Cosmological constant theories

Are there any hypotheses on the expansion of the universe, which have a cosmological constant, or some other parameter, that results in a universe with an ever increasing rate of acceleration for the expansion of space time?

• Well, there's the currently accepted theory, $\Lambda CDM$. It uses a cosmological constant and the expansion of the universe asymptotically approaches an exponential. So that fits the parameters – Jim Mar 27 '15 at 19:10
• Ok, that has the hubble constant, which seems to have a constant acceleration and therefore an exponentialy increasing velocity for spacetime expansion. What about a case where da/dt>0? – Poemandres SugarKane Humblehof Mar 27 '15 at 19:20
• No, $a(t)=e^{Ht}$ asymptotically, which means that $\dot a(t)$, $\ddot a(t)$, and so on are all increasing too. Exponentially increasing velocity means the acceleration has to be exponentially increasing too – Jim Mar 27 '15 at 19:22
• i've always thought it interesting that, when expressed in a consistent set of units, that $\Lambda \approx 3 \Omega_\lambda H^2$. in Planck units, $H\approx 10^{-61}$ and $\Lambda \approx 10^{-122}$. seems as if there is a link between the observed Hubble constant and the cosmological constant. – robert bristow-johnson Mar 27 '15 at 21:17
• – Yukterez Mar 28 '15 at 0:21