D-term Inflation Models Research Articles

Preheating and reheating constraints in supersymmetric braneworld inflation

We study the evolution of the Universe at early stages, we discuss also preheating in the framework of hybrid braneworld inflation by setting conditions on the coupling constants $\lambda $ and $g$\ for effective production of $\chi$-particles. Considering the phase between the time observable CMB scales crossed the horizon and the present time, we write reheating and preheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in terms of the scalar spectral index $n_{s}$, and prove that, unlike the reheating case, the preheating duration does not depend on the values of the equation of state $\omega ^{\ast }$. We apply the slow-roll approximation in the high energy limit to constrain the parameters of D-term hybrid potential. We show also that some inflationary parameters, in particular, the spectral index $n_{s}$ demand that the potential parameter $\alpha$ is bounded as $\alpha \geq 1$ to be consistent with $Planck$'s data, while the ratio $r$ is in agreement with observation for $ \alpha \leq 1 $ considering high inflationary e-folds. We also propose an investigation of the brane tension effect on the reheating temperature. Comparing our results to recent CMB measurements, we study preheating and reheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in the Hybrid D-term inflation model in the range $0.8\leq \alpha\leq 1.1$\, and conclude that $T_{re}$ and $N_{re}$ require $\alpha \leq 1$, while for $N_{pre}$ the condition $\alpha \leq 0.9$ must be satisfied, to be compatible with $Planck$'s results.

Modulus D-term inflation

We propose a new model of single-field D-term inflation in supergravity, where the inflation is driven by a single modulus field which transforms non-linearly under the U(1) gauge symmetry. One of the notable features of our modulus D-term inflation scenario is that the global U(1) remains unbroken in the vacuum and hence our model is not plagued by the cosmic string problem which can exclude most of the conventional D-term inflation models proposed so far due to the CMB observations.

A viable D-term hybrid inflation model

We propose a new model of the D-term hybrid inflation in the framework of supergravity. Although our model introduces, analogously to the conventional D-term inflation, the inflaton and a pair of scalar fields charged under a U(1) gauge symmetry, we study the logarithmic and exponential dependence on the inflaton field, respectively, for the Kähler and superpotential. This results in a characteristic one-loop scalar potential consisting of linear and exponential terms, which realizes the small-field inflation dominated by the Fayet-Iliopoulos term. With the reasonable values for the coupling coefficients and, in particular, with the U(1) gauge coupling constant comparable to that of the Standard Model, our D-term inflation model can solve the notorious problems in the conventional D-term inflation, namely, the CMB constraints on the spectral index and the generation of cosmic strings.

Affleck-Dine baryogenesis afterD-term inflation and solutions to the baryon-dark matter coincidence problem

We investigate the Affleck-Dine baryogenesis after D-term inflation with a positive Hubble-induced mass term for a B-L flat direction. It stays at a large field value during D-term inflation, and just after inflation ends it starts to oscillate around the origin of the potential due to the positive Hubble-induced mass term. The phase direction is kicked by higher-dimensional Kahler potentials to generate the B-L asymmetry. The scenario predicts nonzero baryonic isocurvature perturbations, which would be detected by future observations of CMB fluctuations. We also provide a D-term inflation model which naturally explain the coincidence of the energy density of baryon and dark matter.

The Starobinsky model from superconformal D-term inflation

We point out that in the large field regime, the recently proposed superconformal D-term inflation model coincides with the Starobinsky model. In this regime, the inflaton field dominates over the Planck mass in the gravitational kinetic term in the Jordan frame. Slow-roll inflation is realized in the large field regime for sufficiently large gauge couplings. The Starobinsky model generally emerges as an effective description of slow-roll inflation if a Jordan frame exists where, for large inflaton field values, the action is scale invariant and the ratio λˆ of the inflaton self-coupling and the nonminimal coupling to gravity is tiny. The interpretation of this effective coupling is different in different models. In superconformal D-term inflation it is determined by the scale of grand unification, λˆ∼(ΛGUT/MP)4.

