The Effective Cosmological Constant in Higher Order Gravity Theories

Fundamental issues as the determination of gravity vacuum state, the mechanism which led the early universe to the today observed large scale structures, and the prediction of what will be the fate of the whole universe are all connected to the determination of cosmological constant. Besides, from several points of view, it seems that Einstein’s theory of gravity must be generalized to higher–order or scalar–tensor theories in order to overcome shortcomings of fundamental physics and cosmology. Both topics have to be connected so that a lot of people is, recently, asking for the recovering of a sort of cosmological constant in extended theories of gravity. With this fact in mind, it is possible to enlarge the cosmic no–hair conjecture to scalar–tensor 1 and higher–order theories by taking into consideration an ”effective” time–dependent cosmological constant which has to become asymptotically the ”true” one yielding a de Sitter behaviour. The original no–hair conjecture claims that if there is a positive cosmological constant, all the expanding universes will approach a de Sitter behaviour. A simplified version of the conjecture can be proved . It is worthwhile to note that in Wald’s paper the cosmological constant is a true constant (put by hands) and the contracted Bianchi identity is not used, then the proof is independent of the evolution of matter. In order to extend no–hair conjecture to generalized theories of gravity, we have to introduce different sets of conditions (with respect to those given in ) since the cosmological constant is not introduced a priori, but it is ”recovered” from dynamics of scalar fields or higher–order geometric terms in the gravitational Lagrangians. Such conditions must not use the ”energy conditions”, but they have to allow the introduction of a sort of effective cosmological constant which asymptotically becomes the de Sitter constant. Furthermore, it is the only term that does not