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

Degenerate Neutrinos and Supersymmetric Inflation

A moderate extension of the minimal supersymmetric standard model which includes a U(1)_(B-L) gauge group (B and L being the baryon and lepton number) and a Peccei-Quinn symmetry, U(1)_PQ, is presented. The hybrid inflationary scenario is automatic and `natural' in this model. The mu problem of the minimal supersymmetric standard model is solved by coupling the electroweak higgses to fields which break U(1)_PQ. Baryon number conservation and, thus, proton stability are automatic consequences of a R-symmetry. Neutrinos are assumed to acquire degenerate masses of about 1.5 eV by coupling to SU(2)_L triplet superfields, thereby providing the hot dark matter of the universe. The inflaton decays into these triplets which, via their subsequent decay, produce a primordial lepton asymmetry later converted into the observed baryon asymmetry of the universe. The gravitino and baryogenesis constraints can be satisfied with `natural' values (of order 10^{-3}) of the relevant coupling constants.Comment: 13 pages, Revtex, minor correction

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

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

Testing Supersymmetric Grand Unified Models of Inflation

We reconsider a class of well motivated supersymmetric models in which inflation is associated with the breaking of a gauge symmetry G to H, with the symmetry breaking scale M~10^16 GeV. Starting with a renormalizable superpotential, we include both radiative and supergravity corrections to derive the inflationary potential. The scalar spectral index n_s can exceed unity in some cases, and it cannot be smaller than 0.98 if the number of e-foldings corresponding to the present horizon scale is around 60. Two distinct variations of this scenario are discussed in which non-renormalizable terms allowed by the symmetries are included in the superpotential, and one finds n_s>=0.97. The models discussed feature a tensor to scalar ratio r<~10^-4, while dn_s/dlnk<~10^-3. If G corresponds to SO(10) or one of its rank five subgroups, the observed baryon asymmetry is naturally explained via leptogenesis.Comment: 1+16 pages, 7 figures; minor revisions, references added, to appear in Phys. Lett.

GUT Scale Inflation, Non-Thermal Leptogenesis, and Atmospheric Neutrino Oscillations

Leptogenesis scenarios in supersymmetric hybrid inflation models are considered. Sufficient lepton asymmetry leading to successful baryogenesis can be obtained if the reheat temperature T_r>10^6 GeV and the superpotential coupling parameter kappa is in the range 10^-6<kappa<10^-2. For this range of kappa the scalar spectral index n_s=0.99+-0.01. Constraints from neutrino mixing further restrict the range of kappa that is allowed. We analyze in detail the case where the inflaton predominantly decays into the next-to-lightest right handed Majorana neutrino taking into account especially the constraints from atmospheric neutrino oscillations.Comment: 1+18 pages, 8 figures. v.2: Abridged and revised, comments and references added, now 1+16 pages, 7 figures, to appear in PL

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

MSSM from SUSY Trinification

We construct a $SU(3)^3$ supersymmetric gauge theory with a common gauge coupling g. Spontaneous breaking of this gauge group at a scale $M_X=1.3\times10^{16}$GeV gives naturally rise exactly to the Minimal Supersymmetric Standard Model $(MSSM)$ and consequently to the experimentally favored values of $sin^2\theta_w$ and $\alpha_s$.The gauge hierarchy problem is naturally solved by a missing-partner-type mechanism which works to all orders in the superpotential. The baryon asymmetry can be generated in spite of the (essential) stability of the proton. The solar neutrino puzzle is solved by the MSW mechanism. The LSP is a natural "cold" dark matter candidate and "hot" dark matter might consist of $\tau$-neutrinos. This model could be thought of as an effective $4d$ theory emerging from a more fundamental theory at a scale $M_c=M_P/\sqrt{8\pi}$ where $a_G\equiv{g^2\over{4\pi}}$ happens to be equal to unity.Comment: 10 pages, LaTeX,UT-STPD-2-9

Standard-smooth 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).Comment: 11 pages including 2 figures, uses Revtex, version to appear in Phys. Rev.