Big Bang/Inflationary Picture

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Melvin McCormick
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2 Big Bng/Infltionry Picture big bng infltionry epoch rdition epoch mtter epoch drk energy epoch DISJOINT

3 Gret explntory power: horizon fltness monopoles entropy Gret predictive power: Ω totl = 1 nerly scle-invrint perturbtions slightly red tilt dibtic gussin grvittionl wves consistency reltions

4 Infltion: How does it work? V w = 1 1 & φ & φ V( φ) V( φ) 1 φ

5 ( ) inflton ρ π σ ρ ρ π G k G r m H = Anlyzing infltion in simple, model-independent wy survivl of the smllest How infltion flttens nd smoothes the universe

6 Anlyzing infltion in simple, model-independent wy 8πG ( ) ρ ρ... σ k 8πG ρinflton 0 m 0 r 4 H = 6 survivl of the smllest

7 ( ) inflton ρ π σ ρ ρ π G k G r m H = Anlyzing infltion in model-independent wy survivl of the smllest Ht e t G H ~ ) ( inflton 8 = = ρ π &

8 How infltion cretes nerly scle-invrint spectrum of density perturbtions: begin with fluctutions in the sclr field on length scles smll compred to H -1 Minkowski fluctutions scle invrint cosmic perturbtions

9 Anlyzing infltion in model-independent wy ε (1 w ) = eqution of stte (w = p/ρ) t 1 with ε < ~ / ε 1 M = mss scle for infltion (ρ ~ V(φ) ~ M 4 ) N = number of e-folds of infltion remining (Plnck units: 8πG=1)

10 Sclr field fluctutions become fluctutions in time when infltion ends which become temperture fluctutions whose mplitude is determined by M nd ε δt T δt/ t 1/ t / ~ 1/ ~ ~ δt t H ~ δφ & φ Hδt H ~ H ρ & ~ ~ φ p ρ p ρ δt T ~ M ε gussin dibtic

11 Wht do we know bout ε? Recll: ~ / ε t 1 nd H & / = 1/ εt And infltion ends fter N e-folds. Tht mens: H H end t = = = e tend end ε ( N ) ε 1 e ~ δ ε or ~ 1 N T T M ~ ~ M N ~ 8M ε

12 spectrl tilt n s? from before: δ T ~ ε ~ ρ ε T M ( n s 1)/ ~ k ε~ 1/ N ρ~ 1/ ε k ~ H I ~ e N n s 1~ d ln d ρ/ ε lnk ~ ε dln ε d N ~ N ns ~ 0.95 Also predicts the run

13 Wht does infltion predict bout Grvittionl wve (tensor) fluctutions A G ~ H ~ ρ ~ M 4 Mny uthors hve climed: becuse the mplitude depends on M 4 it cn vry by mny orders of mgnitude so no cler trget for experiment

14 Flw: The men squre sclr fluctution mplitude is ALSO proportionl to M 4 δ T ~10 5 ~ T M ε M ~10 5/ ε 1/ 4!! So we know the scle of infltion: For ε ~ 1/N, M ~ 10 - (nd mking it smller requires extrordinry fine-tuning)

15 Flw: The men squre sclr fluctution mplitude is ALSO proportionl to M 4 r tensor sclr = 4 M M /ε # 4 =# ε = 16 ε = 16 N r = 16 ε = 16 N ~7%

16 Gret explntory power: horizon fltness monopoles entropy Gret predictive power:??? - Ω totl = 1 nerly scle-invrint perturbtions slightly red tilt (n s ~ 0.95) dibtic gussin grvittionl wves (r ~ 7%) consistency reltions

17 1) Fine-tuning problem? ) So mny models, mny with differing predictions! Two views of infltion: ) theory how the universe ws mde fetureless (smooth, flt,) -- nmely, by period of smoothly vrying ccelerted expnsion (with smoothly vrying w nd H) b) Anything goes: ny kind of ccelerted expnsion produced by sclr field nd potentil

18 the clssic perspective dominntly clssicl process n ordering process in which quntum physics plys smll but importnt perturbtive role

19 the (true) quntum perspective Infltion is dominntly quntum process in which (clssicl) infltion mplifies rre quntum fluctutions resulting in peculir kind of disorder

20 Lecture

21 The clssic picture we present to the public

22 but the truth is:

23 Linde, Linde, Mezhlumin, PRD 50, 456 (1994)

24 Unpredictbility Problem

25 Mybe string theory will sve the dy? Energy Lndscpe vcu w/different properties

26 The Anthropic Principle?

27 Mybe we cn find mesure tht explins why our universe is more probble?

28 Source of the Problem: Infltion is too powerful for our own good

29 Source of the Problem: H smoothing smoothing > H norml >> H tody

30 But wht if H smoothing smoothing << H norml norml?

31 How do we go from smll H to lrge H? H& = π ρ 4 G( p) = H ε H smooth smll nd contrcting! Of course, then big bng not the beginning! but then how do we smooth?!

