Special Topics in Nuclear and Particle Physics Astroparticle Physics Lecture 13 Inflation & Dark Energy Dec., 15 Sun Kee Kim Seoul National University
(CMB) : 1 1 LSS? (Horizon problem) LSS sound horizon (Flatness problem)
(Horizon Problem) LSS θ d H (t ls ) d p (t ls ) (1+ z ls ) t ls t (1+ z ls ) ~ 1.7! LSS.. (Horizon Problem)
(Flatness Problem) Friedman!R R H 8π 3 Gρ kc R Ω ρ / ρ C ρ C 3H 8πG Ω(t) 1 kc!r(t) R t /3!R t 1/3 R!R const. t > t mr Ω(t mr ) 1 Ω(t ) 1! R(t )!R(t mr ) R(t mr ) R(t ) t mr t /3 O(1 4 ) Ω(t ) 1 <.1 Ω(t mr ) 1 < 1 6
(Flatness Problem) t > t > mr t bbn R! ( t R! ( t ( Ω( t ) 1) ) ' $ ' $ bbn mr Rbbn Tbbn 1 ~ (1 ( ( ) 1) ) % " % " O Ω tmr bbn Rmr Tmr & # & # 1/ R ~ t, R! 14 ( Ω( t bbn ) 1) O(1 ) to have Ω 1 ~ t ) 1/ ~ R 1 Planck Ω 1 1 5 1 ( flatness problem)
(Inflation) Ιnflation scenario ( Alan Guth, 198)? - any initial curvature could be stretched flat à answer to the flatness problem -expansion rate is greater than light speed à answer to the horizon problem A large cosmological constant? An example Higgs field in GUT scale : false vacuum à true vacuum Slow roll over à large cosmological constant!
Friedmann!R R 8π 3 Gρ kc R + 3 ρ 8πG Friedmann R! R 3 nd Friedmann!!R R 4π 3 G(ρc + 3P) R e /3t! de Sitter Universe!!R > ρc + 3P < P ωρc ω < 1 3,
1 du TdS PdV du U S V ds U V S dv P U V S U V ρ c 8πG const. P U V S ρ c ω 1.
φ(x,t) L T V 1 µφ µ φ + V(φ) T µν µ φ µ φ g µν L ρ 1! φ + 1 ( φ) + V(φ) P 1! φ 1 ( 6 φ) V(φ) φ(x,t) ρ P V(φ) V 1 µ φ + 1 4 λ φ 4
V(φ) φ
(Inflation) ti tf R(t f ) R(t i ) eh (t f t i ), H 8πG 3 ρ GUT 1-34 s ct 1 6 m ct 1 6 m 1 6 m 1 34 4 1 17 1 m. : 1-34 s 1m. : e H (t f t i ) 1m /1 6 m ~ 1 6 H (t f t i ) ~ 6
(Inflation) : 1m /1 6 m ~ 1 6 H (t f t i ) ~ 6 Friedmann Ω(t) 1 kc!r(t) R(t f ) R(t i ) eh (t f t i ) Ht Ω(t) 1 e Ω(t f ) 1 e H (t f t i ) 1 5 Ω Ο(1) Ω 1. - Ω1
-.., R -4..
(density contrast) δ (x) ρ(x) ρ ρ VL3 δ (x) δ (k)e ik x k (k x,k y,k z ) k x πn x / L : k k. Power spectrum : P(k) δ (k) λ π / k : SDSS (Sloan Digital Sky Survey) ~ 1 Mpc CMB - ( k)
P(k) k n n n 1 Harrison Zel dovich spectrum VL3 δ (x) δ (k)e ik x k (k x,k y,k z ) k x πn x / L : k k. Power spectrum : λ π / k : SDSS (Sloan Digital Sky Survey) ~ 1 Mpc CMB - ( k)
SDSS (Sloan Digital Sky Survey) http://www.sdss3.org/images/gallery/sdss_pie.jpg
BBN CMB Energy budget Ω Ω Ω m b 1. ±. Ω DM + Ω.44 ±.4 b.7 ±.4 Ω 1 > Ω () + Ω r m () What is missing? ~.3
Friedman R! R kc 8πG + ( ρ + ρ + ρ r m R 3 ) ρ 8πG H 8πG ( ρ 3 r + ρm + ρ ) kc R ρ C 3H 8πG, Ω i ρ i ρ C ρ i H, Ω k ( t) kc ( RH ) H (t) H [ Ω r (t) + Ω m (t) + Ω (t) + Ω k (t)] R R( t) R R 1 1+ z, Ω ~, ~ 1 r Ω 4 m 3 H (t) H Ω r ()(1+ z) 4 + Ω m ()(1+ z) 3 + Ω () + Ω k ()(1+ z)
H (t) H Ω r ()(1+ z) 4 + Ω m ()(1+ z) 3 + Ω () + Ω k ()(1+ z) R(t ) R(t ) 1+ z t H dt t (1 + Z R! R dt dz z ) H 1 R dr dt ( 1+ dz z & dz / $ % 1+ ) H dt z #! " t t 1 H Z dz 4 3 1/ [ Ω ()(1 + z) + Ω ()(1 + z) + Ω () + Ω ()(1 + z) ] (1 + z) r m k t, ( ) t, z
