The expanding universe

Name: The expanding universe
Uploaded: 2017-07-13T01:21:22+00:00
Duration: PTM43S7
Channel: Neil Wilson
Description: The expanding universe

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 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 Expanding Universe lect 2

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

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 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 ( 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 Expanding Universe lect 2

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

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

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

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

Summary 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 Expanding Universe lect 2

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 Expanding Universe lect 2

Planck era GUT era kT Today’s lecture TeV t Expanding Universe lect 2

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

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

Relativistic particles Radiation dominated kT >> 100 GeV 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) Expanding Universe lect 2

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

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 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 Expanding Universe lect 2

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? 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* 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 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) Expanding Universe lect 2

Status around a few GeV 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 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 Expanding Universe lect 2

Questions?

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

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

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

pauze QUESTIONS?

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

Decoupling temperature
Rewrite in function of fraction x of ionised hydrogen atoms strong drop of x between kT ≈ 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 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, …) 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 Expanding Universe lect 2

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

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 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

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 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 ? 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 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 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 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 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 … 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) 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 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 Expanding Universe lect 2

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

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

Questions?

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

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 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 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 MeV annihilation rate W << H A residu of baryons and antibaryons freeze out Expect oefening 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! 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 Expanding Universe lect 2

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 Expanding Universe lect 2

The expanding universe

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