Abstract
The cosmic microwave background power spectra are studied for different families of single field new and chaotic inflation models in the effective field theory approach to inflation. We implement a systematic expansion in $1/{N}_{e}$, where ${N}_{e}\ensuremath{\sim}50$ is the number of e-folds before the end of inflation. We study the dependence of the observables (${n}_{s}$, $r$ and $d{n}_{s}/d\mathrm{ln}k$) on the degree of the potential ($2n$) and confront them to the WMAP3 and large scale structure data: This shows in general that fourth degree potentials ($n=2$) provide the best fit to the data; the window of consistency with the WMAP3 and LSS data narrows for growing $n$. New inflation yields a good fit to the $r$ and ${n}_{s}$ data in a wide range of field and parameter space. Small field inflation yields $r<0.16$ while large field inflation yields $r>0.16$ (for ${N}_{e}=50$). All members of the new inflation family predict a small but negative running $\ensuremath{-}4(n+1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\ensuremath{\le}d{n}_{s}/d\mathrm{ln}k\ensuremath{\le}\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. (The values of $r$, ${n}_{s}$, $d{n}_{s}/d\mathrm{ln}k$ for arbitrary ${N}_{e}$ follow by a simple rescaling from the ${N}_{e}=50$ values.) A reconstruction program is carried out suggesting quite generally that for ${n}_{s}$ consistent with the WMAP3 and LSS data and $r<0.1$ the symmetry breaking scale for new inflation is $|{\ensuremath{\phi}}_{0}|\ensuremath{\sim}10{M}_{\mathrm{Pl}}$ while the field scale at Hubble crossing is $|{\ensuremath{\phi}}_{c}|\ensuremath{\sim}{M}_{\mathrm{Pl}}$. The family of chaotic models features $r\ensuremath{\ge}0.16$ (for ${N}_{e}=50$) and only a restricted subset of chaotic models are consistent with the combined WMAP3 bounds on $r$, ${n}_{s}$, $d{n}_{s}/d\mathrm{ln}k$ with a narrow window in field amplitude around $|{\ensuremath{\phi}}_{c}|\ensuremath{\sim}15{M}_{\mathrm{Pl}}$. We conclude that a measurement of $r<0.16$ (for ${N}_{e}=50$) distinctly rules out a large class of chaotic scenarios and favors small field new inflationary models. As a general consequence, new inflation emerges more favored than chaotic inflation.
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