Supersymmetry and Inflation

A variant of hybrid inflation which is applicable in a wide class of supersymmetric grand unified models and reproduces the observed temperature perturbations of cosmic background radiation with natural values of the parameters is presented. The theory is consistent with the unification of the minimal supersymmetric standard model gauge couplings as measured at LEP. The termination of inflation is smooth and does not produce any topological defects. Numerical investigation of the cosmological evolution of the system shows that for almost all initial values of the fields we do get an adequate amount of inflation. Finally, the "reheating" process following inflation and the production of the baryon asymmetry of the universe via a primordial lepton asymmetry are briefly discussed and some important implications for right handed neutrino Majorana masses are investigated.Comment: 5 pages LaTeX 1 eps figure. Talk presented at SUSY 96,Maryland,May 1996. Published in Nuclear Physics B(Proc.Suppl.) 52A(1997)242-24

New shifted hybrid inflation

A new shifted hybrid inflationary scenario is introduced which, in contrast to the older one, relies only on renormalizable superpotential terms. This scenario is automatically realized in a concrete extension of the "minimal" supersymmetric Pati-Salam model which naturally leads to a moderate violation of Yukawa unification so that, for mu>0, the predicted b-quark mass is acceptable even with universal boundary conditions. It is shown that this extended model possesses a classically flat "shifted" trajectory which acquires a slope via one-loop radiative corrections and can be used as inflationary path. The constraints from the cosmic background explorer can be met with natural values of the relevant parameters. Also, there is no disastrous production of magnetic monopoles after inflation since the Pati-Salam gauge group is already broken on the "shifted" path. The relevant part of inflation takes place at values of the inflaton field which are not much smaller than the "reduced" Planck scale and, thus, supergravity corrections could easily invalidate inflation. It is, however, shown that inflation can be kept intact provided that an extra gauge singlet with a superheavy vacuum expectation value, which originates from D-terms, is introduced and a specific form of the Kaehler potential is used. Moreover, it is found that, although the supergravity corrections are sizable, the constraints from the cosmic background explorer can again be met by readjusting the values of the parameters which were obtained with global supersymmetry.Comment: 18 pages including 1 figure, uses JHEP3.cls, minor corrections, version to appear in JHE

MSSM and Large tanβtan\beta from SUSY Trinification

We construct a supersymmetric model based on the semi-simple gauge group $SU(3)_c \times SU(3)_L \times SU(3)_R$ with the relation $tan\beta \simeq m_t/m_b$ automatically arising from its structure. The model below a scale $\sim 10^{16}$ GeV gives naturally rise just to the minimal supersymmetric standard model and therefore to the presently favored values for $sin^2 \theta_w$ and $\alpha_s$ without fields in representations higher than the fundamental.Comment: 9 pages, LaTeX, UT-STPD-3-9

New smooth hybrid inflation

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 hybrid 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.Comment: 15 pages including 5 figures, uses Revtex, version to appear in PR

Neutrino Masses and Mixing from Supersymmetric Inflation

A supersymmetric model based on a left-right symmetric gauge group is proposed where hybrid inflation, baryogenesis and neutrino oscillations are linked.This scheme, supplemented by a familiar ansatz for the neutrino Dirac masses and mixing of the two heaviest families and with the MSW resolution of the solar neutrino puzzle, implies that $m_{\nu_{\tau}}$ lies between 1 and 9 eV. The mixing angle $\theta_{\mu \tau}$ is predicted to lie in a narrow range which will be partially tested by the Chorus/Nomad experiment.Comment: 6 pages, 2 postscript figures, uses spocl.sty To be published in the proceedings of COSMO-97,International Workshop on Particle Physics and the Early Universe,15-19 September 1997, Ambleside,Lake District,Englan

F-Term Hybrid Inflation Followed by a Peccei-Quinn Phase Transition

We consider a cosmological set-up, based on renormalizable superpotential terms, in which a superheavy scale F-term hybrid inflation is followed by a Peccei-Quinn phase transition, resolving the strong CP and mu problems of the minimal supersymmetric standard model. We show that the field which triggers the Peccei-Quinn phase transition can remain after inflation well above the Peccei-Quinn scale thanks to (i) its participation in the supergravity and logarithmic corrections during the inflationary stage and (ii) the high reheat temperature after the same period. As a consequence, its presence influences drastically the inflationary dynamics and the universe suffers a second period of reheating after the Peccei-Quinn phase transition. Confronting our inflationary predictions with the current observational data, we find that, for about the central value of the spectral index, the grand unification scale can be identified with its supersymmetric value for the relevant coupling constant \kappa=0.002 and, more or less, natural values, +/-(0.01-0.1), for the remaining parameters. On the other hand, the final reheat temeperature after the Peccei-Quinn phase transition turns out to be low enough so as the gravitino problem is avoided.Comment: 15 pages including 8 figures, version published in Phys. Rev.