) Neutrinos decouple and evolve independently neutrino freeze-out -> relic neutrinos Should populate the universe today as Cosmic Neutrino Background CνB what are expected number density and temperature today? Can we detect these neutrinos? Could they be dark matter? 2014-15 Expanding Universe lect 2

Cosmic Neutrino Background At a few MeV Number density of neutrinos ≈ number density of photons But photons are boosted by reaction In the end the photons have a higher temperature than the neutrinos with expected Temperature of neutrinos today expected density of relic neutrinos today: for given species (νe, νμ, ντ ) 2014-15 Expanding Universe lect 2

Overview of radiation dominated era g* kT(GeV) TeV GeV MeV 106.75 10 3.4 Quarks confined in hadrons Neutrino Decoupling and nucleosynthesis Run out of relativistic particles ep recombination Transition to matter dominated universe 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 © Rubakov Ωbaryons Part 7 Ωrad Part 4&6 Todays lecture Ωneutrino Part 5 ΩCDM Part 5 2014-15 Expanding Universe lect 2

Questions?

Part 6 matter and radiation decoupling Recombination of electrons and light nuclei to atoms Atoms and photons decouple at Z ~ 1100

Radiation-matter decoupling At tdec ≈ 380.000 years, or z ≈1100, or T ≈ 3500K matter decouples from radiation and photons can move freely & remain as today’s CMB radiation Matter evolves independently - atoms & molecules are formed → stars, galaxies, … Before tdec universe is ionised and opaque Population consists of p, H, e, γ + light nuclei + neutrinos 2014-15 Expanding Universe lect 2

Protons and neutral hydrogen At kT ~ 3 MeV neutrino freeze-out and start of BB nucleosynthesis – most p and n bound in light nuclei (part 7) Photon density much higher than proton density observations Up to t ≈ 100.000 y thermal equilibrium of p, H, e, γ When kT < I=13.6 eV Ne and Np = free e and p NH = bound H atoms Tdec? 2014-15 Expanding Universe lect 2

Protons and neutral hydrogen number density of free protons Np and of neutral hydrogen atoms NH as function of T At which T will universe run out of ionised hydrogen? temperature at decoupling f(T) m=electron mass 2014-15 Expanding Universe lect 2

Decoupling temperature Rewrite in function of fraction x of ionised hydrogen atoms strong drop of x between kT ≈ 0.35 - 0.25 eV or T between 4000 – 3000 K  ionisation stops around T~3500K period of recombination of e and p to hydrogen atoms Recombination stops when electron density is too small 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Decoupling time Reshift at decoupling Full calculation When electron density is too small there is no H formation anymore → Photons freeze out as independent population = CMB start of matter dominated universe We are left with atoms, CMB photons and relic neutrinos + possibly relic exotic particles (neutralinos, …) 2014-15 Expanding Universe lect 2

Era of matter-radiation equality since Density of baryons = density of photons when Density of matter (baryons + Dark Matter) = density of photons + neutrinos when Matter dominates over relativistic particles when Z < 3000 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 z~1000 z~3000 © J. Frieman 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Summary T(K) Energy per particle Time t(s) 2014-15 Expanding Universe lect 2

Expanding universe : content part 1 : ΛCDM model ingredients: Hubble flow, cosmological principle, geometry of universe part 2 : ΛCDM model ingredients: dynamics of expansion, energy density components in universe Part 3 : observation data – redshifts, SN Ia, CMB, LSS, light element abundances - ΛCDM parameter fits Part 4: radiation density, CMB Part 5: Particle physics in the early universe, neutrino density Part 6: matter-radiation decoupling Part 7: Big Bang Nucleosynthesis Part 8: Matter and antimatter 2014-15 Expanding Universe lect 2

Questions?

Part 7 (chapter 6) Big Bang Nucleosynthesis formation of light nuclei when kT ~ MeV Observation of light element abundances Baryon/photon ratio ΩBAR

Expanding Universe lect 2 Overview 1 at period of neutrino decoupling when kT ~ 3 MeV Anti-particles are annihilated – particles remain (part 8) Fate of baryons? → Big Bang Nucleosynthesis model Protons and neutrons in equilibrium due to weak interactions n and p freeze-out at ~ 1 MeV - Free neutrons decay Neutrons are ‘saved’ by binding to protons → deuterons observed 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Overview 2 When kT << I(D)=2.2 MeV dissociation of D stops At kT ~ 60 KeV all neutrons are bound in nuclei Onset of primordial nucleosynthesis – formation of nuclei model of BBN predicts abundances of light elements today At recombination (380’000 y) nuclei + e- → atoms + CMB photons Atoms form stars, … → Large Scale Structures (LSS) Consistency of model: light element abundances CMB and LSS observations depend on ? 2014-15 Expanding Universe lect 2

neutron – proton equilibrium When kT ~ 3 MeV neutrinos decouple from e, γ particle population consists of Most anti-particles are annihilated Tiny fraction of nucleons is left Protons and neutrons in equilibrium due to weak interactions with neutrinos And neutron decay τ = (885.7 ± 0.8)s Weak interactions stop when W << H →n & p freeze-out 2014-15 Expanding Universe lect 2

neutron/proton ratio vs Temperature As soon as kT << 1 GeV nucleons are non-relativistic Probablity that proton is in energy state in [E,E+dE] During equilibrium between weak interactions at nucleon freeze-out time tFO kT ~ 0.8MeV Free neutrons can decay with τ = (885.7 ± 0.8)s 2014-15 Expanding Universe lect 2

