Several physicists and bloggers, e.g. Jacques Distler, Peter Woit and especially Sean Carroll who may be considered a true expert in these questions and who added a very new article after this article of mine was published, recently noticed a paper that claimed that the cosmological constant was not needed. Instead, the accelerating expansion was conjectured to be a consequence of fluctuations of a scalar field (and the associated stress energy tensor) whose wavelength was longer than the Hubble radius i.e. the size of the visible Universe, roughly speaking.
- hep-th/0503117 by Kolb, Matarrese, Notari, Riotto
An additional influence of other, unobservable patches of a "greater Universe" would have to involve a very non-local mechanism - one that we can't quite rule out, but one that violates the rules of local field theory drastically and that would have to be explained by a better, non-local theory. It is conceivable that there is some new kind of non-locality at astronomical scales, but it is one of those extraordinary claims that require extraordinary evidence - for example a working theory of quantum gravity that implies such a new effect.
Moreover, it is natural to expect that the acceleration in this framework would not be isotropic (it would not be independent of the direction because of an extra "dipole moment" and other moments) - something that contradicts the observations. Also, Éanna É. Flanagan has a very different (and perhaps too technical) argument in his today's paper:
At any rate, Éanna assumes locality, and with this assumption, it seems clear that the paper of Kalb et al. cannot be correct without the need for complicated calculations such as those of Éanna.