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 \varphi ( 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 inflation à la Ginsburg-Landau in which the inflaton potential is a polynomial in the field \varphi and has the universal form V ( \varphi ) = N M ^ { 4 } w ( \varphi / [ \sqrt { N } M _ { Pl } ] ) , where w = { \cal O } ( 1 ) , M \ll M _ { Pl } is the scale of inflation and N \sim 60 is the number of efolds 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 n _ { s } -1 = { \cal O } ( 1 / N ) , r = { \cal O } ( 1 / N ) while the running index turns to be dn _ { s } / d \ln k = { \cal O } ( 1 / N ^ { 2 } ) and therefore can be neglected .
The energy scale of inflation M \sim 0.7 \times 10 ^ { 16 } GeV is completely determined by the amplitude of the scalar adiabatic fluctuations .
A complete analytic study plus the Monte Carlo Markov Chains ( MCMC ) analysis of the available CMB+LSS data ( including WMAP5 ) with fourth degree trinomial potentials showed : ( a ) the spontaneous breaking of the \varphi \to - \varphi 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 most probable values : n _ { s } \simeq 0.964 , r \simeq 0.051 .
This value for r is within reach of forthcoming CMB observations .
The present data in the effective theory of inflation clearly prefer new inflation .
Study of higher degree inflaton potentials show that terms of degree higher than four do not affect the fit in a significant way .
In addition , horizon exit happens for \varphi / [ \sqrt { N } M _ { Pl } ] \sim 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 conditions 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 tensor perturbations is purely attractive and leads to a suppression of the curvature and tensor CMB quadrupoles .
A MCMC analysis of the WMAP+SDSS data including fast-roll shows that the quadrupole mode exits the horizon about 0.2 efold before fast-roll ends and its amplitude gets suppressed .
In addition , fast-roll fixes the initial inflation redshift to be z _ { init } = 0.9 \times 10 ^ { 56 } and the total number of efolds of inflation to be N _ { tot } \simeq 64 .
Fast-roll fits the TT , the TE and the EE modes well reproducing the quadrupole supression .
A thorough study of the quantum loop corrections reveals that they are very small and controlled by powers of ( H / M _ { Pl } ) ^ { 2 } \sim { 10 } ^ { -9 } , a conclusion that validates the reliability of the effective theory of inflation .
The present review shows how powerful is the Ginsburg-Landau effective theory of inflation in predicting observables that are being or will soon be contrasted to observations .