Slow-roll inflation can be studied as an effective field theory .
The form of the inflaton potential consistent with the data is V ( \phi ) = N M ^ { 4 } w \left ( \frac { \phi } { \sqrt { N } M _ { Pl } } \right ) where \phi is the inflaton field , M is the inflation energy scale , and N \sim 50 is the number of efolds since the cosmologically relevant modes exited the Hubble radius until the end of inflation .
The dimensionless function w ( \chi ) and field \chi are generically \mathcal { O } ( 1 ) .
The WMAP value for the amplitude of scalar adiabatic fluctuations yields M \sim 0.77 \times 10 ^ { 16 } GeV .
This form of the potential encodes the slow-roll expansion as an expansion in 1 / N .
A Ginzburg-Landau ( polynomial ) realization of w ( \chi ) reveals that the Hubble parameter , inflaton mass and non-linear couplings are of the see-saw form in terms of the small ratio M / M _ { Pl } .
The quartic coupling is \lambda \sim \frac { 1 } { N } \left ( \frac { M } { M _ { Pl } } \right ) ^ { 4 } .
The smallness of the non-linear couplings is not a result of fine tuning but a natural consequence of the validity of the effective field theory and slow roll approximation .
Our observations suggest that slow-roll inflation may well be described by an almost critical theory , near an infrared stable gaussian fixed point .
Quantum corrections to slow roll inflation are computed and turn to be an expansion in powers \left ( H / M _ { Pl } \right ) ^ { 2 } .
The corrections to the inflaton effective potential and its equation of motion are computed , as well as the quantum corrections to the observable power spectra .
The near scale invariance of the fluctuations introduces a strong infrared behavior naturally regularized by the slow roll parameter \Delta \equiv \eta _ { V } - \epsilon _ { V } = \frac { 1 } { 2 } ( n _ { s } -1 ) + r / 8 .
We find the effective inflaton potential during slow roll inflation including the contributions from scalar curvature and tensor perturbations as well as from light scalars and Dirac fermions coupled to the inflaton .
The scalar and tensor superhorizon contributions feature infrared enhancements regulated by slow roll parameters .
Fermions and gravitons do not exhibit infrared enhancement .
The subhorizon part is completely specified by the trace anomaly of the fields with different spins and is solely determined by the space-time geometry .
This inflationary effective potential is strikingly different from the usual Minkowski space-time result .
Quantum corrections to the power spectra are expressed in terms of the CMB observables : n _ { s } , r and dn _ { s } / d \ln k .
Trace anomalies ( especially the graviton part ) dominate these quantum corrections in a definite direction : they enhance the scalar curvature fluctuations and reduce the tensor fluctuations .