We show that double inflation is naturally realized in Kähler moduli inflation, which is caused by moduli associated with string compactification. We find that there is a small coupling between the two inflatons which leads to amplification of perturbations through parametric resonance in the intermediate stage of double inflation. This results in the appearance of a peak in the power spectrum of the primordial curvature perturbation. We numerically calculate the power spectrum and show that the power spectrum can have a peak on observationally interesing scales. We also compute the TT-spectrum of CMB based on the power spectrum with a peak and see that it better fits WMAP 7-years data.
We study a model of accidental inflation in type IIB string theory where inflation occurs near the inflection point of a small Kähler modulus. A racetrack structure helps to alleviate the known concern that string-loop corrections may spoil Kähler Moduli Inflation unless having a significant suppression via the string coupling or a special brane setup. Also, the hierarchy of gauge group ranks required for the separation between moduli stabilization and inflationary dynamics is relaxed. The relaxation becomes more significant when we use the recently proposed D-term generated racetrack model.
We discuss the cosmological gravitino problem in inflation models in which the inflaton potential is constructed from Kähler potential rather than superpotential: a representative model is $\overline{\text{D}3}$-induced geometric inflation. A critical ingredient in this type of models is the coupling of the inflaton and Polonyi (supersymmetry-breaking) field in the Kähler potential, which is needed to build the inflaton potential. We point out the same coupling let the inflaton dominantly decay into a pair of inflatino and gravitino causing the gravitino problem. We propose some possible solut…
In this paper we present an initial exploration of the Calabi-Yau landscape in the context of Kahler moduli inflation. We review how the slow-roll requirement on the scalar potential translates to a geometric constraint on the Kahler geometry of the vacuum. This constraint leads to a hard bound on the moduli space geometry and we consider the effects of this constraint on the string landscape that arises in type IIB string compactifications on an O3/O7 orientifold. Most notably we find that the inflationary constraint is independent of the moduli space dimension and only 6.57% of geometries in…
We discuss a new class of tribrid inflation models in supergravity, where the shape of the inflaton potential is dominated by effects from the Kähler potential. Tribrid inflation is a variant of hybrid inflation which is particularly suited for connecting inflation with particle physics, since the inflaton can be a D-flat combination of charged fields from the matter sector. In models of tribrid inflation studied so far, the inflaton potential was dominated by either loop corrections or by mixing effects with the waterfall field (as in "pseudosmooth" tribrid inflation). Here we investigate the…
We study the cosmological inflation from the viewpoint of the moduli stabilization. We study the scenario that the superpotential has a large value during the inflation era enough to stabilize moduli, but it is small in the true vacuum. This scenario is discussed by using a simple model, one type of hybrid models.
We propose a simple but effective mechanism to realize an inflationary early universe consistent with the observed WMAP, Planck and/or BICEP2 data, which would be incorporated in various supersymmetric models of elementary particles constructed in the (effective) five-dimensional spacetime. In our scenario, the inflaton field is identified with one of the moduli appearing when the fifth direction is compactified, and a successful cosmological inflation without the so-called eta problem can be achieved by a very simple moduli stabilization potential. We also discuss the related particle cosmolo…
We assess which Kahler potentials in supergravity lead to viable single-field inflationary models that are consistent with Planck. We highlight the role of symmetries, such as shift, Heisenberg and supersymmetry, in these constructions. Also the connections to string theory are pointed out. Finally, we discuss a supergravity model for arbitrary inflationary potentials that is suitable for open string inflation and generalize it to the case of closed string inflation. Our model includes the recently discussed supergravity reformulation of the Starobinsky model of inflation as well as an interes…
We review the effects of heavy scalar fields during inflation in the framework of $\mathcal N = 1$ supergravity. Such heavy scalars can be geometric moduli from string compactifications or stabilizer fields from a different sector of the theory. Even when these fields are heavier than the Hubble scale during inflation, they generically cause backreactions which alter the dynamics of the system. Severe problems may arise when the heavy fields break supersymmetry, which is quite generic for Kähler moduli. We illustrate these effects in two examples, chaotic inflation and Starobinsky-like inflati…
