PPP11 Tamkang University 13,14 May, 015 Misao Sasaki Yukawa Institute for Theoretical Physics Kyoto University
General Relativity 1 8 G G R g R T ; T 0 4 c Einstein (1915) GR applied to homogeneous & isotropic universe ds g dx dx c dt a () t d K a 8 ; Kc G 3 a Pc 0 a a 3 a Friedmann (1916) open : K 1 flat : K 0 closed: K 1 H a a : expansion rate (Hubble parameter)
3 Progress in Cosmology (1) 1 st stage: 1916 ~ 1980 1916~ General Relativity/Friedmann Universe 199 Hubble s law: V=H 0 R cosmological redshift 1946~ Big-Bang theory/nuclear astrophysics 1960~ High redshift objects/quasars 1965 Discovery of relic radiation from Big-Bang Cosmic Microwave Background: T 0 =.7K 1970~ BBNucleosynthesis vs Observed Abundance Existence of Dark Matter
Big-Bang Universe and CMB 4 Recombination of thermal plasma protons and electrons z=10 3 z : redshift z( t) a0 at () electron proton Quasars Galaxies CMB photons Last Scattering Surface Big-Bang 400,000 yr 10 9 yr 10 10 yr today
Big Bang theory has been firmly established 5 wavelength[mm] COBE/FIRAS ( 94) 00 sigma error-bars CMB spectrum at T=.75K (redshifted by 10 3 from LSS) frequency[ghz]
6 Establishment of homogeneous & isotropic Big-Bang Universe Model
Progress in Cosmology () 7 nd stage: 1980 ~ 013 1980~ Revelation of Large Scale Structure Cosmological Perturbation Theory Particle Cosmology/Inflationary Universe 199 Detection of CMB anisotropy (COBE) Evidence for Inflationary Universe 003 Accurate CMB angular spectrum (WMAP) Confirmation of Flatness of the Universe Strong evidence for Dark Energy 013 High precision CMB spectrum (Planck) Very strong evidence for Inflation
8 CMB Full Sky Map isotropic component T CMB =.73 K COBE-DMR (1990) WMAP (003~) Planck (013~) WMAP 7th year data ( T/ T CMB ) -5 0 10 Large Scale Structure Planck 013 ( T/ T CMB ) 700 10-5
CMB Anisotropy Spectrum 9 angle : l Planck 013 T ( n1) T ( n) 1 C 4 0 P (cos ).
Horizon Problem 10 Why the detection of T/T at >10º was so important? Because in the standard Friedmann universe, the size of causal volume (horizon size) grows like ~ ct. While, the expansion of the universe is slower than ~ ct because gravity is attractive (if + 3P >0) decelerated expansion The angle sustaining the horizon size at LSS is ~ 1º. Thus, any causal, physical process cannot produce correlation on scales >1º. But (T/T) >10º 0 means there exists non-zero correlation.
There are ~10 4 causally independent patches on LSS 11 Last Scattering Surface (t=4x10 5 yr) ~1º horizon size Now (t~10 10 yr) Big-Bang (t=0)
Progress in Cosmology () 1 nd stage: 1980 ~ 013 1980~ Revelation of Large Scale Structure Cosmological Perturbation Theory Particle Cosmology/Inflationary Universe 199 Detection of CMB anisotropy (COBE) Evidence for Inflationary Universe 003 Accurate CMB angular spectrum (WMAP) Confirmation of Flatness of the Universe Strong evidence for Dark Energy 013 High precision CMB spectrum (Planck) Very strong evidence for Inflation
Inflationary Universe 13 Universe dominated by a scalar (inflaton) field For sufficiently flat potential: 8G 1 ( ) ( ) 3 H 3 1 H V( ) H V V V() H is almost constant ~ exponential expansion = inflation slowly rolls down the potential: slow-roll (chaotic) inflation Inflation ends when starts damped oscillation. decays into thermal energy (radiation) Birth of Hot Bigbang Universe Linde (1983)
Hubble horizon during inflation 14 a(t)~e Ht ; H~const. A small region of the universe c H -1 Universe expands exponentially, while the Hubble horizon size remains almost constant. An initially tiny region can become much larger than the entire observable universe solves the horizon problem.
length scales of the inflationary universe 15 log L L=c H -1 L a(t) Size of the observable universe Inflationary Universe Bigbang Universe log a(t)
Flatness of the Universe 16 small universe expands by a factor >10 30 Size of our observable universe looks perfectly flat Birth of a gigantic universe Flatness can be explained only by Inflation
Seed of Cosmological Perturbations 17 Zero-point (vacuum) fluctuations of : () ik x k te k k c k 3 H k () t k 0 ; ( t) a ( t) ( t) harmonic oscillator with friction term and time-dependent k physical wavelength k const. (t) a(t) frozen when > c H -1 (on superhorizon scales) gravitational wave (tensor) modes also satisfy the same eq.
