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Perturbations Inflaton fluctuations ⇥ P R Primordial spectrum of curvature perturbations CMB temperature anisotropies from inflation k Larger scales Scalar spectral index k Smaller scales ( 68% CL ) The primordial power spectrum is nearly scale-‐invariant.
S = ⇤ d 4 x ⇥ g ⇥ R 16 G + X V (⇥) Scalar perturbations Tensor perturbations ds 2 = (1 + 2A)dt 2 +2 i Bdtdx i + a 2 (t) [(1 + 2R) ij + h ij ] dx i dx j Scalar S (2) s = dtd 3 xa 3 Q s Ṙ 2 c 2 s a 2 ( R)2 For standard potential-‐driven inflation Q s = ˙2 c 2 2H 2 , s =1 The amplitude of curvature perturbations can be estimated by solving the equation of motion which follows from the above action. The conditions for the avoidance of ghosts and Laplacian instabilities Q s > 0 c 2 s > 0 ,
Page 1 and 2: S. Tsujikawa, J. Ohashi, S.Kuro
Page 3 and 4: Old inflation (Sato, Kazanas, G
Page 5: Standard slow-‐roll inflation
Page 9 and 10: Discrimination between inflaton
Page 11 and 12: S.T., J. Ohashi, S. Kuroyanagi,
Page 13 and 14: Horndeski’s paper in 1973
Page 15 and 16: Power spectrum of curvature per
Page 17 and 18: We can apply our general resul
Page 19 and 20: Planck constraints on Brans-Dicke g
Page 21 and 22: Higgs inflation There are severa
Page 23 and 24: Running kinetic couplings 0.3 0.25
Page 25 and 26: f NL B R f NL ・・・nonlinear e
Page 27 and 28: Observational constraints on power-
Page 29: Potentials favored from observat

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