  In a recent paper, a new conformally flat metric was introduced, describing
an expanding scalar field in a spherically symmetric geometry. The spacetime
can be interpreted as a Schwarzschild-like model with an apparent horizon
surrounding the curvature singularity. For the above metric, we present the
complete conformal Lie algebra consisting of a six-dimensional subalgebra of
isometries (Killing Vector Fields or KVFs) and nine proper conformal vector
fields (CVFs). An interesting aspect of our findings is that there exists a
gradient (proper) conformal symmetry (i.e., its bivector vanishes) which
verifies the importance of gradient symmetries in constructing viable
cosmological models. In addition, the 9-dimensional conformal algebra implies
the existence of constants of motion along null geodesics that allow us to
determine the complete solution of null geodesic equations.
