Cosmology and the origin of structure

Transcription

1 1 Cosmology and the origin of structure ocy I: The universe observed ocy II: Perturbations ocy III: Inflation Primordial perturbations CB: a snapshot of the universe 38, AB correlations on scales 38, light years today age=38, yrs age= erbstschule für ochenergiephysi Maria Laach ocy Kolb Fermilab & The University of Chicago Sachs-Wolfe opaque More than 38, light years in less than 38, years? v c ; log λ log 1 ( = a a) cosmology 3/ non-inflationary a a (MD) (D) λ λ a non-inflationary cosmology v c for velocity through space no limit on expansion velocity of space acausal requires accelerated expansion last scattering log a log λ log ; inflationary ( ) λ cosmology a (MD) λ a a (D) a (I) inflationary cosmology 1 = a a 3/ scale factor a a a normal a < ρ + 3p > Newton a GG ρ + 3p Einstein ( ) end inflation last scattering a aa a λ log a time scale factor a accelerated a > ρ + 3p < vacuum energy? time

2 log ; log λ δρ and δt Inflation, as a whole, can be divided into three parts 1. Beginning eternal inflation, wave function of the universe, did the universe have a beginning????. Middle density perturbations, gravitational waves, (particle production in the expanding universe) δ quantum fluctuations alarming phenomenon log a 3. End defrosting, heating, preheating, reheating, baryogenesis, phase transitions, dar matter, (particle production in the expanding universe) Erwin Schrödinger, Physica 6, 899 (1939) Introduction: proper vibrations [positive and negative frequencies] cannot be rigorously separated in the expanding universe. this is a phenomenon of outstanding importance. With particles it would mean production or annihilation of matter, merely by expansion, Alarmed by these prospects, I have examined the matter in more detail. Conclusion: The proper vibrations of the expanding universe There will be a mutual adulteration of positive and negative frequency terms in the course of time, giving rise to the alarming phenomenon The proper vibrations of the expanding universe Erwin Schrödinger, Physica 6, 899 (1939) Creation of a single pair of particles per ubble volume per ubble time with ubble energy Alarming? 6 m s Mpc V t E ( c ) Mpc 1 years 33 1 ev Uncertainty in the Quantum Vacuum Disturbing the vacuum Strong gravitational field particle production (awing radiation) W + W - e + e - quar anti-quar Blac ole anti particle particle Nothing is something!

3 3 Imprint of Inflation Inflation Big Bang plus 1-35? seconds Big Bang plus 38, Years Big Bang plus 14 Billion Years Seeds of Structure + Gravitational Waves A pattern of vacuum quantum fluctuations (the alarming phenomenon) Scalar field of mass M Fourier modes [a(τ) = expansion scale factor] 3 dx 3/ ( π) a( τ) i x * i x ( x, τ ) h( τ ) e a h( τ = + ) e a Mode equation (τ = conformal time) Scalar field of mass M Fourier modes [a(τ) = expansion scale factor] 3 dx i x * i x ( x, τ ) h ( ) ( ) 3/ e a h e a ( ) a( ) τ π τ τ = + Mode equation (τ = conformal time) h ( τ) + + M a + ( 6ξ 1) a a h ( τ) = h ( τ) + ω ( τ) h ( τ) = Particle creation in nonadiabatic region ω ω Inflaton also determines mass density (gauge freedom) Gauge invariant variable Scalar metric perturbations: ds = a ( τ) 1+ d 1 dx = ψ δ intrinsic curvature perturbations on comoving hypersurfaces {( ψ) τ ( ψ) } Inflaton field perturbations: ( x, t) = ( t) + δ( x, t) Gauge invariant variable: Variational formalism for quantization: 4 M Pl 1 S = d x g + ( ) V( ) 16π FW scalar gµν ( x, t) = gµν ( t) + δ gµν ( x, t) Inflaton field ( xt, ) = ( t) + δ( xt, ) ( τ ) Scalar perturbations in terms of a field u u = aδ + zψ = z z = a ( µ 1 µ u ( τ ) ) S = d x u u m u d z m = u mass changes with time Minowsi space (conformal time)

