Semi-classical treatment of $k$-essence effect on cosmic temperature
  A phenomenological model is described for Cosmic Microwave Background
Radiation (CMBR) evolution with dark energy an essential ingredient in the form
of a $k-$essence scalar field. The following features of this evolution can be
successfully obtained from this model: (a) the {\it observed} variation of the
rate of change of scale factor $a(t)$, i.e. $\dot a$, with time and (b) the
{\it observed} value of the epoch when the universe went from a decelerating
phase to an accelerated phase. These two features have been matched with
graphical transcriptions of SNe Ia data. The model also indicates that the
evolution is sensitive to the presence of inhomogeneity and this sensitivity
increases as one goes further into the past. Further, the value of the
inhomogeneity parameter determines the epoch of switch over to an accelerated
phase. A positive value of inhomogeneity parameter leads to switch over at
earlier epochs, while a negative value leads to switch over at later epochs. If
the value of the inhomogeneity parameter is a bit negative then the crossover
point from deceleration to acceleration gives better agreement with the
observed value.
