The recent observational data from the Planck satellite and ground based experiments support the standard cosmological model, defined by just a few independent parameters. Two of them require a theoretical explanation: the tilt of the power spectrum of the inflationary CMB fluctuations n_{s}, and the level of inflationary gravitational waves, B-modes, r< 0.07. I will describe the recently developed class of inflationary models based on the Poincare disk model of hyperbolic geometry, which is beautifully represented by the Escher's picture Circle Limit IV. In such models, n_{s} is very close to the Planck result n_{s} =0.965, whereas the amplitude of the gravitational waves can take various values proportional to the square of the radius of the Poincare disk. These models predict seven distinct targets for the B-mode experiments in the range r = 10^{-2} -10^{-3}, motivated by string theory.

Held Tuesdays at 4:30 pm in the William R. Hewlett Teaching Center, room 200. Refreshments in the lobby of Varian Physics at 4:15 pm.

Winter 2016/2017, Committee: A. Linde (Chair), S. Kivelson, S. Zhang