Two cosmological models, the age of the Universe, and dark energy
  The prevailing cosmological model with the lambda-term, in which the space is flat, is studied (section 1). The corresponding age of the Universe (t0) is calculated (assuming a Hubble constant consistent with the measurements of the Hubble telescope), as well as the deceleration parameter (q0). The latter is found negative, showing an accelerating Universe, but the former is insufficient to account for the actually estimated value. Nevertheless, with more recent values of the parameters involved, this model actually gives a result consistent with the estimated value. But there is a severe defect in the prevailing model, concerning the so-called dark energy, necessary to be introduced. Then, another model without the lambda-term, and based on the time-symmetric theory of the author, is studied (section 3), after an introduction to this theory (section 2). In this model the space is open, but the overall space-time is flat. It is not accelerating (it retains a constant rate of expansion). In this model, with q0 = 0, an age of the Universe results, which is consistent again, within the limits of accuracy, with the estimated value. But the great advantage of this model is that it does not require at all the existence of the ambiguous dark energy. 
Evangelos Chaliasos