TESTING FOR FEATURES IN THE PRIMORDIAL POWER SPECTRUM

Well-known causality arguments show that events occurring during or at the end of inflation, associated with reheating or preheating, could contribute a blue component to the spectrum of primordial curvature perturbations, with the dependence k3. We explore the possibility that they could be observably large in CMB, LSS, and Lyman-α data. We find that a k3 component with a cutoff at some maximum k can modestly improve the fits (Δχ2 = 2.0, 5.4) of the low multipoles (ℓ ~ 10–50) or the second peak (ℓ ~ 540) of the CMB angular spectrum when the three-year WMAP data are used. Moreover, the results from WMAP are consistent with the CBI, ACBAR, 2dFGRS, and SDSS data when they are included in the analysis. Including the SDSS galaxy clustering power spectrum, we find weak positive evidence for the k3 component at the level of Δχ2′ = 2.4, with the caveat that the nonlinear evolution of the power spectrum may not be properly treated in the presence of the k3 distortion. To investigate the high-k regime, we use the Lyman-α forest data (LUQAS, Croft et al., and SDSS Lyman-α); here we find evidence at the level Δχ2′ = 3.8. Considering that there are two additional free parameters in the model, the above results do not give a strong evidence for features; however, they show that surprisingly large bumps are not ruled out. We give constraints on the ratio between the k3 component and the nearly scale-invariant component, r3 < 1.5, over the range of wave numbers 2.3 × 10-3 Mpc -1 < k < 8.2 Mpc -1. We also discuss theoretical models which could lead to the k3 effect, including ordinary hybrid inflation and double D-term inflation models. We show that the well-motivated k3 component is also a good representative of the generic spikelike feature in the primordial perturbation power spectrum.

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 ${m}_{\ensuremath{\Phi}}>1.0H$.

PERTURBATIONS FROM D-TERM INFLATION

We investigated a simple D-term inflation with taking account of higher order corrections in the Kähler potential. These terms may solve the cosmic string problem in D-term inflation model. The mass per unit length of cosmic strings formed after inflation can be suppressed enough. In addition, the change of the potential slope leads simultaneously a more tilted scalar spectral index ns ≃ 0.96 – 0.97 than that in the model without these corrections.

Non-Gaussianity from tachyonic preheating in hybrid inflation

In a previous work we showed that large non-Gaussianities and nonscale-invariant distortions in the cosmic microwave background power spectrum can be generated in hybrid inflation models, due to the contributions of the tachyon (waterfall) field to the second order curvature perturbation. Here we clarify, correct, and extend those results. We show that large non-Gaussianity occurs only when the tachyon remains light throughout inflation, whereas $n=4$ contamination to the spectrum is the dominant effect when the tachyon is heavy. We find constraints on the parameters of warped-throat brane-antibrane inflation from non-Gaussianity. For F-term and D-term inflation models from supergravity, we obtain nontrivial constraints from the spectral distortion effect. We also establish that our analysis applies to complex tachyon fields.

Hiding cosmic strings in supergravityD-term inflation

The influence of higher-order terms in the K\"{a}hler potential of the supergravity D-term inflation model on the density perturbation is studied. We show that these terms can make the inflaton potential flatter, which lowers the energy scale of inflation under the COBE/WMAP normalization. As a result, the mass per unit length of cosmic strings, which are produced at the end of inflation, can be reduced to a harmless but detectable level without introducing a tiny Yukawa coupling. Our scenario can naturally be implemented in models with a low cut-off as in Type I or Type IIB orientifold models.

D3/D7 Brane Inflation and Semilocal Strings

Among the inflationary models based on string theory, the D3/D7 model has the advantage that the flatness of the inflaton potential can be protected even with moduli stabilization. However, the Abrikosov-Nielsen-Olesen BPS cosmic strings produced at the end of original D3/D7 inflation lead to an additional contribution to the CMB anisotropy. To make this contribution consistent with the WMAP results one needs an extremely small gauge coupling in the effective D-term inflation model. Such couplings may be difficult to justify in string theory. Here we develop a generalized version of the D3/D7 brane model, which leads to semilocal strings, instead of the topologically stable ANO cosmic strings. We show that the semilocal strings have unbroken supersymmetry when embedded into supergravity with FI terms. The energy of these strings is independent of their thickness. We confirm the existing arguments that strings of such type disappear soon after their formation and do not pose any cosmological problems, for any value of the gauge coupling. This should simplify the task of constructing fully realistic models of D3/D7 inflation.

