New Type Scalar Fields for Cosmic Acceleration

We present a model where a non-conventional scalar field may act like dark energy leading to cosmic acceleration. The latter is driven by an appropriate field configuration, which result in an effective cosmological constant. The potential role of such a scalar in the cosmological constant problem is also discussed. ∗e-mail: [email protected] June 2006 During the last years, evidence of an accelerating expansion of the Universe, first published in [1],[2], has become one of the most striking results in modern cosmology and in physics, in general. The most obvious cause of this acceleration is a cosmological constant, although a large number of alternatives have been proposed [3]. Here we will discuss a rather simple, although non-conventional, scalar model, which may also account for the present Universe acceleration. The scalar field we will consider is a real one and its dynamics is determined by the action S = ∫ dx √ −g ( − 2 ∂μΦ(x) ∂ Φ(x) + k ∂μΦ(x) ∂ Φ(x+α) ) . (1) The parameter k is a numerical constant and the shifts (x+α) in the argument of the scalar field are generated by a 4-vector α, which has only a time component, i.e., α = (α, 0, 0, 0). Hence, for x = (t, x1, x2, x3) we have (x+α) = (t+α, x1, x2, x3). We assumed for simplicity that there is no potential for the scalar field. The unusual feature of the action (3) is that, besides the standard kinetic term, there is also an additional non-local derivative term . A similar term has been discussed first time to my knowledge, by Feynman in his thesis [4] in a classical mechanical context, and in connection to the theory of action at a distance. It can be considered as describing a field interacting with itself in a distant mirror by means of advanced and retarded waves. In a modern picture, modelling our universe as a 3-brane, it could be the result of a scalar interacting in a distant 3-brane through bulk waves. Alternatively, expanding for t >> a, we see that