## The Effective Theory of Inflation in the Standard Model of the Universe and the CMB+LSS data analysis

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Boyanovsky, D.

Destri, C.

de Vega, H. J.

Sanchez, N. G.

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Inflation is part of the Standard Model of the Universe supported by CMB and
large scale structure LSS datasets. This review presents new developments of
inflation in three main chapters. (I): The effective theory of inflation a la
Ginsburg-Landau (GL): the inflaton potential is a polynomial with universal
form making explicit the inflation energy scale M, the Planck mass and the
inflation e-folds number N ~ 60. The slow-roll expansion becomes a systematic
1/N expansion and the inflaton couplings are naturally small as powers of
(M/M_{Pl})^2. The spectral index (n_s - 1) and the ratio of tensor/scalar
fluctuations r are O(1/N), the running index is O(1/N^2). M ~ 0.7 10^{16} GeV
is completely determined by the scalar adiabatic fluctuations amplitude. (II):
A Monte Carlo Markov Chains (MCMC) analysis of the CMB+LSS data (including
WMAP5) with our analytic theoretical results yields: a lower bound for r (new
inflation): r > 0.023 (95%CL), r > 0.046 (68%CL); the preferred inflation
potential is a double well, even function of the field yielding as most
probable values n_s ~ 0.964, r ~ 0.051. This value for r is within reach of
forthcoming CMB observations. Slow-roll inflation is generically preceded by a
short fast-roll stage which leads to a suppression of the CMB quadrupoles. MCMC
analysis of the WMAP+SDSS data shows that fast-roll fits the TT, TE and EE
modes well reproducing the quadrupole suppression and fixes the total number of
efolds of inflation to be N_{total} ~ 64. (III) Quantum loop corrections are
very small and controlled by powers of (H /M_{Pl})^2 ~ 10^{-9} which validates
the effective theory of inflation. We show how powerful is the GL theory of
inflation in predicting observables.

Comment: Review article, 134 pages, 41 figures. Int. J. Mod. Phys. A24, 3669-3864 (2009). A few last improvements

Comment: Review article, 134 pages, 41 figures. Int. J. Mod. Phys. A24, 3669-3864 (2009). A few last improvements

##### Keywords

Astrophysics - Cosmology and Nongalactic Astrophysics, General Relativity and Quantum Cosmology, High Energy Physics - Phenomenology, High Energy Physics - Theory