Fayet–Iliopoulos terms in supergravity and cosmology

We clarify the structure of N = 1 supergravity in 1+3 dimensions with constant Fayet–Iliopoulos (FI) terms. The FI terms gξ induce non-vanishing R-charges for the fermions and the superpotential. Therefore the D-term inflation model in supergravity with constant FI terms has to be revisited. We present all corrections of order gξ/M2P to the classical supergravity action required by local supersymmetry and provide a gauge-anomaly-free version of the model. We also investigate the case of the so-called anomalous U(1) when a chiral superfield is shifted under U(1). In such a case, in the context of string theory, the FI terms originate from the derivative of the Kähler potential and they are inevitably field dependent. This raises an issue of stabilization of the relevant field in applications to cosmology. The recently suggested equivalence between the D-term strings and D-branes of type II theory shows that brane–anti-brane systems produce the FI terms in the effective 4d theory, with the Ramond–Ramond axion shifting under the U(1) symmetry. This connection gives the possibility to interpret many unknown properties of systems in the more familiar language of 4d supergravity D-terms, and vice versa. For instance, the shift of the axion field in both cases restricts the possible forms of the moduli-stabilizing superpotential. We provide some additional consistency checks of the correspondence of D-term strings to D-branes and show that instabilities of the two are closely related. Surviving cosmic D-strings of the type II theory may be potentially observed in the form of D-term strings of 4d supergravity. We study such string solutions of supergravity with constant FI terms with one half supersymmetry unbroken and explain some of the puzzling properties of the zero modes around cosmic strings, such as the difference between the numbers of fermionic and bosonic modes.

Dilaton and moduli fields in D-term inflation

We investigate the possibility of D-term inflation within the framework of type-I string-inspired models. Although the D-term inflation model has the excellent property that it is free of the so-called $\ensuremath{\eta}$ problem, two serious problems appear when we embed D-term inflation in string theory: the magnitude of the FI term and the rolling motion of the dilaton. In the present paper, we analyze the potential of D-term inflation in type-I-inspired models and study the behavior of dilaton and twisted moduli fields. Adopting the nonperturbative superpotential induced by gaugino condensation, the twisted moduli can be stabilized. If the dilaton is in a certain range, it evolves very slowly and does not run away to infinity. Thus D-term-dominated vacuum energy becomes available for driving inflation. By studying the density perturbation generated by the inflation model, we derive the constraints on model parameters and give some implications on D-term inflation in type-I-inspired models.

Growth of inflaton perturbations and the post-inflation era in supersymmetric hybrid inflation models

It has been shown that hybrid inflation may end with the formation of non-topological solitons of the inflaton field. As a first step towards a fully realistic picture of the post-inflation era and reheating in supersymmetric hybrid inflation models, we study the classical scalar field equations of a supersymmetric hybrid inflation model using a semianalytical ansatz for the spatial dependence of the fields. Using the minimal D-term inflation model as an example, the inflaton field is evolved using the full 1-loop effective potential from the slow-rolling era to the ${U(1)}_{\mathrm{FI}}$ symmetry-breaking phase transition. Spatial perturbations of the inflaton corresponding to quantum fluctuations are introduced for the case where there is spatially coherent ${U(1)}_{\mathrm{FI}}$ symmetry breaking. The maximal growth of the dominant perturbation is found to depend only on the ratio of superpotential coupling $\ensuremath{\lambda}$ to the gauge coupling g. The inflaton condensate fragments to non-topological solitons for $\ensuremath{\lambda}/g\ensuremath{\gtrsim}0.09.$ The possible consequences of nontopological soliton formation in fully realistic supersymmetric hybrid inflation models are discussed.

