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Home , Inflation (cosmology)

on the beach, Puerto Vallarta , Mexico 13/01/2011

InflationInflation inin aa generalgeneral reionizationreionization scenarioscenario

Stefania Pandolfi, University of Rome “La Sapienza”

“Harrison-Zel’dovich primordial spectrum is consistent with observations” S.Pandolfi, A. Cooray, E. Giusarma, E. W. Kolb, A. Melchiorri, O. Mena, P.Serra Phys.Rev.D82:123527,2010 , arXiv:1003.4763v1[astro-ph.CO]

“Impact of general scenario on reconstruction of inflationary parameters” S. Pandolfi, E.Giusarma, E.W.Kolb, M. Lattanzi, A.Melchiorri, O.Mena, M.Pena, P.Serra, A.Cooray, Phys.Rev.D82:087302,2010 ,arXiv:1009.5433 [astro-ph.CO] Outline

 Inflation  Harrison-Zel’dovich model  CMB Observables and present status  Parametrizations of Reionization History  Sudden Reionization  Mortonson & Hu PC’s  Analysis and Results I and II  Forecast future constraints: the mission  Conclusions InflationInflation 11 • Period of accelerating expansion in the very early • It explains why the Universe is approximately homogeneous and spatially flat • Dominant paradigm for explaining the initial conditions for and CMB • Two types of perturbation created during inflation : scalar and tensor (or GW perturbation ) TheThe simplestsimplest way:way: thethe InflatonInflaton φφφφφφ 1 φ + φ + φ = ρ = V (φ) + φ&2 && 3H & V (' ) 0 2 1 p = −V (φ) + φ&2 2 InflationInflation 22  The slope of the ’’s potential must be sufficiently shallow to drive exponential expansion  The amplitude of the potential must be sufficiently large to dominate the of the Universe

 Slow -roll condition Having inflation requires that the “slow -roll ” parameters

ε << 1 ; η << 1

Zoology of models Within these condition the number of models available to choose from is large depending of the relation between the two slow -roll parameters . CMBCMB ObservablesObservables  KeyKey observationalobservational teststests thatthat cancan bebe predictedpredicted fromfrom aa givengiven inflationaryinflationary modelmodel areare nn :: spectralspectral indexindex ofof densitydensity perturbationsperturbations rr :: ratioratio ofof thethe gravitationalgravitational waveswaves toto densitydensity perturbationsperturbations  TheseThese areare relatedrelated toto thethe slowslow --rollroll parametersparameters atat thethe lowestlowest orderorder inin thethe SRASRA asas n ≅ 1 − 4 ε + 2η P r ≡ T = 16 ε P R HarrisonHarrison --ZelZel ’’dovichdovich spectrumspectrum

 InflationInflation predictspredicts n ≈ 1 butbut n ≠ 1

 AA majormajor pointpoint toto clarifyclarify isis ifif HZHZ ’’ss n=1n=1 is ruled out from currrent observations or not.

≠  IfIf n 1 thisthis wouldwould provideprovide anan indicationindication forfor thethe dynamicaldynamical evolutionevolution ofof thethe expansionexpansion raterate asas perturbationperturbation areare beingbeing producedproduced WMAP7

Komatsu, E., et.al (2010) WMAP7

Komatsu, E., et.al (2010) SuddenSudden ReionizationReionization

CAMB Notes, Antony Lewis

AsAs wewe dondon ’’tt knowknow preciselyprecisely thethe detailsdetails ofof thethe reionizationreionization historyhistory wewe shouldshould considerconsider moremore generalgeneral reionizationreionization scenariosscenarios MHMH ’’ss ReionizationReionization Following Mortonson & Hu we can parametrize the reionization history as a free function of the by decomposing the free electron fraction as

 The principal components Sµ (z) are the eigenfunctions of the Fisher matrix of an ideal , limited , experiment .

 mµ are the amplitudes of the S µ (z)  xfid (z) is the WMAP fiducial model at which the FM is computed

M. J. Mortonson and W. Hu ApJ 686, L53 (2008) ResultsResults -- partpart II

z CMB All = WMAP7 +BICEP +QUAD +ACBAR w(z) = w + w 0 a 1 + z OpticalOptical DepthDepth It is interesting to consider the constrains on the optical depth , derived by integrating xe(z) up to z=32

WMAP7 alone CMB all CMB all + BAO

Contours at 68% and 95% c.l in the n vs τττ plane for different dataset CosmologyCosmology withwith HZHZ ’’ss n=1?n=1?

