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Holographic Inflation

Using the de Sitter/CFT correspondence we describe a scenario of holographic inflation which is driven by a three dimensional boundary field theory. We find that inflationary constraints severely restrict the $β$--function, the anomalous dimensions and the value of the $C$--function of the boundary theory. The scenario has model independent predictions such as $ε<< η$, $n_T<0.04$, $P_{tensor}/P_{scalar}<0.08$ and $H<10^{14} GeV$. We consider some simple boundary theories and find that they do not lead to inflation. Thus, building an acceptable holographic inflation model remains a challenge. We also describe holographic quintessence and find that it closely resembles a cosmological constant.