Inflation and the origin of structure in the Universe
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1 Phi in the Sky, Porto 0 th July 004 Inflation and the origin of structure in the Universe David Wands Institute of Cosmology and Gravitation University of Portsmouth
2 outline! motivation! the Primordial Density Perturbation! reasons to use zeta! perturbations from inflation in the early universe! inflaton scenario! vs curvaton scenario! or modulated reheating! relation to observations! conclusions
3 Standard model of structure formation primordial perturbations in cosmic microwave background gravitational instability new observational data offers precision tests of cosmological parameters the nature of the primordial perturbations large-scale structure of our Universe
4 Wilkinson Microwave Anisotropy Probe February 003 coherent oscillations in photon-baryon plasma due to primordial density perturbations on super-horizon scales
5 where do the primordial perturbations come from?
6 Cosmological inflation: Starobinsky (980) Guth (98) period of accelerated expansion in the very early universe requires negative pressure e.g. self-interacting scalar field V(φ) speculative and uncertain physics φ just the kind of peculiar cosmological behaviour we observe today dark energy!
7 Vacuum fluctuations V(φ) awking 8, Starobinsky 8, Guth & Pi 8 small-scale/underdamped zero-point fluctuations large-scale/overdamped perturbations in growing mode linear evolution Gaussian random field δφ 4π k 3 δφ k k = a 3 (π ) π = δφ k φ e ik η a k fluctuations of any scalar light fields (m<3/) `frozen-in on large scales
8 how do we relate scalar field fluctuations during inflation to primordial density perturbations of photons, baryons, etc?
9 describing the primordial density perturbation use zeta! i = δρi ψ & ρ i gauge-invariant combination of the gauge-dependent density perturbation, δρ i, and spatial curvature, ψ dimensionless density perturbation on spatially flat hypersurfaces equal to the perturbed expansion δn=-δt first introduced for total density perturbation by Bardeen et al (983) constant on large scales for perfect fluid with equation of state, P i (ρ i ) Wands, Malik, Lyth & Liddle (000)
10 Reasons to use :. constant on large scales for adiabatic perturbations. physically-defined quantity hence gauge-invariant naturally extended to non-linear perturbations
11 gauge-invariance at first- and second-order: +K + = ' ψ δρ ρ = Malik & Wands, Class Quantum Grav (004) ( ) = ' ' '' ' ' ' ' ' ' ' ρ δρ ψ β ρ ρ ρ δρ ψ ψ ρ δρ δρ δρ ρ ψ δρ ρ i i
12 Reasons to use :. constant on large scales for adiabatic perturbations. physically-defined quantity hence gauge-invariant naturally extended to non-linear perturbations 3. constancy on large scales follows directly from conservation equation valid even in alternative gravity theories e.g., brane inflation
13 conserved cosmological perturbations Lyth & Wands, Phys Rev D (003) For every quantity, y, that obeys a local conservation equation dy = dt f (y) where is the locally-defined ubble rate along comoving worldlines there is a conserved perturbation (local integration constant) = δt = x δ y f (y) where δ y is a evaluated on hypersurfaces separated by uniform expansion N = dt (such as ψ=0 hypersurfaces on large scales)
14 Primordial Density Perturbation perturbed cosmic fluid consists of photons, γ, neutrinos, ν, baryons, B, cold dark matter, CDM, ( and dark energy, X ) total density perturbation, or curvature perturbation relative density perturbations, or isocurvature perturbtns = special case of adiabatic perturbations: i & ρi i & ρ ( ) S = i 3 i γ & ρ = 0 = i S i i γ = γ = constant i & ρ
15 Cosmological perturbations on large scales Cosmological perturbations on large scales adiabatic perturbations e.g., perturb along the background trajectory adiabatic perturbations stay adiabatic entropy perturbations perturb off the background trajectory e.g., baryon-photon isocurvature perturbation: x y y x T y y x x δ δ δ = = & & y y x x & & δ δ = 0 B B B n n n n n n δ δ δ γ γ γ
16 inflaton scenario: during inflation scalar field fluctuation, δφ necessarily adiabatic primordial perturbations ( ) γ = B = ν = cdm = σ during matter+radiation era density perturbation, δρ time = δσ & σ = δρ & ρ for adiabatic perturbations on super-horizon scales & = 0
