We discuss the possibility that we are living in a non-singular superinflationary universe and dominated by dark energy. Motivated from superstring and M-theory, the cosmology introduced here is based on the effective action of the dilaton scalar field in the presence of the matter source term. Many novel and interesting consequences are revealed through this work and discussed in some details.Keywords Higher-dimensions · Dilaton field · Scalar field · Phantom energy · Dark energy · Superinflation Following the recent advances in sting, superstring and Mtheory, we believe that extra-dimensions really exist at very high energy limit, that is, at the Planck energy regime. However, as we are living in a four-dimensional spacetime, the extra-dimension is invisible and furthermore, we expect that the later decays in time. The recent discovery of dark energy as a theoretical explanation of the accelerated expansion of the Universe is a big unattended surprise in cosmology. In fact, the recent observations of the Type SNeIa supernovae, cosmic microwave background (CMB) anisotropies, the large scale galaxies structures of the universe and SachsWolfe effects have led to the idea that our universe undergoes accelerated expansion at the present epoch tending to a flat de-Sitter space-time as predicted by inflation theory (−1.14 < w < −0.93 at 68% confidence level and has special effects that have only been detected on the largest scales of our Universe and then only in the past ten years (Alcaniz 2004). Several theoretical models, theories and possible solutions have been proposed, but the most popular ones are the cosmological constant or vacuum energy with a constant equation of state, or a variant of it known as quintessence simulated by a slowly rolling scalar field whose energymomentum tensor is dominated by the contribution of the field potential energy which drives a period of accelerated expansion. Unfortunately, both models are encountered by the huge fine-tuning problem required for its magnitude and the coincidence problem: why does the acceleration happen around a redshift of unity, at around 10 billion years? Other leading candidates are K-essence with modified kinetic energy (Armendariz-Picon et al. ), etc. Unfortunately, we still ignore which of these models are the most viable or more realistic than the others. The largest part of these models have significant drawbacks and suffer from serious finetuning problems e.g. fine tuning of parameters for different type of potentials which model quintessence and stability of radiative corrections from the matter sector. In addition, in many of these models, time varying dark energy is expected. With no doubt, the mystery of cosmic acceleration may be the richest, with broad connections to other important questions in modern cosmology and in elementary particle physics. One more serious additional problem that occurs on most of these phenomenological theories including the standard Big Bang model is the initial singularity problem. This serious problem still persists...
