On A Cosmological Invariant as an Observational Probe in the Early
  Universe
  k-essence scalar field models are usually taken to have lagrangians of the
form ${\mathcal L}=-V(\phi)F(X)$ with $F$ some general function of
$X=\nabla_{\mu}\phi\nabla^{\mu}\phi$. Under certain conditions this lagrangian
in the context of the early universe can take the form of that of an oscillator
with time dependent frequency. The Ermakov invariant for a time dependent
oscillator in a cosmological scenario then leads to an invariant quadratic form
involving the Hubble parameter and the logarithm of the scale factor. In
principle, this invariant can lead to further observational probes for the
early universe. Moreover, if such an invariant can be observationally verified
then the presence of dark energy will also be indirectly confirmed.
