  We construct a bulk spacetime from a boundary CFT, $O(N)$ free scalar model,
at finite temperature using a smearing technique, called a conformal flow. The
bulk metric is constructed as an information metric associated with the
boundary thermal state. Near the boundary (UV region), an asymptotically AdS
spacetime is obtained with a leading order perturbation of scalar mode. Based
on the falloff behavior of the perturbations and the $O(N)$ symmetry in the
CFT, we argue that the corresponding bulk theory is a modified gravity with
scalar mode such as $f(R)$ gravity rather than Einstein's general relativity
coupled minimally to matter fields. Moving to Einstein frame, we show that the
metric is asymptotically the same as the AdS black brane solution. On the other
hand, deep in the bulk (IR region), the spacetime turns out to be conformally
equivalent to the near horizon limit of AdS extremal black brane, though it is
no longer a solution of $f(R)$ gravity, and hence more general classes of
modified gravity need to be considered.
