Inflationary density perturbations - Institute for Particle Physics ...

outline! some motivation! Primordial Density Perturbation(and conserved quantities on large scales)! constraints on single-field models! predictions from multi-field models! conclusions

Cosmological inflation: Starobinsky (1980)Guth (1981)• period of accelerated expansionin the very early universe• requires negative pressuree.g.self-interacting scalar fieldV(φ)• speculative and uncertain physicsφ• just the kind of peculiar cosmologicalbehaviour we observe today

Motivation:inflation in very early universe testable throughprimordial perturbation spectra! radiation/matter density perturbations! + gravitational waves (we hope)gravitationalinstabilitynew observational data offers precision tests of cosmologicalparameters and the Primordial Density Perturbation

Primordial Density Perturbatione.g., epoch of primordial nucleosynthesiscosmic fluid consists of– photons, γ, neutrinos, ν, baryons, B, cold dark matter, CDM,(+quintessence?)! total density perturbation, orcurvature perturbationR ≈δρδρ/ρ! relative density perturbations, orisocurvature pertbns S i =δ(n i /n γ )/(n i /n γ )! large-angle CMB: (∆T/T) lss ≈ [ R - 2S m ] / 5

Conserved cosmological perturbationsLyth & Wands in preparationtimet 2t 1ABFor every quantity, x, that obeys a local conservation equationdxdNspace= y( x), e.g.& ρ = −3Hρwhere dN = Hdt is the locally-defined expansion along comoving worldlinesthere is a conserved perturbationwhere perturbation δ x = x A -x Bis a evaluated on hypersurfacesseparated by uniform expansion ∆N=∆lnamζ ≡ δN=xmδ xy(x)

where do these perturbations come from?

perturbations in an FRW universe:waveequation2δ & φ+ 3Hδφ&− ∇ δφ =Characteristic timescales for comoving wavemode k– oscillation period/wavelength a / k– Hubble damping time-scale H -1• small-scales k > aH under-damped oscillator• large-scales k < aH over-damped oscillator (“frozen-in”)0vacuumcomoving Hubble lengthH -1 / afrozen-inoscillatescomovingwavelength, k -1conformal timeinflationaccelerated expansion(or contraction)radiation or matter eradecelerated expansion

Wilkinson Microwave Anisotropy Probe February 2003coherent oscillationsin photon-baryon plasmafrom primordial densityperturbationson super-horizon scales

Vacuum fluctuationsV(φ)Hawking ’82, Starobinsky ’82, Guth & Pi ‘82• small-scale/underdamped zero-point fluctuations• large-scale/overdamped perturbations in growing modelinear evolution ⇒ Gaussian random field2δφ≈4πk3δφ2kk = aH3(2π) 2πfluctuations of any light fields (m M PlNiemeyer; Brandenberger & Martin (2000)effect likely to be small for H

Inflaton -> matter perturbationsR =for adiabatic perturbations on super-horizon scales R & = 0during inflationscalar field fluctuation, δφscalar curvatureon uniform-fieldhypersurfacesHδσ& σduring matter+radiation eradensity perturbation, δρtimescalar curvatureon uniform-densityhypersurfacesR =Hδρ& ρζ ζ = ζ = ζ = ζ=cdm( ) necessarily adiabatic primordial perturbations γ B νσ

Inflaton scenario:high energy / not-so-slow roll1. large field ( ∆ϕ < M Pl )e.g. chaotic inflationsee, e.g., Lyth & RiottoKinney, Melchiorri & Riotto (2001)0

can be distinguished by observations• slow time-dependence during inflation-> weak scale-dependence of spectran = 1 − 6ε + 2η• tensor/scalar ratio suppressed at low energies/slow-rollT2R2= 16ε

WMAP constraints (I)• Microwave background only (WMAPext)Peiris et al (2003)r< 1.28Harrison-Zel’dovichspectralindexn R≈ 1 − 6ε + 2ηn → 1, r → 0

WMAP constraints (II)• Microwave background + 2dF + Ly-alphaPeiris et al (2003)r< 1.28spectralindexn R≈ 1 − 6ε + 2η

WMAP constraints (III)• Microwave background + 2dF + Ly-alphaPeiris et al (2003)dn R/dln k= −0.055+ 0.028−0.029n R=1 .13±0.08r< 1.28

scale-dependent tilt?dlnk≈ −dn R2( 3ε− η)2ξ −8ε2• third slow-roll parameterξ ≡VV4M Pl , φ264πV, φφφ– involving four derivatives of the potential, not two– the beginning of the end for slow-roll?• inflaton effective mass is not constantdη≈ − 2 ξ + 2εηdNslow-roll inflation could be just a passing phase!