Generation of Curvature Perturbation 18 curvature perturbation R -Y : gravitational potential ( 3) 4 R a is frozen on flat (R=0) 3-surface (t=const. hypersurface) Inflation ends/damped osc starts on =const. 3-surface. t T const., 0 end of inflation hot bigbang universe x i 0 0 0 0
Theoretical Predictions 19 Amplitude of curvature perturbation: H k / ah Mukhanov (1985), MS (1986) Power spectrum index: 1 18 M pl 8G ~. 410 GeV: Planck mass 4 k ( ) 3 H n 1 P ( ) S 1 3 S k Ak ; ns MP k/ ah V V V 3 V Tensor (gravitational wave) spectrum: 4 n P ( k) r ( ( ) 8 k 3 1 P T T 3 T ( k ) A k ; nt ) 8 P k S consistency relation Liddle-Lyth (199)
CMB Anisotropy from Curvature Perturbation 0 Photons climbing up from gravitational potential well are redshifted. E obs Y 0 d E emit For Planck distribution, T n T T obs ( ) 1 Y( x emit ) Temit xemit nd ; n line of sight In an expanding universe, this is modified to be There is also the standard Doppler effect: T ( n ) n v ( xemit ) T T 1 ( n ) Y( x emit ) T 3 Sachs-Wolfe effect
T 1 ( n ) Y( x LSS) n v ( x LSS) ( minor corrections) T 3 1 Y v Observer Last Scattering Surface (LSS)
Amplitude of curvature perturbation: H k / ah Mukhanov (1985), MS (1986) Power spectrum index: 4 k ( ) 5 1 4 16 ob s ~ 10 V / ( ) ~ 10 GeV M P 3 H n 1 P ( ) S 1 3 S k Ak ; ns MP k/ ah 1 ~. 8G 18 410 GeV: Planck mass V V 3 V V ns, Planck 1 0. 040 0. 0073 ns 1~ 0. 04 for a typical model Tensor (gravitational wave) spectrum: 4 n P ( k) r ( ( ) 8 k 3 1 P T T 3 T ( k ) A k ; nt ) 8 P k S Liddle-Lyth (199) to be observed...
CMB constraints on inflation Planck XX (015) 3 scalar spectral index: n s ~ 0.96 tensor-to-scalar ratio: r < 0.1 3 d log[ k PS ( k)] ns 1 dlog k PT ( k) r P ( k) S single-field models with constant n s are severely constrained
4 Inflation as the Origin of Large Scale Structure
Post WMAP/Planck Era 5 Standard (single-field, slow-roll) inflation predicts almost scaleinvariant Gaussian curvature perturbations. Observational data are consistent with theoretical predictions. almost scale-invariant spectrum: highly Gaussian fluctuations: gauss local f NL ns 3 f local 5 NL gauss 0.968 0.006 (68% CL) Planck 015 XIII 0.8 5.0 (68% CL) Planck 015 XVII only to be confirmed by tensor (=GW) modes?!
6 signature of primordial GWs spacetime(graviton) vacuum fluctuations from inflation Starobinsky (1979) B-mode polarization in CMB anisotropy Seljak & Zaldarriaga (1996) E-mode (even parity) B-mode (odd parity) = cannot be produced from density fluctuations
7 No trace of primordial B-mode had been found so far
Discovery(?) of primordial GWs 8 BICEP (014) --- r = 0. sky map B-mode spectrum If confirmed, it proves [ large field models* ) of ] primordial inflation & quantum gravity! * ) >M Planck ~10 18 GeV : a challenge for string theorists l
dust [K ] BICEP Planck-BICEP/Keck 9 (014) (015) r =0. without dust B-mode spectrum r P P T S ( k) ( k) r detected B-mode seems mostly to be due to galactic dust Yet, r ~ 0.05 is still possible, which would confirm primordial inflation & quantum gravity!
observational indication running spectrum broken spectrum 30 H -1 0 break Abazajian et al., arxiv:1403.59 [astro-ph.co] broken spectrum is favored with r~0.1 Bayesian evidence
31 a signature from physics beyond inflation?
