New inflation versus chaotic inflation, higher degree potentials, and the reconstruction program in light of WMAP 3-year data

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.