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A new expression to the total age of the Universe is derived in terms of theaverage deceleration parameter. This kinematic result holds regardless of thecurvature of the universe as well as of the underlying gravity theory. Itremains valid even in the context of brane-world motivated cosmologies. Sincethe present age parameter of the Universe is accurately adjusted to $H_0t_0 =1$, it is shown that the time averaged value of the deceleration parameter iszero. This also means that the cosmic age today is exactly the one predicted bya relativistic flat cosmological model filled by K-matter, a fluid satisfyingthe equation of state $p = -{{1/3}}\rho$. By assuming the validity of thisrelation (in an average long time meaning), it is argued that the deceleratingstages of the expansion must exactly be compensated by the accelerated phases,as if the observed Universe coasts forever. If this is true, the presentaccelerating stage must be followed by a subsequent decelerating phase aspredicted by some recent scalar field and brane-world motivated cosmologies.

Age of the Universe, Average Deceleration Parameter and Possible Implications for the End of Cosmology