Inflationary cosmology after Planck. Takahiro Tanaka (YITP)

Transcription

1 Inlationary cosmology ater Planc Taahiro Tanaa (YITP)

2 Big Bang Cosmology The universe starts with a ireball. Friedmann Universe ~Hubble s law ucleosynthesis Baryon/Photon~0-9~-0 Cosmic Microwave Bacground Beginning o Particle Cosmology

3 Various motivations or Large domain o baryon/anti-baryon domain Superhorion scale correlation Monopole problem K. Sato Horion problem Flatness problem A. Guth Inlation solves all problems just by assuming an early phase o exponential expansion o the universe. Initial singularity avoidance A. Starobinsy L M R R / 6M grav pl + Initial density perturbation

4 Evolution o scales Horion scale: H - Distance that light can travel or the cosmic expansion timescale i x In linear perturbation, dierent modes evolve independently. Comoving wavenumber: log(length scale) ixed comoving wave number horion sie inlation =log (scale actor)

5 Various inlation models False vacuum inlation (Old inlation) V False vacuum decay Small nucleation rate or inlation Some region continues to inlate Diicult to terminate inlation / too large luctuation A synchronied cloc to control the transition is necessary

6 V ( ) Standard slow roll inlation slowly rolling ield ew inlation, Chaotic inlation A. Linde (98,3) ds dt a t dx L V potential term dominant Expansion rate: H a a H 8G 3 Ht a e exponential expansion 8 G V 3 plays the role o synchronied cloc

7 Generation o density perturbation Quantum luctuation o inlaton during inlation: V 0 t 3Ht 0 a Time-dependent harmonic oscillator exp(-w /) w w H : sub-horion w wider wave unction w Muhanov, Viatcheslav(98) Hawing(98) Starobinsy(98) Guth, Pi (98) Bardeen(98) Kodama-Sasai PTP supplement (984) :adiabatic evolution w w H : super-horion reee out at w H (/a) 3 ~H

8 Super-horion dynamics δ ormalism- Super-horion dynamics is locally described by the FRW universe. Friedmann I Friedmann Super horion t t I I t = t F inal uniorm energy density hypersurace Initial lat hypersurace I t x t ; t x,, e-olding number I aively, ds dt is conserved or single ield inlation on super horion scale. H t H H t Starobinsy (985) Salope & Bond (990) Sasai & Stewart(996) Sasai & TT(998), Lyth et al.(005) ; t, x e a e t t ij H dt dx t ; t, I i dx j

9 Single ield inlation log(length scale) ixed comoving wave number horion sie inlation =log (scale actor)

10 Tensor perturbations L grav M T T pl R tensor M h 4 pl h M pl H M Direct probe o the energy scale o inlation. h pl canonically normalied gravitational wave perturbation

11 Formulas or slow roll inlation Slow roll parameters V V V V V 4 :squared amplitude o curvature perturbation n s 6 s :tilt o the spectrum n r n t h 6 :tensor-to-scalar ratio :tilt o tensor perturbation

12 CMB map by COBE satellite Amplitude o luctuation is about 0-5.

13 CMB map by WMAP satellite Amplitude o luctuation is about 0-5.

14 CMB map by Planc satellite Amplitude o luctuation is about 0-5.

15 Success o inlationary model WMAP9yr+SPT+ACT 0.00 n s r 0.3 K WMAP

16 Planc(03) n s r K ( ) ( )

17 Scalar-tensor ratio rom power spectrum it Constraints on inlation models (WMAP) Spectral tilt WMAP+BAO+H 0 (not latest) Starobinsy inlation L M R R / 6M grav pl Einstein gravity + single scalar V /3 e 3 M 4

18 Constraints on inlation models (ater Planc) + dn s /d(log ) (slightly misleading) power low potentials are not saved + e (eective number o n species)

19 Large tensor rom inlation Large tensor perturbation requires large ield inlation V r 6 8 V SUGRA: Scalar ield potential V e K K D W 8 3W Canonical choice o Kähler potential is : Lyth bound D K W W K W :inetic term K, or which. Exponential growth o potential or >. -problem: m =O(H ) K A solution is to choose K d d V H 3H inetic term is canonical V V Kawasai, Yamaguchi and Yanagida (000)

20 Realiing Large ield inlation String: Moduli/brane in internal space: >> M pl long internal space. diicult to be compatible I the volume o internal space is large, it is also disavored: M pl M 8 0D Vol 6 Small and small bacreaction to the whole internal space strong stabiliation Monodromy Silverstein, Westphal (008) Roughly speaing, wrapping around a circle -lation scalar ields Dimopoulos, Kachru, McGreevy, Wacer (005) lager H slower rolling smaller and identiied

