Induced wormholes due to quantum effects of spherically reduced matter in large N approximation

Using one-loop effective action in large N and s-wave approximation we discuss the possibility to induce primordial wormholes at the early Universe. An analytical solution is found for self-consistent primordial wormhole with constant radius. Numerical study gives the wormhole solution with increasing throat radius and increasing red-shift function. There is also some indication to the possibility of a topological phase transition. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] 1 It is a well known fact that spherical reduction of Einstein gravity (see, for example [1]) leads to specific 2d dilatonic gravity which belongs to the general class of 2d dilatonic gravities [2]. Spherical reduction of 4d matter leads to 2d dilaton coupled matter theories. Recently, 2d conformal anomaly for dilaton coupled scalars has been found in ref.[3] (see also [4, 5, 6]). Integrating this conformal anomaly one finds the anomaly induced effective action [4, 5] (in s-wave and large N approximation) which was written in ref.[7] in most complete form. A wide spectrum of physical problems may be addressed using the above effective action. Let us only mention some of most interesting: anti-evaporation of multiple horizon black holes [7, 8]. Hawking radiation [9] in dilatonic supergravity [5], quantum cosmological models in dilatonic supergravity [10], study of semi-classical energy-momentum tensor in the presence of dilaton [11], etc. In the present work we would like to discuss one more of these physical phenomena: the appearance of spherically symmetric wormholes due to the anomaly induced effective action. The wormholes represent handles of topological origin. They may be considered as bridges joining two different Universes or two separate regions of the same Universe [12]. It is known that wormholes cannot occur as solution of classical gravity-matter theory due to violations of energy conditions in classical relativity [12]. Hence, it is natural to expect their manifestations only at the quantum level (or yet in the theory like Born-Infeld D-brane or M-theory, for review, see [13]). Recently, using quantum scalar stress-energy tensor calculated on spherically symmetric background in [14] the back reaction problem (i.e. self-consistent wormholes in semiclassical gravity) has been investigated in ref.[15] (see also [16]). It has been indeed numerically found a semiclassical quantum solution representing a wormhole connecting two asymptotically spatially flat regions [15]. This result is extremely interesting and it should be verified in another models and (or) approximations, taking into account the fact that the approach developed in [15] is not completely free from some serious drawbacks [16]. In the present work we show the possibility of inducing wormholes in the early Universe, making use of the effective action method [17] (large N and swave approximation is used). We will start from the action of Einstein gravity with N minimal scalars S = − 1 16πG ∫