A Brane World Solution to the Cosmological Constant Problem

We consider a model with two parallel (positive tension) 3-branes separated by a distance L in 5-dimensional spacetime. If the interbrane space is antideSitter, or is not precisely anti-deSitter but contains no event horizons, the effective 4-dimensional cosmological constant seen by observers on one of the branes (chosen to be the visible brane) becomes exponentially small as L grows large. 11.10.Kk, 04.50.+h, 98.80.-k, 98.80.Hw Typeset using REVTEX [email protected] [email protected] 1 Recent observational data [1] indicate that there is a positive cosmological constant in the universe, which, compared to the Planck or the electroweak scale, is many orders of magnitude smaller than expected within the context of ordinary gravity and quantum field theory. This is the well-known cosmological constant problem [2]. Here we propose a solution to this problem in which the cosmological constant becomes exponentially small compared to all the other scales in the model. The scenario is a variant of the Randall-Sundrum model [3]. Let us consider two parallel 3-branes (or two stacks of 3-branes) in 5-D spacetime separated by a distance L in the fifth dimension which is not necessarily compactified. Let the brane on the left be the visible brane, with positive brane tension σ0. The brane on the right has positive brane tension σL 6= σ0, generally. Assume that the bulks outside the branes are anti-deSitter(AdS) spaces, with cosmological constants −Λl and −Λr, respectively. There may be numerous solutions of the 5-D Einstein equations for the behavior of the bulk between the branes, but let us focus attention on the simplest, an AdS space with bulk cosmological constant −Λm. (We discuss other possibilities briefly below, and in more detail elsewhere.) We shall see that Λm may be expressed as a function of L,Λl,Λr, σ0, σL and the 5-D gravitational coupling constant κ = 8πG. Thus, we regard Λm as a derived parameter; more generally, in a dynamical 5-D spacetime, Λm may evolve with time as branes move together or apart. For this simplest model for the interbrane spacetime, we can determine the effective 4-D cosmological constant Λeff in terms of Λl, Λr, σ0, σL, L and κ . We show that for large L, Λeff ≈ F (κ,Λl,Λr, σ0, σL)e −2α0L (1) where F is independent of L and the positivity of the 4-D Newton constant GN requires α0 = κ σ0/3− √ κΛl/6 > 0. For α0L≫ 1, the effective 4-D cosmological constant becomes exponentially small in this simple model without any fine tuning of the parameters. In a S/Z2 orbifold version of the model, the only bulk is between the branes, and Λeff ≈ 2σ0 (σL + σ0) (σL − σ0) e 2σ0L/3. (2)