4 4 Variational formalism for quantization: 4 M Pl 1 S = d x g + ( ) V( ) 16π g x t = g t + g x t FW tensor µν (, ) µν ( ) δ µν (, ) Tensor perturbations in terms of a field v v = gravitons ν h ij 4 1 S = d x ( v µ v m ( ) µ v τ v ) 1 1 da m ( τ ) = v adτ mass changes with time Inflaton field u ( τ) + u ( τ) = ( z = a / ) Minowsi space (conformal time) Quantum generation of perturbations: Expand u in Fourier modes Wave equation for mode functions for u 1 d z Initially only homogeneous ( = ) mode. As evolve, mass is complicated function of time. Create nonzero momentum modes (perturbations). u z P ( ) Power Spectrum Slow-roll parameters Slow-roll parameters: 1 Pl ( ) Pl ( ) Pl ( ) ( ) m m m ε ( ) ; η ( ) ; ξ ( ) 4 π ( ) 4 π ( ) 4 π ( ) 1 d z = a 1+ ε η+ ε εη+ η + ξ ε < 1 for inflation to occur expect η and ξ also to be less than unity 1 d z so expect slow-roll part of to be slowly varying 1 d z = a ( 1+ something small and not wildly varying) Quantum generation of perturbations: Perturbations model-dependent function of and how changes during inflation. V( ) ( ) ε( ), η( ), ξ( ), { } Characterize perturbations in terms of: P( * ) scalar perturbation at = * dln P ( * ) n scalar spectral index dln PI ( * ) tensor perturbation at = * dln PI ( * ) nt tensor spectral index dln Some simple questions: Who is the inflaton? 1. Was inflation normal (i.e., 3-D FW)?. Can dynamics of inflation be described in terms of a single scalar field? 3. What was the expansion rate during inflation? 4. What was the general shape of the inflaton potential? 5. What was the more or less exact shape of the inflaton potential? 6. Can inflation tell us anything about physics at very high energy scales (unification, string, Planc)? V ( )? inflaton

5 5 Model Classification * Type I: single-field, slow-roll models (or models that can be expressed as such) V() large-field (Ia) hybrid (Ic) Type Ia: large-field models Type Ib: small-field models Type Ic: hybrid models V() Type II: anything else (branes, pre-big-bang, etc.) V() small-field (Ib) *Used for superstrings, supernovae, superconductors, Quantum generation of perturbations: ( ) { P n P n } Input inflation potential V : ( *) I( *) T Observer-friendly parameters: PI ( * ) Q P( * ) + PI( * ) n r P ( ) Consistency relation: ( ) nt = r 1 r+ 1 n Inflaton potential V ( ): Q n r or if free parameter { } { n r} * r.5 1. Dodelson, Kinney, Kolb astro-ph/97156 large field: ε < η< ε small field: η < ε hybrid: < ε < η n r = tensor scalar = n = scalar spectral ( ) index l arrison-zel dovich Spectrum? WMAP team - Peiris et al. 1. priors?. chain vs. grid? 3. marginalize? 4. data sets used? 5. definition of r? 6. Barger, Lee, Marfatia Kinney, Kolb, Melchiorri, iotto Leach & Liddle Inflation models that fit CMB 1. -Z consistent, i.e.,. r= still consistent 3. (no strong evidence for running) 4. (n=1 still consistent) 5. 4 still OK? Kinney, Kolb, Melchiorri, iotto Large Small ybrid

6 6 Polarization pattern Stebbins, Kosowsy, Kamionowsi Selja & Zaldarriaga Kinney astro-ph/98659 E modes B modes (gravitational waves) inflaton potential V ( ) econstruction Bond, Abney, Copeland, Grivell, Kolb, Liddle, Lindsey, Turner, Sourdeep Copeland, Kolb, Liddle, Lindsey ev. Mod Phys. 97 parameterized spectra rnn,, Grivell & Liddle astro-ph/99637 microwave anisotropies C l econstruction V scalar V tensor V ( ) ( ) ( ) 1. tensor spectral index in terms of scalar & tensor (consistency relation). nowledge of the scale of V requires tensor Power-law spectrum ( α ) V( ) = V exp / M Pl 1 reconstructions Power-law spectrum ( α ) V( ) = V exp / M Pl 1 reconstructions

7 7 Comparison to observation: 1. a (nearly exact) power-law. spectrum of gaussian 3. super-ubble-radius 4. scalar perturbations (seeds of structure) & 5. tensor perturbations (gravitational waves) 6. related by a consistency relation 7. in their growing mode 8. in a spatially flat universe. Issues 1. Transplancian physics probe of short-distance physics?. Defrosting preheating, reheating,. 3. Particle production WIMPZILLAS, gravitons,. 4. Why only one inflaton? isocurvature perturbations 5. Extra dimensions, brane, bul, etc.? new dynamics Cosmology and the origin of structure ocy I: The universe observed ocy II: Perturbations ocy III: Inflation erbstschule für ochenergiephysi Maria Laach ocy Kolb Fermilab & The University of Chicago