digging deeper:• additional fields may play an important role• initial state• ending inflation• enhancing inflationnew inflationhybrid inflationassisted inflationwarm inflationbrane-world inflation• producing density perturbations• may yield additional information• non-gaussianity• isocurvature (non-adiabatic) modes

Inflation -> primordial perturbations (II)scalar field fluctuationstwo fields (σ,χ)curvature of uniform-field slicesR =*isocurvatureS =*Hδσ& σHδχ& σ⎛⎜⎝RS⎞⎟⎠⎛1=⎜primordial⎝0k

examples:• field dynamics during inflationPolarski & Starobinsky; Sasaki & Stewart; Garcia-Bellido &Wands; Steinhardt & Mukhanov; Adams, Ross & Sarkar;Langlois… (1996+)• variable couplings during/after reheatingDvali, Gruzinov & Zaldariaga; Kofman (2003)• late-decaying scalar : the curvaton scenarioEnqvist & Sloth; Lyth & Wands; Moroi & Takahashi (2001+)

curvaton scenario:Lyth & Wands, Moroi & Takahashi, Enqvist & Sloth(2002)assume negligible curvature perturbation during inflation 2R *= 0light during inflation, hence acquires isocurvature spectrumlate-decay, hence energy density non-negligible at decaylarge-scale density perturbationgenerated entirely bynon-adiabatic modesafter inflationR22= T RSS2*≈ΩTRS≈ Ω χ , decay2χ , decay2S *≈δρρχχ( δρχ χ/ ρ )2•negligible gravitational waves•100%correlated residual isocurvature modes•detectable non-Gaussianity if Ω χ,decay

primordial isocurvature perturbations from curvaton?Moroi & Takahashi; Lyth, Ungarelli & Wands ‘03• cdm, neutrinos, baryon asymmetry all created after curvaton decaysζ( ζγ= ζν= ζ = ζ ) ≈ Ωχ, decayζχ=cdm B⇒ S = 0i• cdm/baryon asymmetry created at high energies before curvaton decayζ = ζγ≈ Ωχ, decayζχ, ζm=0⇒S m= −3ζ• 100% correlation between curvature and “residual” isocurvature mode• naturally of same magnitude• neutrino asymmetry (ξ

Observational constraintsGordon & Lewis, astro-ph/0212248v2using CMB + 2dF + HST + BBNisocurvature / curvature ratioB = S B / ζpre-WMAP95%c.f. Peiris et alf iso = S cdm /ζ≈ 0.1 Band marginalised overcorrelation angle-> f iso < 0.33post-WMAP

isocurvature perturbations from curvaton (II)• cdm/baryon asymmetry created by curvaton decayζ = ζ= ζγ≈ Ωχ,decayζχ, ζmχLyth, Ungarelli & Wands ’02Gupta, Malik & Wands in preparation⇒S m=( )χ , decay− Ω ζ = 3⎜ζ3 1χ , decayχ⎛1− Ω⎜⎝ Ωχ , decay⎟ ⎞⎠• curvature and isocuravture perturbations naturally of same magnitude• relative magnitude related to non-Gaussianity

non-Gaussianitysimplest kind of non-Gaussianity:Komatsu & Spergel (2001)Wang & Kamiokowski (2000)recall that for curvatoncorresponds toδρρ≈δρΩχ ,decayδρρδρ≈ρsignificant constraints on f NL from WMAP f NL < 134χχ⎛≈⎞⎛⎜⎝Ωδ1ρ⎞⎟ +ρ ⎠χ ,decayf NL2⎛ δ1ρ⎞⎜ ⎟⎝ ρ ⎠⎛⎜ δχ ⎛ δχ ⎞+ ⎜ ⎟⎜ χ⎝ ⎝ χ ⎠1ρδχ1≈ Ωχ,decay⎜⎟ , fNL≈χΩχ,decay⎝⎠2⎞⎟⎟⎠Lyth, Ungarelli & Wands ‘02hence Ω χ,decay > 0.01 and 10 -5 < δχ/χ < 10 -3

observable parameters• inflaton regime– curvature & tensor perturbations– n s & tensor/scalar ratio = n t• curvaton regime– curvature + isocurvature perturbations– n s = n iso & isocurvature/curvature ratio• intermediate regime– n s , n iso , n corr , n t , tensor/scalar, iso/curvature, correlationWands, Bartolo, Matarrese & Riotto, ‘02

Conclusions:1. Observations of tilt of density perturbations(n≠1) and gravitational waves (ε>0) candistinguish between slow-roll models2. Isocurvature perturbations and/or non-Gaussianity may provide valuable info3. Non-adiabatic perturbations in multi-field modelsare an additional source of curvature perturbationson large scales4. Consistency relations remain an important testin multi-field models - can falsify slow-roll inflation5. More precise data allows/requires us to studymore detailed models!