32 Recll how infltion worked: 8πG ( ) ρ ρ... σ k 8πG ρinflton 0 m 0 r 4 H = 6 Expnding universe: survivl of the smllest

33 Wht if the universe is contrcting? 8πG ( ) ρ ρ... σ k 8πG ρinflton 0 m 0 r 4 H = 6 survivl of the lrgest

34 ( ) inflton ρ π σ ρ ρ π G k G r m H = survivl of the lrgest ) (1 0 8 G φ ρ π w Wht if the universe is contrcting?

35 ( ) inflton ρ π σ ρ ρ π G k G r m H = survivl of the lrgest ) (1 0 8 G φ ρ π w w >> 1 Wht if the universe is contrcting?

36 ( ) inflton ρ π σ ρ ρ π G k G r m H = ) (1 0 8 G φ ρ π w w >> 1 A NEW NON-INFLATIONARY SMOOTHING MECHANISM: no ccelertion; not fter the big bng; not superluminl; not nerly de Sitter; Wht if the universe is contrcting?

37 ( ) inflton ρ π σ ρ ρ π G k G r m H = ) (1 0 8 G φ ρ π w w >> 1 nd no chotic mixmster behvior Wht if the universe is contrcting?

38 ( ) inflton ρ π σ ρ ρ π G k G r m H = ) (1 0 8 G φ ρ π w w >> 1 nd H smooth << H norml Wht if the universe is contrcting?

39 ( ) inflton ρ π σ ρ ρ π G k G r m H = ) (1 0 8 G φ ρ π w w >> 1 nd mkes scle-invrint fluctutions!! Wht if the universe is contrcting?

40 Nerly scle-invrint density perturbtions? the reverse of infltion H -1 ~ t nd (t) ~ t 1/ε with ε >> 1 nd t 0 -

41 scle-invrint fluctutions? pproch: quntum fluct. exit horizon & re-enter lter ( t) ε ~ t (1 w ) 1 ε ~( H 1 ) 1 ε n s 1: expnding contrcting ε < 1 ε > 1 ε << 1 ε >> 1 (or w >> 1) n s 1 = ε dln ε dn n s 1 = ε dln ε dn

42 scle-invrint fluctutions? pproch: quntum fluct. exit horizon & re-enter lter ( t) ε ~ t (1 w ) 1 ε ~( H 1 ) 1 ε expnding ε < 1 contrcting ε > 1 n 1: ε << 1 n s s dln ε 1 = ε dn dul ε 1/ ε ε >> 1 (or w >> 1) n s dln ε 1 = ε dn

43 Ekpyrotic contrction Herclitus ek-pyr-o-sis: (Gr.) conflgrtion

44 How to get w >> 1? brnes V φ w = 1 1 & φ & φ V( φ) V( φ) >> 1 Y = distnce = e cφ

45 The Cyclic Model of the Universe bng rdition mtter drk energy ekpyrotic contrction crunch

46 Big Bng/Infltionry Picture big bng infltionry epoch rdition epoch mtter epoch drk energy epoch DISJOINT

47 Wht bout the Tolmn Entropy Problem? Or violting the lws of thermodynmics? Richrd Tolmn size of the universe t

48 How cn we distinguish which model is right?

49 Curiously, precision tests cn distinguish the two key qulittive differences between infltion nd ekpyrotic/cyclic models H smoothing is exponentilly different grvittionl wves w is orders of mgnitude different locl non-gussinity

50 non-gussinity generted when modes re outside the horizon ( locl NG) ζ ~ (δρ/ρ) = ζ L f NL ζ 5 L Mldcen Komtsu & Spergel f NL ~ ε observed NL 110 > f > 9 observed NL 147 > f > 7 (WMAP5 tem) (Ydv & Wndelt)

51 Wht is t stke

54 our vision is limited: the future is blek

55 wht we see is typicl

56 Lndscpe of Possibilities?... or the End of Science?

58 our vision extends beyond the big bng: the future is hopeful wht we see is typicl

59 Appendix I The discussion of the cyclic model ws only the tip of the iceberg: Some interesting topics we did not discuss: Getting through the bounce (non-singulr vs. singulr bounces) How cycling might ddress the cosmologicl constnt problem The xion problem nd how cycling might ddress it Conversion of sclr fluctutions to temperture fluctutions from 4d nd 5d point of view (entropic mechnism) Genertion of sclr-induced grvittionl wves

60 Appendix II Some References More efficient thn going to the rxiv: Check my website to find to collection of rticles rnging from populr to dvnced: I might recommend: The Cyclic Model Simplified See lso recent review rticle by Jen-Luc Lehner (bit more technicl, but more up-to-dte: lot of progress hs been mde in just the lst yer) For populr discussion of both infltion & cyclic: Endless Universe by Neil Turok nd myself (lmost ll the ides but no equtions) An interesting vrint by Khoury, Ovrut & Buchbinder is Clled the new ekpyrotic model (look on the rxiv)

Outline. I. The Why and What of Inflation II. Gauge fields and inflation, generic setup III. Models within Isotropic BG

Outline. I. The Why and What of Inflation II. Gauge fields and inflation, generic setup III. Models within Isotropic BG Outline I. The Why nd Wht of Infltion II. Guge fields nd infltion, generic setup III. Models within Isotropic BG Guge-fltion model Chromo-nturl model IV. Model within Anisotropic BG Infltion with nisotropic