MH reionization WMAP7, n parameter WMAP7, n=1 85

80 ] −1

Mpc 75 −1 [Km s 0 70 H

65

0.020 0.022 0.024 0.026 Ω h2 b Principal Components

WMAP7 CMB ALL CMB ALL + LRG7 PLANCK

68% and 95% c.l. WMAP7 constraints in the mµ vs.n plane in a generalized reionization scenario described by the MHU parametrization . PartPart IIII

 + Tensors modes r

 + Running of the scalar spectral index d n n = run d ln k

“Impact of general reionization scenario on reconstruction of inflationary parameters” S. Pandolfi, E.Giusarma, E.W.Kolb, M. Lattanzi, A.Melchiorri, O.Mena, M.Pena, P.Serra, A.Cooray, arXiv:1009.5433 [astro-ph.CO] Zoology of the inflationary models Sudden Reionization Results, part IIa : tensor MH ’s Reionization

solid curves p=2 Large 0.6 WMAP7 dashed curves p=4

N = 60 0.4

r N = 50 0.2 Small Field Hybrid 0.6 Large Field CMB ALL 0 0.8 0.9 1 1.1 1.2 n 0.4 s r “Impact of general reionization scenario on 0.2 reconstruction of inflationary parameters” Small Field S. Pandolfi, E.Giusarma, E.W.Kolb, M. Hybrid Lattanzi, A.Melchiorri, O.Mena, M.Pena, 0 P.Serra, A.Cooray, 0.8 0.9 1 1.1 1.2 n arXiv: 1009.5433 [astro-ph.CO] s Results, part IIb : Sudden Reionization tensor + running MH ’s Reionization

0.8 solid curves p=2 WMAP7 dashed curves p=4 0.6 Large Field

N = 60

r 0.4 N = 50 0.2 0.8 Small Field Hybrid CMB ALL 0 0.6 Large Field 0.8 0.9 1 1.1 1.2 n s

r 0.4 “Impact of general reionization scenario on reconstruction of inflationary parameters” S. Pandolfi, E.Giusarma, E.W.Kolb, 0.2 Small Field M. Lattanzi, A.Melchiorri, O.Mena, M.Pena, Hybrid P.Serra, A.Cooray, 0 arXiv: 1009.5433 [astro-ph.CO] 0.8 0.9 1 1.1 1.2 n s Forcasts from Planck

n = 0.96 r = 0.05 sudden reionization

“Impact of general reionization scenario on reconstruc tion of inflationary parameters” S. Pandolfi, E.Giusarma, E.W.Kolb, M. Lattanzi, A.Melchiorri, O.Mena, M.Pena, P.Serra, A.Cooray, arXiv: 1009.5433 [astro-ph.CO] ConclusionsConclusions ≅  Inflation predicts n 1 but n ≠ 1

= ±  WMAP7 data n .0 967 .0 014 68( % CL ) but assuming Sudden Reionization

 A modified Reionization history weakens the bound on the spectral index; hybrid models are back allowed by data.

 Assuming an HZ primordial spectrum and a modified Reionization lead a viable cosmology

 Near future data from the Planck satellite mission are needed to solve this question The end For inflation produced by a single , during the slow- roll phase, the kinetic energy of the field is negligible and the potential is nearly constant: φ& 2 ρ φ = V (φ ) + ≈ V (φ ) ≈ const. 2 π 2 8 G This gives rise to a (quasi-) de Sitter phase: H = V(φ) 3 The perturbations in the field are proportional to the value of the Hubble parameter at the of horizon crossing:

 H  2 2G ()∆φ =  hc  = V (φ) 2 k  2π  3π

Since V( φ) is not actually constant, but slowly-varying , we expect a weak dependence of the amplitude of the perturbations on the wavenumber

If the perturbations were originated from the dynamics of a scalar field the spectrum should not be exactly scale invariant Polarization Power Spectrum Monte Carlo Reconstruction Kinney astro -ph/0206032

 Taking higher derivatives of H, one can construct an in finite hierarchy of slow- roll parameters  The evolution of the slow-roll parameters is described by the flow equations

 Given a solution to these equations, the observable quantities can be evaluated. To second order in slow roll, these are given by

The solution to the flow equations also allows one to reconstruct the form of the potential V( φ) Monte Carlo reconstruction of the

inflationary potentials Kinney astro-ph/0206032

WMAP7 - Sudden CMBALL - Sudden

WMAP7 – MH CMBALL – MH MHMH ’’ss ReionizationReionization

Eigenfunctions for fiducial models with different z_max and constant x_e=0.15 (top), x_e=0.3 (bottom). For both fiducial models z_min=6