Cosmic string from D-term inflation and curvaton

We study effects of the cosmic string in the D-term inflation model on the cosmic microwave background (CMB) anisotropy. In the D-term inflation model, gauged cosmic string is usually formed, which may significantly affect the CMB anisotropy. We see that its study imposes important constraint. In order to realize the minimal model of D-term inflation, we see that the coupling constant λ in the superpotential generating the inflaton potential should be significantly small, λ≲O(10−4–10−5). We also discuss that a consistent scenario of the D-term inflation with λ∼1 can be constructed by adopting the curvaton mechanism where the cosmic density fluctuations are generated by a primordial fluctuation of a late-decaying scalar field other than the inflaton.

Inflaton condensate fragmentation in hybrid inflation models

Inflation ends with the formation of a Bose condensate of inflatons. We show that in hybrid inflation models this condensate is typically unstable with respect to spatial perturbations and can fragment to condensate lumps. The case of D-term inflation is considered as an example and it is shown that fragmentation occurs if \lambda > 0.2g, where \lambda is the superpotential coupling and g is the U(1)_{FI} gauge coupling. Condensate fragmentation can result in an effective enhancement of inflaton annihilations over decays as the main mode of reheating. In the case of D-term inflation models in which the Standard Model fields carry U(1)_{FI} charges, if condensate fragmentation occurs then reheating is dominated by inflaton annihilations, typically resulting in the overproduction of thermal gravitinos. Fragmentation may also have important consequences for SUSY flat direction dynamics and for preheating.

Adiabatic and isocurvature fluctuations of Affleck-Dine field in D-term inflation model

Adiabatic and isocurvature fluctuations of Affleck-Dine field in D-term inflation model

Adiabatic and isocurvature fluctuations of Affleck–Dine field in D-term inflation model

We reconsider fluctuations of Affleck–Dine (AD) field in a D-term inflation model. Contrary to the previous analysis, we find that the spectrum of the adiabatic fluctuations is almost scale invariant even if the AD field has a large initial value. Furthermore, we study the isocurvature fluctuations of the AD field and estimate the ratio of the isocurvature to adiabatic power spectrum. The dynamics of the inflaton and AD fields sets the upper bound for the value of the AD field, leading to a lower limit for isocurvature perturbation. It is shown that the recent cosmic microwave background data give a constraint on the D-term inflation and the AD field.

The dynamics of Affleck–Dine condensate collapse

In the MSSM, cosmological scalar field condensates formed along flat directions of the scalar potential (Affleck–Dine condensates) are typically unstable with respect to formation of Q-balls, a type of non-topological soliton. We consider the dynamical evolution of the Affleck–Dine condensate in the MSSM. We discuss the creation and linear growth, in F- and D-term inflation models, of the quantum seed perturbations which in the non-linear regime catalyse the collapse of the condensate to non-topological soliton lumps. We study numerically the evolution of the collapsing condensate lumps and show that the solitons initially formed are not in general Q-balls, but Q-axitons, a pseudo-breather which can have very different properties from Q-balls of the same charge. We calculate the energy and charge radiated from a spherically symmetric condensate lump as it evolves into a Q-axiton. We also discuss the implications for baryogenesis and dark matter.

Observable Isocurvature Fluctuations from the Affleck-Dine Condensate

In D-term inflation models, Affleck-Dine baryogenesis produces baryonic isocurvature fluctuations. In most cases the Affleck-Dine condensate is unstable with respect to collapse to B-balls, which can transform the baryon number perturbations into perturbations in the number of dark matter neutralinos. The requirement that the deviation of the adiabatic perturbations from scale invariance is not too large imposes a lower bound on the magnitude of the isocurvature fluctuations. In general this is larger than about ${10}^{\ensuremath{-}4}\phantom{\rule{0ex}{0ex}}times$ the adiabatic perturbation, and, for the particular case of late decaying B-balls, larger than about ${10}^{\ensuremath{-}2}\phantom{\rule{0ex}{0ex}}times$ the adiabatic perturbation, which should be observable by MAP and PLANCK.