Inflation and CMB. V. Mukhanov. Sektion Physik, LMU, München

Transcription

1 Inflaton and CMB V. Mukhanov Sekton Physk, LMU, München

2 Expandng Unverse: Facts Isotropy of Background Radaton COB δε E, Boomerang, Maxma,.... "photo" of the early Unverse, 1 5 n bg scales up to ct 1 28 cm when ts sze was n thousand tmes smaller that now ε Hubble law r r = at () χ v r = & r com r r v r aχcom r rate of expanson

3 Matter Dstrbuton Intal Condtons 43 At The the sze "ntal" l should moment be t compared = 1 sec, wth the sze the of sze the homogeneous, of causally sotropc part of the Unverse was 33 connect ed regon ct 1 cmbgger than l l ct ct a ct & & 28 1 cm a a ct Gravty s attractve force a! ntal rate of expanson current rate of expanson 9 a& & δε ε 5 In 1 causally dsconnected regon s / 1. In radaton domnated Unverse a& / a& 1 3!!! Homogenety, sotropy problem

4 Intal veloctes 43 At "ntal mome nt" ( t 1 se c) E kn E kn pot 2 a&... a& + E !!! For a gven matter dstrbuton error % would lead to falure n creaton of "our-type" Unvers e n"ntal veloctes" Flatness (=ntal veloctes) problem Int al cond tons we re VERY SPE CIAL (non gen erc)!?

5 Root of the problem: Gravty s attractve force Conjecture : Gravt perod of the Unverse evoluton a& 1 a & >> y was REPULSIV Edurng some a& / a& 1? noproblem s? How gravty can become "repulsve"? 4π G a&& = ( ε+3p ε a ) a 3 energy densty pressure acceleraton Only f ε +3p< a&& > "antgravty" INFLATION s the stage of accelerated expanson of the Unverse when the energy domnance condton s broken

6 a& decelerated Fredmann expanson a& a& t INFLATION Necessary condtons for successful nflaton: a & << a & 1 O () 1 E pot a& Ω = + Ω 1 Predcton kn E a& of nflaton! ct Transton from nflaton to Fredmann era should be "smooth" 2 t t

7 Scenaros R 1, α 4 S = 2, α +...RR + f ϕϕ ϕϕ, ( ), α V ϕ +... gd x 16π G 2 2 Hgher dervatve "new", chaotc,... scenaros If 1 "Old", "New" k 1 nflaton ε = & ϕ 2 + V ( ϕ) New, 2 chaotc... Chaotc ( Lnde, 1 p= & ϕ 2 Extended V( ϕ) 2 2 & ϕ V( ϕ) then p ε and ( ε p) ε 83) Natural, Supernatural <<, Hybrd, +3Power 2law < Fast oscllatng,... Whch concrete scenaro was realzed???

8 Quantum fluctuatons and galaxes Man bonus from nflaton- generaton of prmordal spectrum of nhomogene tes (Mukhanov, Chbsov, 81) Inflaton "washes away" all pre-nflatonary nhomogenetes However, n all scales there always reman nevetable quantum fluctuatons Example: Quantum metrc fluctuatons n Mnkowsk space lpl Today n galactc 1 33 h λ λ λ cm scales h < 1 58 Can quantum fluctuatons be amplfed up to -5 "needed" value 1 n expandng Unverse???

9 Perturbatons ( xt, ) = ( t) + ( xt, ) ϕ ϕ δϕ TT k ds = (1 + 2 Φ) dt a ( t)((1 2 Φ ) δk + hk ) dx dx gravtatonal potental gravty waves

10 Quantum metrc fluctuatons are bg enough n the scales close to the Planckan sc -5 (1 ) -33 ale (1 cm) only Purpose : Transfer these fluctuatons 28 to galactc scales (1 cm) r r Consder plane wave pertur baton: δϕ, Φ exp com ( k x) For gven k, λ ( cm) a/ k a( t) and the change com ph com of the ampltude wth tme depends on how bg s λ compared to the curvature scale (sze of Ensten lft) H phys 1 = a/ a&

11 3 p 1 δϕ Φ... and h 2 ε a H 1 h const δϕ p / H 1 ε

12 Scale Galactc scales H a/ a (no nflato) n 1 = & No nflaton-no chance ph to get bg fluctuatons n galactc scales λ a 1 H H 1 = a a & a a& aat &() & t a a

13 ( p ε ) 1/2 δϕ / Φ, 2 3 h Φk k 2 3 k h k Scalar perturbaton Gravty waves H 1 1/2 H ε 1 ε 1/2 2 p 1 3 < dε p k Ha+ Pl k Ha k Ha.92 Φ () k k < = O 1n <.97 1= S ε 1 S p / d ε lnε ε ε n 2 3 k h k = O < 1 () ε ε Pl k Ha 1/2 λ phys 1/2 T p () 1/2 1+ p = O 1 c S 1 k Hak Ha S + ε ε

14 Φ λ ct rec

15 Summary Input from HEP??? Idea and basc propertes of nflaton are esta blshed: Inflaton s the stage of accelerated expanson of the unverse wth graceful ext to Fredmann stage??? Homogenety, sotropy and flatness of the Unverse mechansm for the orgn of perturbat ons plus solutons of numeros "man made" problems ( monopoles,...) Robust predctons: 5 Spatally flat Unverse : Ω total = 1± 1 Near ly scale nvarant spectrum ( n S,96) Perturbatons are Gau ssan Gravty waves??? Energy scale of nflaton predcton of the perturbatons ampltude, concrete n s Transton from nflaton to Fredmann, reheatng mechansm The orgn of small number 1 characterzng perturbat ons -5

16 Comparson wth observatons: Present δt δt 1 ( ϕ) ( ϕ+ θ) = (2l+ 1) CPC l l(cos θ) T T ϕ 4π l 1 θ

17 Ω m 2 2 Ω b n Ω = 1,2±,2 =,99±,4(?) tot H = 71 km/sec Mpc Ω h =,24 ±,1 (4.4% baryons) b S Ω h =,14 ±,2 (27% darkmatter) m Ω m Ω b??? B-polarzaton ( proof pf grav. waves)

18 Comparson wth observatons: Future

19 "What really nterests me s whether God had any choce when he created the World" A. Ensten Inflaton was nevtable!!! (t s unque opportunty to create World startng from generc ntal condtons wth mnmal efforts)

20 Q & A Q : Does nflaton have a serous compet tor? A Q : : No PBB and TD vs. INFLATION Inflaton PBB TD Causalty + + n/a "No-har" + - n/a Graceful ext Perturbatons + -? n/a + -? - Could we get from observatons somethng useful for "M-theor y"? A: Unfortunately not too much...

21 Q : Can we get n nflatonary models Ω A: <1, large devatons from scale nvarence, nongaussan perturbatons? In prncple YES addng extra fne-tuned parameters n the model, BUT prce 7 > 1 compared to 1/3 for standard nflaton perfomance Q : Does nflaton completely solve the problem of ntal condtons? A:??? Q : What was before nflaton???"god? creates??? new worlds constantly" Q : Instanton "The world and tme had both one begnnng. The world was made not n tme, but smulteneously wth tme " Zohar 1,89a Sant Augustne of Hppo, Can prenflatonary stage have observatonally varfable consequences? A: Probably not, but who knows...?