H t dz ( 1+ z) + z 4 3 1/ [ Ω ()(1 + z) + Ω ()(1 + z) + Ω () + Ω ()(1 ) ] r m k Flat, matter dominated universe ( ) Ω r k ( ) ~, Ω (), Ω () t 3H ~ 9 Gyear in contradiction to some old stars >1 Gyears
H t dz ( 1+ z) + z 4 3 1/ [ Ω ()(1 + z) + Ω ()(1 + z) + Ω () + Ω ()(1 ) ] r m k Flat, matter+vacuum energy H t & $ % Ωr m k # & 1+! ln$ A " % 1 ( ) ~, Ω () + Ω () 1, Ω () 3 1/ [ Ω ()(1 + z) + (1 Ω ())] A #! A " dz (1 + z) m m 1 3 where A ( 1 Ωm()) 1/ using the change of variable 3 Ω( 1+ z) /(1 Ω) tan θ Ω ( ).7, Ω m ().3 t ~ 13.5 Gyears
Proper distance tt em tt tt d p (t ) cdt Suppose a light signal started at tt em and arrived here at tt At a point tt, the light travels cdt by now cdt is expanded to cdt R( t ) R( t') ' d P ( t ) t t em z R( t) cdt' R( t') cdz' H ( z') dt dz ( 1+ z) H ( z)
Luminosity distance f L d 4π L f : measured flux L : total radiated power by emitting object d L : luminosity distance E E ν λ em em ~ ~ 1 + ν λem z δt δt em 1+ z. E δt em (1 + z) E δt em f π L 4 d P (1 + z ) d d P ( 1 z) d + L ( z) c(1 z) L + z cdz' H ( z' )
Luminosity distance d L ( z) c(1 + z) z cdz' H ( z' ) H (t) H Ω r ()(1+ z) 4 + Ω m ()(1+ z) 3 + Ω () + Ω k ()(1+ z) H ( z) ~ H z 3 1/ ( Ωm ()(1 + z) + Ω + (1 Ωm() Ω )(1 + ) ) d L ( z) c(1 + z cdz' z) 3 H ( Ω ()(1 + z) + Ω + (1 Ω () Ω )(1 + 1/ m m z) ) Standard candle d(z) m M 5log1 d + 5 L m : apparent magnitude M : absolute magnitude d(z) fitting
Type Ia Supernovae One of binary stars become white dwarf, then it accrets matter from normal companion star until it reaches to Chandrasekhar mass(~1.4 solar mass). Explodes after a quick carbon burning. à elemental composition and luminosity are the same. Standard candle Standard candle : Type Ia Supernovae
High-Z Supernova Search Team (B. Schmidt, A. Riess, ) 1 SN Type IA.16<z<.6
Supernova Cosmology Project (S. Perlmutter, ) 4 SN Type IA.16<z<.6
m : apparent magnitude M : absolute magnitude m M 5log1 d + 5 L
ρ π 3 8 3 G R kc R R +! ρ π 3 8 3 G R R! τ )/ ( 1 1 ) ( ) ( t t e t R t R ρ π τ G 8 3 3 à As the vacuum energy density is constant, more the space expands more is the vacuum energy and more the negative pressure à causing the space to expand further Vacuum energy dominated universe
Transition from decceleration to acceleration ( R!! ( t) q t) R( t) H ( t ) Acceleration Equation deduced from F.E. R!! ( t) 8πG ( ρc + 3P) R( t) 3c q( t) Ω Ω ~ 1 r r ( t) + ()(1 + Ω m 1 Ω z) ()(1 + m 4 ( t) Ω + z) 3 1 Ω Ω m ()(1 + z) 3 Ω (q>) (q<) 1 & Ω # ()(1 ) 3 Ωm + z Ω 1+ z M $ ()! % Ωm " z.7, t ~ 7 Gyears Very recent! M ~ M 1/3 P γ P P m ρ γ c ρ / 3 P ωρ q(t ) 1 c [ Ω m(t ) + (1+ 3ω )Ω (t )] c
High-Z Supernova Search Team (B. Schmidt, A. Riess, ) 1 SN Type IA 13 z>1
Transition from decceleration to acceleration ρ ρ ρ ρ now was not important t
SN Ia? SN Ia : SN ( )? SN Ia >, : z SN Ia. > SN Ia -? :? >
(Dark Energy) (w<-1/3),
Mostly Dark matter, Dark energy Composition of Universe CDM Model Ω Ω matter + Ω 1. Known ~ 4%