Emergent Universe Scenario in Modified Gauss-Bonnet Gravity
  We present modified Gauss-Bonnet gravity without matter in four dimensions
which accommodates flat emergent universe (EU) obtained in Einstein's general
theory of gravity with a non-linear equation of state. The EU model is
interesting which is free from big-bang singularity with other observed
features of the universe. It is assumed that the present universe emerged out
from a static Einstein universe phase exists in the infinite past. To obtain a
flat EU model we reconstructed mimetic modified $f(G)$-gravity ($G$
representing Gauss-Bonnet terms) without matter. The functional form of
f(G)-gravity is determined which accommodates the early inflation and late
accelerating phases without matter.