Nucleosynthesis onset Non-relativistic neutrons form nuclei through fusion: formation of deuterium Photodisintegration of 2H stops when kT ≈ 60 KeV << I(D)=2.2MeV free neutrons are gone And deuterons freeze-out 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 Nuclear chains Chain of fusion reactions Production of light nuclei ΛCDM model predicts values of relative ratios of light elements We expect the ratios to be constant over time Comparison to observed abundances today allows to test the standard cosmology model 2014-15 Expanding Universe lect 2

Observables: He mass fraction helium mass fraction Is expected to be constant with time – He in stars (formed long time after BBN) has only small contribution model prediction at onset of BBN : kT ~60keV, t~300s Observation today in gas clouds … 2014-15 Expanding Universe lect 2

Abundances of light elements Standard BB nucleosynthesis theory predicts abundances of light elements today – example Deuterium Observations today Abundances depend on baryon/photon ratio BBN Starts kT≈80keV t(s) 2014-15 Expanding Universe lect 2

Parameter: baryon/photon ratio ratio of baryon and photon number densities Baryons = atoms Photons = CMB radiation In standard model : ratio is constant since BBN era (kT~80 keV, t~20mins) Should be identical at recombination time (t~380’000y) Observations : abundances of light elements, He mass fraction → t~20mins CMB anisotropies from WMAP → t~380’000y 2014-15 Expanding Universe lect 2

Abundances and baryon density ΩBh2 Observations Of light elements Measure He mass fraction η10 CMB observations with WMAP measure abundances ΩBh2 Model Predictions Depend on η10 ΩBh2 η10 2014-15 Expanding Universe lect 2

Expanding Universe lect 2 CMB analysis Baryon-photon ratio from CMB analysis PDG 2013 pdg.lbl.gov 2014-15 Expanding Universe lect 2

Light element abundances PDG 2013 pdg.lbl.gov 2014-15 Expanding Universe lect 2

Questions?

Part 8 (chapter 6) matter-antimatter asymmetry Where did the anti-matter go?

Expanding Universe lect 2 What about antimatter ? Antiparticles from early universe have disappeared! Early universe: expect equal amount of particles & antiparticles - small CP-violation in weak interactions Expect e.g. primary charged galactic cosmic rays: detect nuclei and no antinuclei Annihilation of matter with antimatter in galaxies would yield intense X-ray and γ-ray emission – not observed Few positrons and antiprotons fall in on Earth atmosphere : in agreement with pair creation in inter-stellar matter Antiparticles produced in showers in Earth atmosphere = secundary cosmic rays 2014-15 Expanding Universe lect 2

Baryon number conservation Violation of baryon number conservation would explain baryon - anti-baryon asymmetry Baryon number conservation = strict law in laboratory If no B conservation -> proton decay is allowed Some theories of Grand Unification allow for quark-lepton transitions Search for proton decay in very large underground detectors, e.g. SuperKamiokande No events observed → Lower limit on lifetime 2014-15 Expanding Universe lect 2

Baryons and antibaryons Assume net baryon number = 0 in early universe Assume equilibrium between photons, baryons and anti-baryons up to ~ 2 GeV Around 10-20 MeV annihilation rate W << H A residu of baryons and antibaryons freeze out Expect oefening 2014-15 Expanding Universe lect 2

Baryons and antibaryons Baryons, antibaryons and photons did not evolve since baryon/anti-baryon freeze-out Expect that today Observe Explanation? Much too large! 2014-15 Expanding Universe lect 2

Baryon-antibaryon asymmetry Is the model wrong? Zacharov criterium : 3 fundamental conditions for asymmetry in baryon anti-baryon density: starting from initial B=0 one would need Baryon number violating interactions Non-equilibrium situation leading to baryon/anti-baryon asymetry CP and C violation: anti-matter has different interactions than matter Search at colliders for violation of C and CP conserving interactions Alpha Magnetic Spectrometer on ISS: search for antiparticles from space 2014-15 Expanding Universe lect 2

Expanding universe : content part 1 : ΛCDM model ingredients: Hubble flow, cosmological principle, geometry of universe part 2 : ΛCDM model ingredients: dynamics of expansion, energy density components in universe Part 3 : observation data – redshifts, SN Ia, CMB, LSS, light element abundances - ΛCDM parameter fits Part 4: radiation density, CMB Part 5: Particle physics in the early universe, neutrino density Part 6: matter-radiation decoupling Part 7: Big Bang Nucleosynthesis Part 8: Matter and antimatter 2014-15 Expanding Universe lect 2