We present a two stage hybrid inflationary scenario in non-minimal supergravity which can predict values of the tensor-to-scalar ratio of the order of few times 0.01. For the parameters considered, the underlying supersymmetric particle physics model
possesses two inflationary paths, the trivial and the semi-shifted one. The trivial path is stabilized by supergravity corrections and supports a first stage of inflation with a limited number of e-foldings. The tensor-to-scalar ratio can become appreciable while the value of the scalar spectral index remains acceptable as a result of the competition between the relatively mild supergravity corrections and the strong radiative corrections to the inflationary potential. The additional number of e-foldings required for solving the puzzles of hot big bang cosmology are generated by a second stage of inflation taking place along the semi-shifted path. This is possible only because the semi-shifted path is almost perpendicular to the trivial one and, thus, not affected by the strong radiative corrections along the trivial path and also because the supergravity effects remain mild. The requirement that the running of the scalar spectral index remains acceptable limits the possible values of the tensor-to-scalar ratio not to exceed about 0.05. Our model predicts the formation of an unstable string-monopole network, which may lead to detectable gravity wave signatures in future space-based laser interferometer observations.
It is shown that, in supergravity models of inflation where the gauge kinetic function of a gauge field is modulated by the inflaton, we can obtain a new inflationary attractor solution, in which the roll-over of the inflaton suffers additional imped
ance due to the vector field backreaction. As a result, directions of the scalar potential which, due to strong Kaehler corrections, become too steep and curved to normally support slow-roll inflation can now naturally do so. This solves the infamous eta-problem of inflation in supergravity and also keeps the spectral index of the curvature perturbation mildly red despite eta of order unity. This mechanism is applied to a model of hybrid inflation in supergravity with a generic Kaehler potential. The spectral index of the curvature perturbation is found to be 0.97 - 0.98, in excellent agreement with data. The gauge field can act as vector curvaton generating statistical anisotropy in the curvature perturbation. However, this anisotropy could be possibly observable only if the gauge coupling constant is unnaturally small.
We consider the extension of the supersymmetric Pati-Salam model introduced in order to solve the b-quark mass problem in supersymmetric theories with Yukawa unification, universal boundary conditions and mu>0. This model naturally leads to the new s
hifted and new smooth hybrid inflation scenarios, which, however, yield, in minimal supergravity, too large values of the spectral index n_s. We show that this problem can also be resolved within the same model by a two-stage inflationary scenario based only on renormalizable superpotential interactions. The first stage is of the standard and the second of the new smooth hybrid type. The cosmological scales exit the horizon during the first stage of inflation and acceptable n_ss can be achieved by restricting the number of e-foldings of our present horizon during this inflationary stage. The additional e-foldings needed for solving the horizon and flatness problems are naturally provided by the second stage of inflation. Monopoles are formed at the end of the first stage of inflation and are, subsequently, diluted by the second stage of inflation so that their density in the present universe is utterly negligible.
We discuss a new inflationary scenario which is realized within the extended supersymmetric Pati-Salam model which yields an acceptable b-quark mass for universal boundary conditions and mu>0 by modestly violating Yukawa unification and leads to new
shifted, new smooth, or standard-smooth hybrid inflation. Inflation takes place along a semi-shifted classically flat direction on which the U(1)_{B-L} gauge group remains unbroken. After the end of inflation, U(1)_{B-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 semi-shifted 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_s=1, the predicted fractional contribution f_{10} of strings to the temperature power spectrum at multipole l=10 is about 0.039. Also, for f_{10}=0.10, which is the best-fit value, we obtain that n_s is about 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 semi-shifted hybrid inflation.
We consider the extended supersymmetric Pati-Salam model which, for mu>0 and universal boundary conditions, succeeds to yield experimentally acceptable b-quark masses by moderately violating Yukawa unification. It is known that this model can lead to
new shifted or new smooth hybrid inflation. We show that a successful two-stage inflationary scenario can be realized within this model based only on renormalizable superpotential interactions. The cosmological scales exit the horizon during the first stage of inflation, which is of the standard hybrid type and takes place along the trivial flat direction with the inflaton driven by radiative corrections. Spectral indices compatible with the recent data can be achieved in global supersymmetry or minimal supergravity by restricting the number of e-foldings of our present horizon during the first inflationary stage. The additional e-foldings needed for solving the horizon and flatness problems are naturally provided by a second stage of inflation, which occurs mainly along the built-in new smooth hybrid inflationary path appearing right after the destabilization of the trivial flat direction at its critical point. Monopoles are formed at the end of the first stage of inflation and are, subsequently, diluted by the second stage of inflation to become utterly negligible in the present universe for almost all (for all) the allowed values of the parameters in the case of global supersymmetry (minimal supergravity).
We consider the extension of the supersymmetric Pati-Salam model which solves the b-quark mass problem of supersymmetric grand unified models with exact Yukawa unification and universal boundary conditions and leads to the so-called new shifted hybri
d inflationary scenario. We show that this model can also lead to a new version of smooth hybrid inflation based only on renormalizable interactions provided that a particular parameter of its superpotential is somewhat small. The potential possesses valleys of minima with classical inclination, which can be used as inflationary paths. The model is consistent with the fitting of the three-year Wilkinson microwave anisotropy probe data by the standard power-law cosmological model with cold dark matter and a cosmological constant. In particular, the spectral index turns out to be adequately small so that it is compatible with the data. Moreover, the Pati-Salam gauge group is broken to the standard model gauge group during inflation and, thus, no monopoles are formed at the end of inflation. Supergravity corrections based on a non-minimal Kaehler potential with a convenient choice of a sign keep the spectral index comfortably within the allowed range without generating maxima and minima of the potential on the inflationary path. So, unnatural restrictions on the initial conditions for inflation can be avoided.
Inflationary models with a superheavy scale F-term hybrid inflation followed by an intermediate scale modular inflation are considered. The restrictions on the power spectrum P_R of curvature perturbation and the spectral index n_s from the recent da
ta within the power-law cosmological model with cold dark matter and a cosmological constant can be met provided that the number of e-foldings N_HI* suffered by the pivot scale k_*=0.002/Mpc during hybrid inflation is suitably restricted. The additional e-foldings needed for solving the horizon and flatness problems are generated by modular inflation with a string axion as inflaton. For central values of P_R and n_s, the grand unification scale comes out, in the case of standard hybrid inflation, close to its supersymmetric value M_GUT=2.86 x 10^16 GeV, the relevant coupling constant is relatively large (0.005-0.14), and N_HI* is between 10 and 21.7. In the shifted [smooth] hybrid inflation case, the grand unification scale can be identified with M_GUT for N_HI*=21 [N_HI*=18].
