Lecture 8: Single Component Universes & Cosmological Constant in Extragalactic Astronomy, Study notes of Physics

Download Lecture 8: Single Component Universes & Cosmological Constant in Extragalactic Astronomy and more Study notes Physics in PDF only on Docsity! Physics 133: Extragalactic Astronomy and Cosmology Lecture 8 -- April 15, 2009 Previously • Friedmann Equation, Fluid Equation, and an Equation of State describes the evolution of a(t) depending on content and geometry of the universe. • The cosmological constant, a flavor of dark energy, is an extra term and can induce acceleration. Currently supported by observations. What kind of Universe? ε may have many components. • We have a framework, but the solutions may not be analytic when all components are included. • Let’s investigate models made from single components and fitted to the observed expansion rate, H0 • Comparison with observations will tell us the answer γ,ν What kind of Universe? Relativistic ε from CMB and Stars • CMB photons dominate over other photons (e.g starlight); ΩCMB,0~5 X 10-5; relic from era when universe was hot and dense enough to be opaque to photons • εγ* ~ n L t0 ~ 0.007 eV/cm3 • Ωγ* / ΩCMB,0~ 0.03 What kind of Universe? Relativistic ε from Neutrinos. • Neutrino backgroung is a relic from earlier time when universe was hot and dense enough to be opaque to neutrinos. • ν, e-, e+, γ all in thermal equilibrium at early times • Photons decoupled at t = 380,000 yr; but neutrinos decoupled at t ~ 2 sec. • Annihilation of e+ by e- transferred heat and entropy to the photons, raising Tγ > Tν • Predict relativistic neutrino background Ων = 0.681 ΩCMB • Relatively low energy neutrinos, similar to CMB photons. Direct detection will be difficult. BBNS and CMB temperature fluctuations provide indirect evidence (and agree). Single component Universes. Curvature only • Let’s start simple… an empty Universe.. • And let’s solve the Friedmann Equation.. [Black board] • Positive curvature is not allowed • Expansion or contraction rate is constant; this means the age is equal to the Hubble time • Redshift-time relation is linear • Redshift-distance relation; can see arbitrarily far • Why can you see further than c/H0? • Objects with high redshifts are seen as they were when the universe was very young, and their proper distance was small Single component Universes. Summary. I • Curvature only: – a(t) linear in time – t0H0=1 – Horizon infinite * HW3#3 due 6pm Thursday. * See you on Friday!