The predictions for all the cosmological observables of any inflationary model depend on the number of e-foldings which is sensitive to the post-inflationary history of the universe. In string models the generic presence of light moduli leads to a late-time period of matter domination which lowers the required number of e-foldings and, in turn, modifies the exact predictions of any inflationary model. In this paper we compute exactly the shift of the number of e-foldings in Kaehler moduli inflation which is determined by the magnitude of the moduli initial displacement caused by vacuum misalig…
We study closed-string moduli stabilization in Higgs-otic inflation in Type IIB orientifold backgrounds with fluxes. In this setup large-field inflation is driven by the vacuum energy of mobile D7-branes. Imaginary selfdual (ISD) three-form fluxes in the background source a $μ$-term and the necessary monodromy for large field excursions while imaginary anti-selfdual (IASD) three-form fluxes are sourced by non-perturbative contributions to the superpotential necessary for moduli stabilization. We analyze Kähler moduli stabilization and backreaction on the inflaton potential in detail. Confirmin…
We study the supergravity hybrid inflation model of Ref.[1] in the presence of a modulus field. The eta-problem is solved by a shift symmetry for the inflaton, which protects the inflaton mass even in the presence of the modulus field. Inflation is (nearly) unaffected by moduli stabilization, provided the scale of supersymmetry breaking in the post-inflation vacuum is small. Therefore the model has the nice phenomenology that it combines low scale supersymmetry breaking with high scale (grand unification scale) inflation.
We analyze the interplay between Kähler moduli stabilization and chaotic inflation in supergravity. While heavy moduli decouple from inflation in the supersymmetric limit, supersymmetry breaking generically introduces non-decoupling effects. These lead to inflation driven by a soft mass term, $m_φ^2 \sim m m_{3/2}$, where $m$ is a supersymmetric mass parameter. This scenario needs no stabilizer field, but the stability of moduli during inflation imposes a large supersymmetry breaking scale, $m_{3/2} \gg H$, and a careful choice of initial conditions. This is illustrated in three prominent exam…
We study moduli stabilization in combination with inflation in heterotic orbifold compactifications in the light of a large Hubble scale and the favored tensor-to-scalar ratio $r \approx 0.05$. To account for a trans-Planckian field range we implement aligned natural inflation. Although there is only one universal axion in heterotic constructions, further axions from the geometric moduli can be used for alignment and inflation. We argue that such an alignment is rather generic on orbifolds, since all non-perturbative terms are determined by modular weights of the involved fields and the Dedeki…
We study the consistency of hybrid inflation and moduli stabilization, using the Kallosh--Linde model as an example for the latter. We find that F-term hybrid inflation is not viable since inflationary trajectories are destabilized by tachyonic modes. On the other hand, D-term hybrid inflation is naturally compatible with moduli stabilization due to the absence of a large superpotential term during the inflationary phase. Our model turns out to be equivalent to superconformal D-term inflation and it therefore successfully accounts for the CMB data in the large-field regime. Supersymmetry break…
We present predictions of the Kähler moduli inflation model for the spectral tilt by parametrising the reheating epoch by an effective equation-of-state parameter and the number of e-foldings of reheating; and taking into account the post-inflationary history of the model. This model has an epoch in which the energy density of the universe is dominated by cold moduli particles. We compare our results with data from the PLANCK mission and find that exotic reheating (with effective equation of state $w_{\rm re}$ greater than 1/3) is required to match the observations. For canonical reheating cas…
In models of inflation obtained from string compactification, moduli vacuum misalignment leads to an epoch in the post-inflationary history of the universe when the energy density is dominated by cold moduli particles. This effect leads to a modification in the number of $e$-foldings ($N_{\rm pivot}$) between horizon exit of the CMB modes and the end of inflation. Taking Kähler moduli inflation as a prototype, the shift in $e$-foldings turns out to be a function of the model parameters which also determines the inflationary observables. We analyse this scenario numerically using publicly avail…
We construct a natural inflation model in supergravity where the inflaton is identified with a modulus field possessing a shift symmetry. The superpotential for the inflaton is generated by meson condensation due to strong dynamics with deformed moduli constraints. In contrast to models based on gaugino condensation, the inflaton potential is generated without $R$-symmetry breaking and hence does not depend on the gravitino mass. Thus, our model is compatible with low scale supersymmetry.
