We study the single field slow-roll inflation models that better agree with the available CMB and LSS data including the three years WMAP data : new inflation and hybrid inflation .
We study these models as effective field theories in the Ginsburg-Landau context : a trinomial potential turns out to be a simple and well motivated model .
The spectral index n _ { s } of the adiabatic fluctuations , the ratio r of tensor to scalar fluctuations and the running index dn _ { s } / d \ln k are studied in detail .
We derive explicit formulae for n _ { s } , r and dn _ { s } / d \ln k and provide relevant plots .
In new inflation , and for the three years WMAP and 2dF central value n _ { s } = 0.95 , we predict 0.03 < r < 0.04 and -0.00070 < dn _ { s } / d \ln k < -0.00055 .
In hybrid inflation , and for n _ { s } = 0.95 , we predict r \simeq 0.2 and dn _ { s } / d \ln k \simeq - 0.001 .
Interestingly enough , we find that in new inflation n _ { s } is bounded from above by n _ { s~ { } max } = 0.961528 \ldots and that r is a two valued function of n _ { s } in the interval 0.96 < n _ { s } < n _ { s~ { } max } .
In the first branch we find r < r _ { max } = 0.114769 \ldots .
In hybrid inflation we find a critical value \mu _ { 0 ~ { } crit } ^ { 2 } for the mass parameter \mu _ { 0 } ^ { 2 } of the field \sigma coupled to the inflaton .
For \mu _ { 0 } ^ { 2 } < \Lambda _ { 0 } M _ { Pl } ^ { 2 } / 192 , where \Lambda _ { 0 } is the cosmological constant , hybrid inflation is ruled out by the WMAP three years data since it yields a blue tilted n _ { s } > 1 behaviour .
Hybrid inflation for \mu _ { 0 } ^ { 2 } > \Lambda _ { 0 } M _ { Pl } ^ { 2 } / 192 fullfills all the present CMB+LSS data for a large enough initial inflaton amplitude .
Even if chaotic inflation predicts n _ { s } values compatible with the data , chaotic inflation is disfavoured since it predicts a too high value r \simeq 0.27 for the ratio of tensor to scalar fluctuations .
The model which best agrees with the current data and which best prepares the way to the expected data r \lesssim 0.1 , is the trinomial potential with negative mass term : new inflation .