Supergravity Corrections Research Articles

Minimal supersymmetric hybrid inflation, flipped [formula omitted] and proton decay

Minimal supersymmetric hybrid inflation utilizes a canonical Kähler potential and a renormalizable superpotential which is uniquely determined by imposing a U(1) R-symmetry. In computing the scalar spectral index ns we take into account modifications of the tree level potential caused by radiative and supergravity corrections, as well as contributions from the soft supersymmetry breaking terms with a negative soft mass-squared term allowed for the inflaton. All of these contributions play a role in realizing ns values in the range 0.96–0.97 preferred by WMAP. The U(1) R-symmetry plays an important role in flipped SU(5) by eliminating the troublesome dimension five proton decay. The proton decays into e+π0 via dimension six operators arising from the exchange of superheavy gauge bosons with a lifetime of order 1034–1036 years.

Supersymmetric hybrid inflation redux

We discuss the important role played during inflation by one of the soft supersymmetry breaking terms in the inflationary potential of supersymmetric hybrid inflation models. With minimal Kähler potential, the inclusion of this term allows the prediction for the scalar spectral index to agree with the value ns=0.963−0.015+0.014 found by WMAP5. In the absence of this soft term, and by taking into account only radiative and supergravity corrections, it is well known that ns⩾0.985. This same soft term has previously been shown to play a key role in resolving the MSSM μ problem. The tensor to scalar ratio r is quite small in these models, taking on values r⩽10−5 in the WMAP5 2σ range of ns.

Supergravity and two-field inflation effects in right-handed sneutrino-modified D-term inflation

We extend previous work on the minimal D-term inflation model modified by right-handed (RH) sneutrino fields to include additional inflaton-sector supergravity corrections and two-field inflation effects. We show that supergravity corrections simultaneously allow ${n}_{s}$ to be within 3-year Wilkinson Microwave Anisotropy Probe limits and the cosmic string contribution to the cosmic microwave background (CMB) power spectrum to be less than 5%. For gauge coupling $g\ensuremath{\le}1$, the CMB contribution from cosmic strings is predicted to be at least 1% while the spectral index is predicted to be less than 0.968 for a CMB string contribution less than 5%. Treating the inflaton-RH sneutrino system as a two-field inflation model, we show that the time-dependence of the RH sneutrino field strongly modifies the single-field results for values of RH sneutrino mass ${m}_{\ensuremath{\Phi}}>0.1H$. The running spectral index is $\ensuremath{\alpha}\ensuremath{\approx}\ensuremath{-}0.0002$ when ${m}_{\ensuremath{\Phi}}<0.1H$ but increases to positive values as ${m}_{\ensuremath{\Phi}}/H$ increases, with $\ensuremath{\alpha}>0.008$ for ${m}_{\ensuremath{\Phi}}>1.0H$.

Kähler potentials for the minimally supersymmetric standard model inflation and thespectral index

Recently it has been argued that some of the fine-tuning problems of the minimallysupersymmetric standard model (MSSM) inflation associated with the existence of a saddlepoint along a flat direction may be solved naturally in a class of supergravity models. Herewe extend the analysis and show that the constraints on the Kähler potentials in thesemodels are considerably relaxed when the location of the saddle point is treated as a freevariable. We also examine the effect of supergravity corrections on inflationarypredictions and find that they can slightly alter the value of the spectral index.As an example, for flat direction field values we find n∼0.92...0.94 while the prediction of the MSSM inflation without any corrections isn∼0.92.

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 nonminimal 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 onmore » the initial conditions for inflation can be avoided.« less

Radiative lifting of flat directions of the MSSM in de Sitter background

The one-loop effective potential for a charged scalar field in de Sitter background is studied. We derive an approximate form for the gauge boson propagator with a general covariant gauge-fixing parameter ξ. This expression is used to derive an effective potential, which agrees with earlier results obtained in Landau gauge, and the independence of ξ explicitly indicates the gauge-invariance of the calculation. Adding the scalar- and fermion-loop contributions, that arise in a supersymmetric Higgs model, we find that the effective potential is vanishing to first order in the Hubble rate H 2 in the absence of additional chiral matter. The contribution due to a chiral multiplet running in the loop is however non-vanishing in the presence of Yukawa couplings to the Higgs field. When applied to a flat direction of the MSSM with VEV w, a logarithmically running correction of order h 2 H 2 w 2 arises, where h is a Yukawa coupling. This is of particular importance for D-term inflation or models endowed with a Heisenberg symmetry, where Hubble scale mass terms for flat directions from supergravity corrections are absent.