We emphasize the importance of effects from heavy fields on supergravity models of inflation. We study, in particular, the backreaction of stabilizer fields and geometric moduli in the presence of supersymmetry breaking. Many effects do not decouple even if those fields are much heavier than the inflaton field. We apply our results to successful models of Starobinsky-like inflation and natural inflation. In most scenarios producing a plateau potential it proves difficult to retain the flatness of the potential after backreactions are taken into account. Some of them are incompatible with non-p…
To obtain natural inflation with large tensor-to-scalar ratio in string framework, we need a special moduli stabilization mechanism which can separate the masses of real and imaginary components of Kähler moduli at different scales, and achieve a trans-Planckian axion decay constant from sub-Planckian axion decay constants. In this work, we stabilize the matter fields by F-terms and the real components of Kähler moduli by D-terms of two anomalous $U(1)_X\times U(1)_A$ symmetries strongly at high scales, while the corresponding axions remain light due to their independence on the Fayet-Iliopoul…
The simple chaotic inflation is highly consistent with the BICEP2 experiment, and no-scale supergravity can be realized naturally in various string compactifications. Thus, we construct a chaotic inflation model in no-scale supergravity inspired from Type IIB string compactification with an anomalous U(1)_X gauged symmetry. We introduce two moduli T_1 and T_2 which transform non-trivially under U(1)_X, and some pairs of fundamental quarks charged under the SU(N) x U(1)_X gauge group. The non-trivial transformations of moduli under U(1)_X lead to a moduli-dependent Fayet-Iliopoulos (FI) term. T…
We present an overview of inflationary models derived from string theory focusing mostly on closed string moduli as inflatons. After a detailed discussion of the eta-problem and different approaches to address it, we describe possible ways to obtain a de Sitter vacuum with all closed string moduli stabilised. We then look for inflationary directions and present some of the most promising scenarios where the inflatons are either the real or the imaginary part of Kaehler moduli. We pay particular attention on extracting potential observable implications, showing how most of the scenarios predict…
We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $α$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $α$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there …
In this talk, I discuss the effects, viability, and predictions of the string-theory-motivated Kähler Moduli Inflation I (KMII) potential, coupled to a light scalar field $χ$, which can provide a possible source for today's dark energy density due to the potential's non-vanishing minimum. Although the model is consistent with the current measured Cosmic Microwave Background (CMB) data, tighter constraints from future observations are required to test the viability of the KMII potential with its minimum equivalent to the observed cosmological constant's energy density $ρ_{Λ_{\mathrm{obs}}}$. We…
It is known that the present electroweak vacuum is likely to be metastable and it may lead to a serious instability during/after inflation. We propose a simple solution to the problem of vacuum instability during/after inflation. If there is a moduli field which has Planck-suppressed interactions with the standard model fields, the Higgs quartic coupling in the early universe naturally takes a different value from the present one. A slight change of the quartic coupling in the early universe makes the Higgs potential absolutely stable and hence we are free from the vacuum instability during/af…
In this paper we address the question how to discriminate whether the gauged isometry group G_Sigma of the Kahler manifold Sigma that produces a D-type inflaton potential in a Minimal Supergravity Model is elliptic, hyperbolic or parabolic. We show that the classification of isometries of symmetric cosets can be extended to non symmetric Sigma.s if these manifolds satisfy additional mathematical restrictions. The classification criteria established in the mathematical literature are coherent with simple criteria formulated in terms of the asymptotic behavior of the Kahler potential K(C) = 2 J(…
