Semishifted hybrid inflation withB−Lcosmic strings

Abstract

We discuss a new inflationary scenario that is realized within the extended supersymmetric Pati-Salam model which yields an acceptable $b$-quark mass for universal boundary conditions and $\ensuremath{\mu}g0$ by modestly violating Yukawa unification and leads to new shifted, new smooth, or standard-smooth hybrid inflation. Inflation takes place along a ``semishifted'' classically flat direction on which the $\mathrm{U}(1{)}_{\mathrm{B}\ensuremath{-}\mathrm{L}}$ gauge group remains unbroken. After the end of inflation, $\mathrm{U}(1{)}_{\mathrm{B}\ensuremath{-}\mathrm{L}}$ breaks spontaneously and a network of local cosmic strings, which contribute a small amount to the curvature perturbation, is produced. We show that, in minimal supergravity, this semishifted inflationary scenario is compatible with a recent fit to data which uses field-theory simulations of a local string network. Taking into account the requirement of gauge unification, we find that, for spectral index ${n}_{\mathrm{s}}=1$, the predicted fractional contribution of strings to the temperature power spectrum at multipole $\ensuremath{\ell}=10$ is ${f}_{10}\ensuremath{\simeq}0.039$. Also, for ${f}_{10}=0.10$, which is the best-fit value, we obtain ${n}_{\mathrm{s}}\ensuremath{\simeq}1.0254$. Spectral indices lower than about 0.98 are excluded and blue spectra are slightly favored. Magnetic monopoles are not formed at the end of semishifted hybrid inflation.