17 brane-world inflaton scenario: 4D inflaton on our brane-world Maartens, Wands, Bassett & eard (000) 5D metric perturbations too complicated to solve at high energies Calculate zeta during slow-roll inflation on the brane (negligible metric back-reaction for V=constant) zeta conserved on large scales until low energies where we can use GR same basic calculation works in different brane-world gravity models relies only on energy conservation on the brane
18 new ideas in inflation: why should the field that drives inflation also be responsible for the primordial density perturbations? the division of labour TE GREATEST improvement in the productive powers of labour, and the greater part of the skill, dexterity, and judgment with which it is any where directed, or applied, seem to have been the effects of the division of labour. Adam Smith, The Wealth of Nations (776)
19 new scenarios for origin of structure: the curvaton scenario weakly-coupled late-decaying scalar field Enqvist & Sloth; Lyth & Wands; Moroi & Takahashi (00+) inhomogeneous / modulated reheating inflaton decay-rate modulated by another light field Dvali, Gruzinov & Zaldariaga; Kofman (003+)
20 curvaton scenario: (i) during inflation - curvaton light during inflation (m<<) - spectrum of isocurvature perturbations from quantum fluctuations = - spectral tilt: n 3 = d δρ ρ ln d ln k δ 3 δ ε + 3 π η * & where ε, η m 3 - assume negligible inflaton density perturbation * ε M Pl << 0 5 negligible gravitational waves << 0 5 M Pl for ε <
21 curvaton scenario: (ii) after inflation - radiation Ω γ plus curvaton Ω << - total density perturbation initially negligible total but (neglecting curvaton decay) ρ γ a -4 and ρ a -3, hence Ω /Ω γ a Ω Ω γ total & ρ = i & ρ 4Ω 3Ω γ total i + 3Ω Ω t t
22 (iii) curvaton decay: Malik, Wands & Ungarelli (003) Gupta, Malik & Wands (004) decay to radiation (before primordial nucleosynthesis): & ρ γ & ρ = 4ρ + Γρ γ = 3ρ Γρ Γ & & ρ ρ γ = ρ γ ρ & Γ & & ργ ρ = & ρ ρ ( ) ( ) γ γ p ( Ω / ( Γ / ) / ) in = Ω σ γ /,in γ /,in /,in ( Γ + ) ubble time Γ / / decay time γ, final = r ( p), in and r( p) Ω, decay
23 why might theorists want a curvaton? many candidate curvatons already exist (in the literature) pseudo-nambu Goldstone bosons, the Affleck-Dine field (baryogenesis), sneutrino (leptogenesis) MSSM flat directions Enqvist et al inflaton may be decoupled from ordinary matter no need for conventional reheating after inflation why should observers care? distinctive observational predictions no gravitational waves possibly detectable non-gaussianity possibly correlated isocurvature perturbations
24 non-gaussianity simplest kind of non-gaussianity: Komatsu & Spergel (00) Wang & Kamiokowski (000) + f NL recall that for curvaton corresponds to Ω,decay Ω,decay δ Ω,,decay f NL δ δ + Ω,decay Lyth, Ungarelli & Wands 0 constraints on f NL from WMAP f NL < 34 hence Ω,decay > 0.0 and 0-5 < δ/ < 0-3
25 c.f. non-gaussianity from inflaton scenario single-field consistency relation: f NL = n s 4 3ε + η << Maldacena (00) Gruzinov; Creminelli & Zaldarriaga (004) easy to disprove the (simplest) inflaton scenario
26 inhomogeneous/modulated reheating: light field during inflation,, modulates inflaton decay rate, Γ() non-adiabatic perturbations (inhomogeneous equation of state) change zeta on large scales after reheating many similarities with curvaton isocurvature fluctuations during inflation, hence same spectral tilt negligible gravitational waves (at least for slow-roll inflation) possible non-gaussianity possible isocurvature perturbations? Dvali, Gruzinov & Zaldariaga; Kofman (003) δ Γ 6 Γ γ
27 correlated dark energy and the CMB quadrupole? Moroi & Takahashi (003); Gordon & u (July 004) large dark energy fluctuations affect only lowest multipoles of the CMB (if c x =) correlated isocurvature perturbations in the dark energy can reduce quadrupole T/T (but leave CMB polarisation largely unaffected) Gordon & u claim -sigma evidence for correlated dark energy perturbations best-fit value? = X γ
28 Conclusions:. Precision cosmology (especially cosmic microwave background data) offer detailed measurements of primordial density perturbations. Inflaton or curvaton/modulated reheating fields during inflation could produce adiabatic density perturbations 3. Primordial isocurvature perturbations and/or non- Gaussianity may provide valuable info about origin of perturbations 4. Late-time curvature perturbation on large scales may depends upon dark energy isocurvature perturbation 5. More precise data allows/requires us to study more detailed models of the inflation and cosmological perturbations
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