Tracking quintessence by cosmic shear

Context. Dark energy can be investigated in two complementary ways, by considering either general parameterizations or physically well-defined models. This article follows the second route a nd explores the observational constraints on quintessence models where the acceleration of our universe is driven by a slow-rolling sca lar field. The analysis focuses on cosmic shear, combined wit h type Ia supernovae data and cosmic microwave background observations. Aims. This article examines how weak lensing surveys can constrain dark energy, how they complement supernovae data to lift some degeneracies and addresses some issues regarding the limitations due to the lack of knowledge concerning the non-linear regime. Methods. Using a Boltzmann code that includes quintessence models and the computation of weak lensing observables, we determine the shear power spectrum and several two-point statistics. The non-linear regime is described by two different mappings. The likelihood analysis is based on a grid method. The data include the “gold set” of supernovae Ia, the WMAP-1 year data and the VIRMOS-Descart and CFHTLS-deep and -wide data for weak lensing. This is the first analysis of h igh-energy motivated dark energy models that uses weak lensing data. We explore larger angular scales, using a synthetic realization of the complete CFHTLS-wide survey as well as next space-based missions surveys. Results. Two classes of cosmological parameters are discussed: i) those accounting for quintessence affect mainly geometrical factors; ii) cosmological parameters specifying the primordial universe strongly depend on the description of the non-linear regime. This dependence is addressed using wide surveys, by discarding the smaller angular scales to reduce the dependence on the non-linear regime. Special care is payed to the comparison of these physical models with parameterizations of the equation of state. For a flat universe and a quintessence inverse power law potential with slopeα, we obtainα < 1 and Q0 = 0.75 +0.03 −0.04 at 95% confidence level, whereas α = 2 +18 −2 , Q0 = 0.74 +0.03 −0.05 when including supergravity corrections.

Supergravity modification ofD-term hybrid inflation: Solving the cosmic string and spectral index problems via a right-handed sneutrino

Supergravity corrections due to the energy density of a right-handed sneutrino can generate a negative mass squared for the inflaton, flattening the inflaton potential and reducing the spectral index and inflaton energy density. For the case of D-term hybrid inflation, we show that the spectral index can be lowered from the conventional value n = 0.98 to a value within the range allowed by the latest WMAP analysis, n = 0.951^{+0.015}_{-0.019}. The modified energy density is consistent with non-observation of cosmic strings in the CMB if n < 0.946. The WMAP lower bound on the spectral index implies that the D-term cosmic string contribution may be very close present CMB limits, contributing at least 5% to the CMB multipoles.

Constraints on supersymmetric hybrid inflation models

We point out that the inclusion of a string component contributing around 5% to the CMBpower spectrum amplitude on large scales can increase the preferred value of the spectral indexns of density fluctuations measured by CMB experiments. While this finding appliesto any cosmological scenario involving strings, we consider in particular modelsof supersymmetric hybrid inflation, which predict , in tension with the CMB data when strings are not included.Using MCMC analysis we constrain the parameter space allowed forF- andD-term inflation.For the F-term model, using minimal supergravity corrections, we find thatlogκ = −2.34 ± 0.38 and M = (0.518 ± 0.059) × 1016 GeV. The inclusion of non-minimal supergravity corrections canmodify these values somewhat. In the corresponding analysis forD-term inflation,we find logκ = −4.24 ± 0.19 and mFI = (0.245 ± 0.031) × 1016 GeV. Under the assumption that these models are correct, these results represent precisionmeasurements of important parameters of a grand unified theory. We consider the possibleuncertainties in our measurements and additional constraints on the scenario from the stochasticbackground of gravitational waves produced by the strings. The best fitting model predicts aB-modepolarization signal ≈0.3 μK rms peaking at . This is of comparable amplitude to the expected signal due to gravitational lensing of the adiabaticE-mode signal on these scales.

