Abstract
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.
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