© North-Holland Publishing Company THE COLLAPSE OF AN ANTI-DE SITFER BUBBLE

I t is an in t r igu ing poss ib i l i ty that the universe is cur ren t ly in a metas tab le phase, a false v a c u u m which will eventual ly decay into a phase of lower energy densi ty. In the semic lass ica l app rox ima t ion , such decays occur through the fo rmat ion and growth of b u b b l e s of the new phase inside the old phase [1]. The fo rmat ion of the bubb les is a q u a n t u m tunne l ing effect, but their subsequent growth is governed by the classical equa t ions of mot ion . If the current vacuum has zero-energy densi ty , the bubb le in te r io rs will have negat ive energy density; their geometr ies will resemble that of an t i -de Si t ter space. Some years ago, F r a n k de Luccia and one of us argued that g rav i t a t i ona l effects rendered these bubb le in ter iors themselves unstable , that the u l t i m a t e fa te of a zero-energy metas tab le vacuum was not merely a t rans i t ion to a new phase b u t also a ca tas t rophic gravi ta t ional col lapse [2]. O u r a r g u m e n t s were highly suggestive, bu t not conclusive. Qui te apa r t f rom def ic iencies in r igor, they rested upon the exact 0 ( 3 , 1 ) invar iance of the solut ion to the c lass ical f ield equat ions descr ibing the evolut ion of the bubb le after its format ion. I t r e m a i n e d a possibi l i ty that the slightest depa r tu re f rom this symmet ry would be suff ic ient to avoid gravi ta t ional collapse, that the pe r tu rba t ion in t roduced by the p resence o f a pa r amec ium would be enough to save the universe. [This is not an e x t r a o r d i n a r y possibi l i ty . A fami l ia r example is a par t ic le moving in an inverse-square