DESY Workshop, Particle Cosmology 30 th September 004 Iflatio : sources of primordial perturbatios David Wads Istitute of Cosmology ad Gravitatio Uiversity of Portsmouth
Cosmological iflatio: Starobisky (1980) Guth (1981) period of accelerated expasio i the very early uiverse requires egative pressure e.g. self-iteractig scalar field V() speculative ad ucertai physics just the kid of peculiar cosmological behaviour we observe today dark eergy!
Iflatioary dyamics: V() N self-iteractig scalar fields: dv ϕ 3 ϕ = 0 dϕ omogeeous ubble expasio: 1 3 = 8π GV ϕ iflatio acceleratio ihomogeeous field perturbatios, waveumber k, coupled to metric perturbatios ψ V > ϕ k ϕ 3ϕ m = 3... ϕ ϕψ a
Vacuum fluctuatios V() awkig 8, Starobisky 8, Guth Pi 8 small-scale/uderdamped zero-poit fluctuatios large-scale/overdamped perturbatios i growig mode liear evolutio Gaussia radom field 4π k 3 k k = a 3 (π ) π = k e ik η a k fluctuatios of ay scalar light fields (m<3/) `froze-i o large scales
weakly scale-depedet d l d l k 1 slowly chagig ubble rate slow evolutio outside horizo fiite mass metric back-reactio (self-gravity) Slow-roll parameters: ε, η 1 3 ε η 4ε m 1 = 6ε η
0 8 3 3 3 = Q a a G m a k Q Q π Self-gravity of iflato field i GR Cosistetly iclude liear metric perturbatios, ψ, usig Mukhaov/Sasaki variable: ψ Q obeys 4D wave equatio: used to calculate correctios, e.g., i slow-roll expasio
Sources of structure: (1) desity perturbatios durig iflatio Iflato field perturbatios lead to adiabatic desity perturbatios o super-ubble scales durig iflatio: ρ V ' Coserved perturbatio: Bardee, Steihardt Turer (1983) = ρ ψ ρ Local eergy coservatio => coserved perturbatio always exists for adiabatic perturbatios o large scales Q Wads, Malik, Lyth Liddle (001) Q
adiabatic perturbatios o large scales adiabatic perturbatios e.g., perturb alog the backgroud trajectory adiabatic perturbatios stay adiabatic o large scales t y y x x = = = 0 B B B γ γ γ d/dt slow-roll attractor
observables i iflato sceario: primordial desity perturbatio -> widow oto iflatio amplitude scale-depedece tesor-scalar ratio 1 V 4 π k = a ε M Pl ( 6ε η) k a 1 = k = a T ( 16ε ) T k = a observatioal cosistecy test Liddle Lyth 93
brae-world iflato sceario: 4D iflato o our brae-world Maartes, Wads, Bassett eard (000) full 5D metric perturbatios at high eergies too complicated to solve i geeral Calculate durig quasi-de Sitter iflatio o the brae (egligible metric back-reactio for V=costat) coserved o large scales util low eergies where we ca use 4D gravity Laglois, Maartes, Sasaki Wads (001) but ca t yet iclude metric perturbatios for vacuum fluctuatio o small scales, l 5D,Plack < λ < l AdS Koyama, Laglois, Maartes Wads (004) hece ca t yet calculate as slow-roll correctios for liear perturbatios
brae-world iflato sceario: primordial desity perturbatio amplitude tesor-scalar ratio 1 V G 4 k a M π = ε Pl k = a ( l ) AdS T F G ( 16ε ) k = a ( lads ) ( l ) AdS T same observatioal cosistecy test uey Lidsey 000
multi-field perturbatios orthogoal fields,χ => ucorrelated vacuum fluctuatios χ χ s additioal source for desity perturbatios Sasaki Stewart 96; Gordo et al 01 χ χ Q adiabatic etropy wave equatios: Q a a G d V d a k Q Q 3 3 8 3 π 0 3 s ds V d a k s s s d d O σ θ
Scale depedece of isocurvature fluctuatios d l s d l k s 1 slowly chagig ubble rate slow evolutio outside horizo fiite mass metric back-reactio (self-gravity) Slow-roll parameters: ε, η ss 1 3 ε η ss 4ε m s 1 = ε s η ss
etropy perturbatios -> desity perturbatios o large scales dθ s dσ χ s θ slow-roll attractor
etropy perturbatios -> adiabatic desity perturbatios o large scales dθ s dσ χ s θ a uique late-time attractor gives oly adiabatic perturbatios at late times
two-field sceario: Wads, Bartolo, Matarrese Riotto 00 primordial desity perturbatio ehaced after ubble exit amplitude scale-depedece gravitatioal waves plus T 1 1 1 V 4 si π k = a si ε M Pl 1 ( 6 4cos ) ε ( η si η si cos η cos ) residual isocurvature modes? correlatio agle cos o-gaussiaity? s ( ε ) si si k= a 16 T ss k= a
Sources of structure: () ihomogeeous reheatig at ed of iflatio Iflato decay rate, Γ, sesitive to moduli fields Γ Γ'χ earlier decay chages local radiatio desity after = Kofma (003); Dvali, Gruziov Zaldarriaga (003) ρ ρ ψ = ργ 4ρ γ ψ = 0 = 1 Γ 6 Γ
Sources of structure: (3) late-decayig scalars after the ed of iflatio Poloyi/moduli problem Eqvist Sloth; Lyth Wads; Moroi Takahashi (001) weakly-coupled massive scalar fields displaced from true vacuum begi to oscillate whe <m, with ρ χ α a -3 come to domiate over radiatio, ρ γ α a- 4 must decay ito radiatio before ucleosythesis = ρ γ 4ρ γ ψ = 0 Ω χ, decay χ curvato mechaism
observatioal sigature? o-gaussiaity simplest kid of o-gaussiaity: Komatsu Spergel (001) Wag Kamiokowski (000) 1 f NL 1 recall that for curvato correspods to 1 Ω χ,decay Ω χ,decay χ χ χ Ω, χ,decay f NL χ χ χ χ Ω 1 χ,decay Lyth, Ugarelli Wads 0 costraits o f NL from WMAP f NL < 134 hece Ω χ,decay > 0.01 ad 10-5 < χ/χ < 10-3
c.f. o-gaussiaity from iflato sceario sigle-field cosistecy relatio: f NL = s 1 4 3ε η << 1 Maldacea (00) Gruziov; Cremielli Zaldarriaga (004) easy to disprove the (simplest) iflato sceario
Coclusios: 1. Precise data allows/requires us to study more detailed models of iflatio ad cosmological perturbatios. Several mechaisms ca produce primordial desity perturbatios o large-scales: iflato perturbatios durig iflatio ihomogeeous rehatig at ed of iflatio late-decayig scalars ( curvato ) after ed of iflatio 3. Distictive observatioal tests: gravitatioal waves (o-)gaussiaity residual (correlated) etropy/isocurvature perturbatios