Dark Energy and the Observable Universe

We consider ever-expanding Big Bang models with a cosmological constant,$\Lambda$, and investigate in detail the evolution of the observable part ofthe universe. We also discuss quintessence models from the same point of view. A new concept, the $\Lambda$-sphere (or $Q$-sphere, in the case ofquintessence) is introduced. This is the surface in our visible universe whichbounds the region where dark energy dominates the expansion, and within whichthe universe is accelerating. We follow the evolution of this surface as theuniverse expands, and we also investigate the evolution of the particle andevent horizons as well as the Hubble surface. We calculate the extent of theobservable universe and the portion of it that can be seen at different epochs.Furthermore, we trace the changes in redshift, apparent magnitude and apparentsize of distant sources through cosmic history. Our approach is different from,but complementary to, most other contemporary investigations, which concentrateon the past light cone at the present epoch. When presenting numerical results we use the FRW world model with$\Omega_{m0} = 0.30$ and $\Omega_{\Lambda0} = 0.70$ as our standardcosmological model. In this model the $\Lambda$-sphere is at a redshift of0.67, and within a few Hubble times the event horizon will be stationary at afixed proper distance of 5.1 Gpc (assuming $h_0 = 0.7$). All cosmologicalsources with present redshift larger than 1.7 have by now crossed the eventhorizon and are therefore completely out of causal contact.Comment: 33 pages, 12 figures. Minor changes from initial version. Accepted for publication in the Astrophysical Journa