Inflation is today a part of the Standard Model of the Universe supported by the cosmic microwave background (CMB) and large scale structure (LSS) datasets. Inflation solves the horizon and flatness problems and naturally generates density fluctuations that seed LSS and CMB anisotropies, and tensor perturbations (primordial gravitational waves). Inflation theory is based on a scalar field ϕ (the inflaton) whose potential is fairly flat, leading to a slow-roll evolution. This review focuses on the following new aspects of inflation. We present the effective theory of inflationà la Ginsburg and Landau, in which the inflaton potential is a polynomial in the field ϕ and has the universal formM M Pl is the scale of inflation and N ∼ 60 is the number of e-folds since the cosmologically relevant modes exit the horizon till inflation ends. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings become naturally small as powers of the ratio (M/M Pl ) 2 . The spectral index and the ratio of tensor/scalar fluctuations are ns − 1 = O(1/N ), r = O(1/N ), while the running index turns out to be dns/d ln k = O(1/N 2 ) and therefore can be neglected. The energy scale of inflation M ∼ 0.7 × 10 16 GeV is completely determined by the amplitude of the scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo Markov chain (MCMC) analysis of the available CMB+LSS data (including WMAP5) with fourth degree trinomial potentials showed: (a) the spontaneous breaking of the ϕ → −ϕ symmetry of the inflaton potential; (b) a lower bound for r in new inflation: r > 0.023 (95% CL) and r > 0.046 (68 CL); (c) the preferred inflation potential is a double-well , even function of the field with a moderate quartic coupling yielding as the most probable values ns 0.964, r 0.051. This value for r is within reach of forthcoming CMB observations. The present data in the effective theory of inflation 3669 Int. J. Mod. Phys. A 2009.24:3669-3864. Downloaded from www.worldscientific.com by YALE UNIVERSITY on 02/02/15. For personal use only. 3670 D. Boyanovsky et al.clearly prefer new inflation. Study of higher degree inflaton potentials shows that terms of degree higher than 4 do not affect the fit in a significant way. In addition, a horizon exit happens for ϕ/[ √ NM Pl ] ∼ 0.9, making higher order terms in the potential w negligible. We summarize the physical effects of generic initial conditions (different from Bunch-Davies) on the scalar and tensor perturbations during slow roll and introduce the transfer function D(k), which encodes the observable initial condition effects on the power spectra. These effects are more prominent in the low CMB multipoles: a change in the initial conditions during slow roll can account for the observed CMB quadrupole suppression. Slow-roll inflation is generically preceded by a short, fast-roll stage. Bunch-Davies initial conditions are the natural initial conditions for the fast-roll perturbations. During fast roll, the potential in the wave equations of curvature and tens...