Non-gaussianity in axion N-flation models

Transcription

1 Non-gaussanty n axon N-flaton models Soo A Km Kyung Hee Unversty Based on arxv: by SAK, Andrew R. Lddle and Davd Seery (Sussex), and earler papers by SAK and Lddle. COSMO/CosPA Unversty of Tokyo 27 th Sep ~ 01 st Oct

2 Asssted nflaton Asssted nflaton (Lddle-Mazumdar-Schnook 1998) s the observaton that multple scalar felds can cooperate to drve nflaton even f each ndvdually s unable to. Each feld feels the acceleraton from ts own potental, but the collectve Hubble frcton from all felds. N-flaton N-flaton (Dmopolos et al 2008) s a realzaton of asssted nflaton usng strng axons. 2

3 Motvatons and assumptons One motvaton for ths dea s that suffcent nflaton can be obtaned wth all felds mantanng sub-planckan values. Another s that t may be possble to relate asssted nflaton to proper fundamental physcs models. Focused on adabatc perturbatons. Random ntal condtons for felds. Assumptons we made; Horzon crossng and Slow-roll approxmatons. 3

4 N-flaton phenomenology The full strng axon potental s, where there are N f felds wth constants Λ and f. Throughout wll gnore possble couplngs btw the felds. Ths has been extensvely explored n the quadratc approxmaton where all felds are close to ther mnma, n whch case they are smply a set of massve felds wth V = Λ 4 1 cos 2πφ f m 2πΛ2 f 4

5 N-flaton phenomenology Regardless of these choces, the Nflaton phenomenology n ths approxmaton s remarkably smple: The tensor-to-scalar rato always equals to the snglefeld values: r = 8/N where N s the number of e- foldngs. The scalar spectral ndex cannot exceed the sngle-feld value, equallng t only n the equal-mass case: n! 1-2/N. Komatsu et al, WMAP7 The non-gaussanty f NL always equals ts sngle-feld value: f NL = 2/N and hence s unobservably small. 5

6 The N-flaton model But.... n fact the quadratc approxmaton to the potental s unlkely to be vald. We should consder the full potental V = Λ 4 1 cos 2πφ f Even f the potentals are all taken to be dentcal, asssted nflaton s an attractor soluton only f d 2 V/dɸ 2 > 0 (Calcagn and Lddle 2008), whch s not true near the maxmum of the potental(s) where the trajectores wll dverge. [ ===> From now on, called the Naxon model ] 6

7 Naxon equatons Wth the full potental, the obervalbes can be calculated usng the so-called δn formalsm P ζ = H2 4π 2 n 1 = 2ɛ 8π2 3H 2 r = 6 5 f NL N, N, = j H2 8π 2 MP 2 1 / Λ 4 j f 2 j ɛ j 1 ɛ 1 ɛ ; ( ; ( 2 H 2 / 1 π 2 P ζ MP 2 =16 ɛ ; ( j N,N,j N,j ( k N,kN,k ) 2 = r ɛ 1+cosα,(, where ɛ M 2 P 2 / ε -!/H 2 ( V V ) 2, " # (V /V) 2 ε Here α =2!ɸ /f, ε s the slow-roll parameter of each feld, dervatves wrt feld and ndcated by a comma, and * ndcates evaluaton at horzon crossng 7

8 Naxon : N tot The number of e-foldngs s gven by N tot ( f 2πM P ) 2 ln 2 ln 2 f 2 1+cosα 2π 2 MP 2 N f, where the last expresson calculates the expectaton value of the sum under assumpton of unformly-dstrbuted angles α. For values of f of order the Planck mass, suffcent nflaton requres a large number of felds, at least hundreds. 8

9 Naxon: n and r A smlar summaton trck, assumng unformly dstrbuted felds, gves an analytc estmate of the spectral ndex as n 1 5 ln 2/N NB: 5 ln 2! 3.5 At the same tme, the tensor-to-scalar rato s hghly suppressed by the small ε of felds close to the maxmum. 9

10 Naxon: n and r Komatsu et al, WMAP7 r WMAP7 excluded at 95% WMAP7 allowed at 95% Black: N* = 50 Red: N* = 60 Ths plot shows smulatons wth several dfferent values of f. Clearly the dependence on N* domnates. n 10

11 Naxon: non-gaussaty The nterestng aspect of the model s the behavor of the non-gaussanty: 6 5 f NL The sum may be domnated by a small number of felds whose α s very close to!. If there are Ñ felds whch domnate wth comparable ε, there s an approxmate form / j N,N,j N,j ( k N,kN,k ) 2 = r ɛ 1 1+cosα,( 6 5 f NL 2π2 N ( MP f ) 2, hence for f of oder M p the f NL may be of order tens. 11

12 Naxon: non-gaussanty (6/5) fnl Mean over realzatons Nf f = MP; N* = 50 12

13 Interpretaton There s nothng partcularly unusual about the predctons of the non-gaussanty n ths model; t s n fact what one would get from a snge feld evolvng n the axon potental. However a sngle-feld model wth those parameters would not be satsfactory, as t would not gve suffcent nflaton and the spectral ndex would be far from unty. The scenaro works because the asssted nflaton mechansm strongly alters the predcted spectral ndex, but has only a margnal effect on the non-gaussanty 13

14 Concluson The axon Nflaton model s a smple constructon whch offers sgnfcant non-gaussanty whle mantanng vable values of other observables. 14

15 Naxon: trspectrum A smlar analyss yelds an estmate of the trspectra uvalents of Eq. (9) are, n τ NL = (4π 4 / N 2 )(M 4 P /f 4 ) (54/25)g NL = (8π 4 / N 2 )(M 4 P /f 4 ) = (6/5f NL ) 2 As seen n the bspectrum plot, there s a large spread of predctons due to the randomness of ntal condtons. However there are predcted correlatons wthn a realzaton, for nstance between r and f NL. 15