Natural Inflation: Particle Physics Models, Power Law Spectra for Large Scale Structure, and Constraints from COBE

Fred Adams; J. R. Bond; Katherine Freese; Joshua Frieman; Angela Olinto

doi:10.1103/PhysRevD.47.426

paper

Natural Inflation: Particle Physics Models, Power Law Spectra for Large Scale Structure, and Constraints from COBE

arXiv:hep-ph/9207245 · doi:10.1103/PhysRevD.47.426

Abstract

A pseudo-Nambu-Goldstone boson, with a potential of the form $V (I ¨ ) = I^^{4} [1 \pm cos (I ¨ / f)], na t u r a l l y g i v esr i se t o in f l a t i o ni f$ f \sim M_{Pl} $an d$ Î\sim M_{GUT} $. W es h o w h o w t hi sc ana r i se in t ec hni co l or - l ik e an d s u p er s t r in g m o d e l s, an d w or k o u t an e x pl i c i t s t r in g e x am pl e in t h eco n t e x t o f m u l t i pl e g a ug in oco n d e n s a t i o nm o d e l s . W es t u d y t h ecos m o l o g y o f t hi s m o d e l in d e t ai l, an df in d t ha t s u f f i c i e n t r e h e a t in g t oe n s u r e t ha t ba r y o g e n es i sc an t ak e pl a cer e q u i r es$ f > 0.3 M_{Pl} $. T h e p r im or d ia l d e n s i t y f l u c t u a t i o n s p ec t r u m g e n er a t e d i s an o n - sc a l e - in v a r ian tp o w er l a w,$ P(k) \propto k^{n_s} $, w i t h$ n_s \simeq 1 - (M^2_{Pl}/8Ïf^2) $, l e a d in g t o m or e p o w er o n l a r g e l e n g t h sc a l es t han t h e$ n_s = 1 $H a r r i so n - Z e l d o v i c h s p ec t r u m . T h es t an d a r d C D M m o d e l w i t h$ 0 \la n_s \la 0.6-0.7 $co u l d in p r in c i pl ee x pl ain t h e l a r g e - sc a l ec l u s t er in g o b ser v e d in t h e A P M an d I R A S g a l a x y s u r v ey s a s w e l l a s l a r g e - sc a l e f l o w s, b u tt h e C O B E mi cr o w a v e ani so t r o p y im pl i ess u c h l o w am pl i t u d es (or hi g hbia s f a c t or s,$ b>2 $) f or t h ese C D M m o d e l s t ha t g a l a x y f or ma t i o n occ u r s t oo l a t e t o b e v iab l e; co mbinin g C O B E w i t h s u f f i c i e n tl y e a r l y g a l a x y f or ma t i o n or t h e l a r g e - sc a l e f l o w s l e a d s t o$ n_s >0.6 $, or$ f > 0.3 M_{Pl} $a s w e l l . F or e x t e n d e d an d p o w er l a w in f l a t i o nm o d e l s, t hi sco n s t r ain t i se v e n t i g h t er,$ n_s > 0.7$; combined with other bounds on large bubbles in extended inflation, this leaves little room for most extended models.

42 pages, (12 figures not included but available from the authors)