Four-dimensional SYM probes in wrapped M5-brane backgrounds

We study the worldvolume supersymmetric gauge theory of M-branes probing backgrounds corresponding to wrapped M5-branes. In the case of M5-branes wrapping a 2-cycle in two-dimensional complex space, we use M2-brane probes to compute the BPS spectra of the corresponding N=2 gauge theory as well as M5-brane probes to calculate field theory parameters such as the gauge coupling, theta angle and complex scalar moduli space metric. This background describes a large class of Hanany-Witten type models when dimensionally reduced to Type IIA 10d string theory. We calculate the instanton action using a D0-brane probe in this limit. For the case of M5-branes wrapping a 2-cycle in three-dimensional complex space, we firstly show an alternative method to derive this solution involving the projection conditions and certain spinor bilinear differential equations. We also consider M5-brane probes of this background, and analyse the corresponding N=1 MQCD gauge theory parameters. In general there were no supergravity corrections to field theory parameters when compared to previous flat-space field theory analysis.

Full one-loop electroweak corrections to the charged Higgs decays into a chargino and neutralino in the MSSM

We calculate the full one-loop electroweak (FEW) corrections to $H^-\to\widetilde{\chi}^-_1\widetilde{\chi}^0_i$ in the minimal supersymmetric standard model (MSSM), and compare with the leading order (LO) corrections including the loops of the (s)quarks only in the third generation and the complete leading order (CLO) corrections including the loops of the (s)quarks in all the three generations. We find that the magnitudes of the FEW corrections can be larger than 10% for $\tan\beta>30$. Moreover, comparing with the FEW corrections, both of the LO and the CLO corrections are negligible small for the mode 1($H^-\to\widetilde{\chi}^-_1\widetilde{\chi}^0_1$) when $\tan\beta<5$, and for the mode 2($H^-\to\widetilde{\chi}^-_1\widetilde{\chi}^0_2$) when $\tan\beta>45$, respectively, since there are not enhancements from the Yukawa couplings. We also calculate the FEW corrections in the minimal supergravity (mSUGRA) scenario, where the FEW corrections can be larger than the LO and the CLO corrections by more than 60% and 50%, respectively.

Inflation with realistic supersymmetricSO(10)

We implement inflation within a realistic supersymmetric SO(10) model in which the doublet-triplet splitting is realized through the Dimopoulos-Wilczek mechanism, the MSSM $\mu$ problem is resolved, and higgsino mediated dimension five nucleon decay is heavily suppressed. The cosmologically unwanted topological defects are inflated away, and from $\delta T/ T$, the $B-L$ breaking scale is estimated to be of order $10^{16}-10^{17}$ GeV. Including supergravity corrections, the scalar spectral index $n_s = 0.99\pm 0.01$, with $|dn_s/ d{\rm ln}k| \lapproxeq 10^{-3}$.

Hybrid inflation, dark energy and dark matter

It has been suggested that the dark energy density ρv∼10−12 eV4 in the universe is associated with a metastable (false) vacuum, while the true vacuum has a vanishing cosmological constant. By including supergravity corrections we show how this is naturally realized in realistic supersymmetric hybrid inflation models. With a fundamental supersymmetry breaking scale ∼TeV, the LSP is not a suitable candidate for cold dark matter. We consider axion physics to overcome this and simultaneously provide a resolution of the MSSM μ problem.

