  I start with a scenario where the universe is an abstract space $\mathcal{M}$
having $d$ dimensions. There is a two dimensional surface embedded in it.
Embedding is a map from the embedded surface to $\mathcal{M}$ that has a field
theory described by Sigma model. I take $d$ directions of $\mathcal{M}$ to be
the generators of a symmetry group SU(n) of the Lagrangian of the embedding.
This means embedding has n flavors.
  Then I introduce spontaneous symmetry breaking in the theory and define the
direction along which the symmetry breaking occurs as time. Next I write down
the modified Einstein's equation including the embedding.
  Then I discuss embedding's relation to the expansion of the universe. After
that I construct an inflationary scenario with embedding as inflaton and
discuss its connection to Starobinsky $R^{2}$ model. Finally, I discuss the
effect of inflation on the non-commutativity of the spacetime.