21 Constraint on non-gaussianity on-gaussianity 0 eects o non-linear dynamics during and ater inlation WMAP 9yr local L 77 (95% CL) equil L orthog L 33 (95% CL) 45 (95% CL) Planc local L equil L orthog L (68% CL) 4 75 (68% CL) 5 39 (68% CL) c L s 800 (95% CL) 0.0 (95% CL)

22 on-gaussianity on-linear dynamics gives non-linear mapping on-linear parameter Gaussian variable In general, mapping is non-local. bispectrum Komatsu and Spergel (00) G G Local interaction only ~ Super horion dynamics In the standard slow roll inlation, non-gaussianity is extremely suppressed. on-gaussianity requires non-standard inlation models. x x x 5 3 G L G 3 3 3,, 3 B 3 3 3/ 3 5 6,, P P P P P P B L

23 log a log (physical scale) Hubble scale scale o interest on Gaussianity is produced ) beore horion crossing ) during super horion evolution 3) at the end o or ater inlation t t F 3 Early generation o non-gaussianity suppressed by slow-roll parameters. (Seery & Lidsey (005)) 3 3 x x x x x x c b a c b a perm 3 3 x x x x d c b a cd b a Super horion part o non-gaussianity Exception is ast roll inlation. ) or 3)are local indicates a time just ater initial horion crossing t=t b a ab a a c t t a c a a a t t, t b a c ab a a t t, 5 6 c c ab b a L

24 on-gaussianity produced at the end o or ater inlation Curvaton (Lyth & Wands (00)) Modulated reheating (Dvali, Gruinov & Zaldarriaga (004)) Modulated waterall Ex.) Curvaton r tot (Bernardeau, Koman and Uan (004), Lyth (004)) Suppose is the dominant component o luctuation. Amplitude is observationally ixed. P r 0-9 r L can be as large as 0 5. r tot starts to roll ater inlation. m

25 on-local on-gaussianity rom noncanonical inetic term Typical example is DBI inlation Alishhiha, Silverstein, Tong (008) Moving D3-brane in a higherdimensional bacground Strong coupling large CFT AdS/CFT L e det I J g G V h T 3 IJ I 3 T y I Speed limit: spatially homogeneous det g Even i V is large, / smaller and

26 Slow sound velocity: c s = - t Brane luctuation propagates at the speed o light in the brane rest rame Brane motion H 35 x equil L 8 c s 08 cs enhanced c s 0. 0 r 6 c s suppressed

27 Curvaton bi-spectrum DBI bi-spectrum /.0 / local-type / / equilateral-type

28 Constraint on non-gaussianity on-gaussianity 0 eects o non-linear dynamics during and ater inlation WMAP 9yr local L 77 (95% CL) equil L orthog L 33 (95% CL) 45 (95% CL) Planc local L equil L orthog L (68% CL) 4 75 (68% CL) 5 39 (68% CL) c L s 800 (95% CL) 0.0 (95% CL)

29 Some anomalies Quadrupole-octopole alignment WMAP: 3 Planc: 9 ~3 (σ level signiicance) で議論されているが 何を書いているのかわからん かなりひどい論文

30 Some anomalies Wavelet statistics: Upper tail probabilities = the raction o the simulations that present a value o a given statistic equal to or greater than the one obtained or the data variance sewness curtosis Too large Too small Too small Too small

31 Some anomalies Hemispherical asymmetry number o pixels over the ull sy is x side Lower tail probabilities or side =048 Small number means that the data is statistically very unliely. Lower tail probabilities or side =6

32 orth sy is too eatureless? Some anomalies Hemispherical asymmetry -pt n. south side =64 3-pt n. pseudocollapased orth 3-pt n. equilateral 4-pt n, rhombic

33 Some anomalies Dipolar power modulation Model it: T n Ap n Iso T n Equivalent plot but in the cosmological dipolar direction

34 Some anomalies Cold/hot Spots

35 Further steps rom observations Constraints on tensor perturbations rom uture observations: r < 0.3 : WMAP r < 0.05 : Planc (polariation data is not released yet. Coming in 04) r < 0.0 : QUIET, PolarBeaR, BICEP, SPTpol, EBEX, Spider r < 0.00 : LiteBIRD, EPIC, PIXIE, COrE, B-Pol

36 Summary Tensor perturbations and non-gaussianities in CMB are still ey issues or understanding inlationary cosmology. Observations o the next generation will reduce the precision o tensor perturbation by actor /0 or more. Various inlation models mae dierent prediction about tensor amplitude and amplitude/shapes o non-gaussianities. Once they are detected, they become powerul tools to distinguish dierent models o inlation.