Hybrid inflation without flat directions and without primordial black holes

We investigate the possibility that the Universe may inflate due to moduli fields,corresponding to flat directions of supersymmetry, lifted by supergravity corrections. Usinga hybrid-type potential we obtain a two-stage inflationary model. Depending on thecurvature of the potential, the first stage corresponds to a period of fast-roll inflation or aperiod of ‘locked’ inflation, induced by an oscillating inflaton. This is followed by a secondstage of fast-roll inflation. We demonstrate that these two consecutive inflationary phasesresult in enough total e-foldings to encompass the cosmological scales. Using natural valuesfor the parameters (masses of order TeV and vacuum energy of the intermediate scalecorresponding to gravity mediated supersymmetry breaking) we conclude that theη-problem of inflation is easily overcome. The greatest obstacle to our scenariois the possibility of copious production of cosmologically disastrous primordialblack holes due to the phase transition switching from the first into the secondstage of inflation. We study this problem in detail and show analytically thatthere is ample parameter space where these black holes do not form at all. Togenerate structure in the Universe we assume the presence of a curvaton field.Finally we also discuss the moduli problem and how it affects our considerations.

Hybrid dark sector: locked quintessence and dark matter

We present a unified model of dark matter and dark energy. The dark matter field is amodulus corresponding to a flat direction of supersymmetry, which couples, in a hybridtype potential, with the dark energy field. The latter is a light scalar, whose direction isstabilized by non-renormalizable terms. This quintessence field is kept ‘locked’ on top of afalse vacuum due to the coupling with the oscillating dark matter field. It is shown that themodel can satisfy the observations when we consider low-scale gauge-mediatedsupersymmetry breaking. The necessary initial conditions are naturally attained by theaction of supergravity corrections on the potential, in the period following the end ofprimordial inflation.

D-term inflation without cosmic strings.

We present a superstring-inspired version of D-term inflation that does not lead to cosmic string formation and appears to satisfy the current cosmic microwave background constraints. It differs from minimal D-term inflation by a second pair of charged superfields that makes the strings nontopological (semilocal). The strings are also Bogomol'nyi-Prasad-Sommerfield strings, so the scenario is expected to survive supergravity corrections. The second pair of charged superfields arises naturally in several brane and conifold scenarios, but its effect on cosmic string formation had not been noticed so far.

Curvaton dynamics

In contrast to the inflaton's case, the curvature perturbations due to the curvaton field depend strongly on the evolution of the curvaton before its decay. We study in detail the dynamics of the curvaton evolution during and after inflation. We consider that the flatness of the curvaton potential may be affected by supergravity corrections, which introduce an effective mass proportional to the Hubble parameter. We also consider that the curvaton potential may be dominated by a quartic or by a non-renormalizable term. We find analytic solutions for the curvaton's evolution for all these possibilities. In particular, we show that, in all the above cases, the curvaton's density ratio with respect to the background density of the Universe decreases. Therefore, it is necessary that the curvaton decays only after its potential becomes dominated by the quadratic term, which results in (Hubble damped) sinusoidal oscillations. In the case when a non-renormalizable term dominates the potential, we find a possible non-oscillatory attractor solution that threatens to erase the curvature perturbation spectrum. Finally, we study the effects of thermal corrections to the curvaton's potential and show that, if they ever dominate the effective mass, they lead to premature thermalization of the curvaton condensate. To avoid this danger, a stringent bound has to be imposed on the coupling of the curvaton to the thermal bath.

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∼1016 GeV. Starting with a renormalizable superpotential, we include both radiative and supergravity corrections to derive the inflationary potential. The scalar spectral index ns 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 ns⩾0.97. The models discussed feature a tensor to scalar ratio r≲10−4, while dns/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.

Racetrack models in theories from extra dimensions

We have investigated moduli stabilization leading to hierarchical supersymmetry breakdown in racetrack models with two moduli fields simultaneously present in the effective racetrack superpotential. We have shown that stabilization of moduli occurs when a shift symmetry of the moduli space becomes gauged. This gauging results in a D-term contribution to the scalar potential that depends on moduli scalars. To break supersymmetry at a minimum created this way in the case where only a single combination of moduli is present in the superpotential one needs supergravity corrections. If the superpotential depends on two independent combinations of moduli, supersymmetry is broken by non-vanishing F-terms without supergravity terms. Some of the minima that we see correspond to a non-vanishing expectation value of the blowing-up modulus in the case of type IIB orientifold models. We point out that the mass of the gauge boson associated with gauged shift symmetry becomes naturally light in warped compactifications.

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.