String Theory Landscape 3 Lerche, Lust & Schellekens ( 87), Bousso & Pochinski ( 00), Susskind, Douglas, KKLT ( 03),... There are ~ 10 500 vacua in string theory vacuum energy density v may be positive or negative typical energy scale ~ M P 4 some of them have v <<M P 4 vacuum energy density taken from http://ipht.cea.fr/
Cosmic Landscape 33 string theory landscape implies an intriguing picture of the early universe multiverse taken from http://ineedfire.deviantart.com/art/psychedelic-multiverse-104313536 Maybe we live in one of these vacua
A universe jumps around in the landscape by quantum tunneling 34 it can go up to a vacuum with larger v de Sitter (ds) space ~ thermal state with T =H/ if it tunnels to a vacuum with negative v, it collapses within t ~ M P / v 1/. so we may focus on vacua with positive v : ds vacua v 0 Sato, Kodama, MS & Maeda ( 81)
Most plausible state of the universe before inflation is ds vacuum with v ~< M P 4 35 ds space = solution with maximal symmetry (ds symmetry) a hyperboloid in 5 dim Minkowski space x 0 ds = O(4,1) ds dt cosh Ht d (3) x A (A=1~4)
quantum tunneling = classically forbidden = imaginary time (~ WKB approximation) ds = O(4,1) false vacuum decay via O(4) symmetric (CDL) instanton forbidden O(4) O(5) = S 4 : 4-sphere in 5 dim Euclidean space allowed O(3,1) Coleman & De Luccia ( 80) inside bubble is an open universe 36 bubble wall false vacuum x R (sphere) t x R (hyperboloid)
creation of open universe MS, Tanaka, Yamamoto & Yokoyama (1993) ds vacuum :O(4,1) 37 nucleation surface bubble wall Euclidean instanton: O(4) nucleated bubble: O(3,1) =open universe t = const slice = open http://www.georgehart.com/skewers/skewer-hyperboloid.html
creation of open universe in conformal diagram 38 ds vacuum :O(4,1) Euclidean bubble: O(4) nucleated bubble: O(3,1) =open universe ds vacuum open universe bubble wall
Open Inflation 39 Universe = inside nucleated bubble = spatially open universe Friedmann eq. H at ( ) : a 1 a M a 3 P negative spatial curvature cosmic scale factor (= curvature radius) 1 1 3 M P H a H Observational data indicate 1-0 = K,0 ~< 10 - : almost flat ( 0 stands for current value) K density parameter
If inflation after tunneling was short enough (N = 50 ~ 60) 1 10 ~ 10 0 3 open universe is still possible eg, anthropic argument by Garriga, Tanaka & Vilenkin 99 40 any signature in large angle CMB anisotropies? Here we argue that we are already seeing a couple of such signatures on large angle CMB dipolar statistical anisotropy tensor-scalar ratio: Planck & BICEP/Keck
log L length scales supercurvature scales curvature radius current Hubble radius? 41 new scale! H -1 N=log a curvature dominated phase transition phase inflationary phase
Dipolar Statistical Anisotropy 4 T T 1 Acos T T iso l l 1 C l l 4
dipole asymmetry observed by WMAP/Planck 43 asymmetry of C l in the direction of ell=1 dipole asymmetry of C l in the direction maximizing the asymmetry
Planck 013 XXIII 44 T T 1 Acos T T iso A 0.07
supercurvature mode 45 MS, Tanaka & Yamamoto ( 94) wavelength > curvature radius supercurvature mode open universe ds vacuum bubble wall scalar field with m 9 H 4 has discrete supercurvature mode
46 Gradient of a field over the horizon scale = Super-curvature mode in open inflation curvature radius size of observable universe may modulate the amplitude of perturbation depending on the direction. leading order effect is dipolar
a viable model Kanno, MS & Tanaka (013) 1 1 1 1 L V ( ) m f c mc c (, c )-sector ~ "axion"-like : inflaton : isocurvature mode with super-curvature perturbation c : curvaton H F : Hubble at H ( ) F m H V mc false vacuum curvature perturbation is almost Gaussian 47 H, c f H ( )
48 P ( k) N H N S c f H ( ) k / a H dipolar modulation through f ( ) c-field is a free field (no direct coupling to inflaton) no significant non-gaussianity, nor quadrupole -field eventually dies out ( because m ~ H ) modulation is larger on larger scales = consistent with Planck 013
49 tensor-scalar ratio Planck-BICEP/Keck 015 resolved if dn s /dlnk<0 (running spectral index) if r >~ 0.05, models with non-constant n s are favored can open inflation explain this? -- Yes!
observational indication running spectrum broken spectrum 50 H -1 0 break curvature radius? Bayesian evidence broken spectrum is favored with r~0.1 Abazajian et al., arxiv:1403.59 [astro-ph.co]
fast-roll phase in open inflation 51 curvature dominant phase right after tunneling, H is dominated by curvature: V a t, t 4 V ( ) H 3M P 1 a fast-roll phase curvature dominance ends 1 at t* H* M P 3/ V for V * ~ 1 M P V V V fast-roll phase lasts for a few e-folds until V becomes small. slow-roll phase
log L length scales supercurvature scales curvature radius current Hubble radius 5 new scale! H -1 N=log a curvature dominated phase transition phase inflationary phase
theoretical (qualitative) predictions 53 suppression of curvature perturbation during the first few e-folds ( large scales) of open inflation H P S (k) : ( ) M pl H H no suppresion in tensor perturbation P ( k ) = T 8H ( ) M pl r P P T S 16 curvature scale at the beginning of fast-roll phase t = t * R H ~ e (say ~ 5) curv O(1) curv 1/ 1 1 K * H 0 R K 0.04
scalar & tensor spectrum in open inflation 54 Linde, MS & Tanaka (1999) White, Zhang &MS (014) scalar tensor (no suppression) scalar suppression begins indeed at smaller scales curvature radius H 0-1 if K 0.003
Summary 55 1. Dipolar statistical anisotropy requires a non-standard inflation scenario Modulation of the fluctuation amplitude by supercurvatue mode in open inflation. If r>~0.05, Planck result may be explained with P s (k) suppressed on large scales Suppression due to fast-roll phase at the beginning of in open inflation These may be signatures from string landscape
56 embedding models in string theory? any other testable predictions? other features in CMB? LSS?...? Maybe we are beginning to see physics beyond inflation! string theory landscape?