The success of the standard cosmological model with a finite cosmological constant raises many problem for fundamental physics. The inflationary model of the very early Universe provides a solution to a number of these problems but it requires the introduction of new physics. There is no physical realisation of the inflaton field. The model has, however, had a notable success in accounting for the origin of the fluctuations from which galaxies and the large-scale structure of the Universe formed. A solution to the origin of the baryon asymmetry of the Universe has yet to be found. Many cosmologists believe that the solution to these problems lies in the very earliest epochs, the Planck era, when gravity itself has to be quantised.