Volume Stabilization and the Origin of the Inflaton Shift Symmetry in String Theory

The main problem of inflation in string theory is finding the models with a flat potential, consistent with stabilization of the volume of the compactified space. This can be achieved in the theories where the potential has (an approximate) shift symmetry in the inflaton direction. We will identify a class of models where the shift symmetry uniquely follows from the underlying mathematical structure of the theory. It is related to the symmetry properties of the corresponding coset space and the period matrix of special geometry, which shows how the gauge coupling depends on the volume and the position of the branes. In particular, for type IIB string theory on K3xT^2/Z with D3 or D7 moduli belonging to vector multiplets, the shift symmetry is a part of SO(2,2+n) symmetry of the coset space [SU(1,1)/ U(1)]x[SO(2,2+n)/(SO(2)x SO(2+n)]. The absence of a prepotential, specific for the stringy version of supergravity, plays a prominent role in this construction, which may provide a viable mechanism for the accelerated expansion and inflation in the early universe.Comment: 12 page

Axionic D3-D7 Inflation

We study the motion of a D3 brane moving within a Type IIB string vacuum compactified to 4D on K3 x T_2/Z_2 in the presence of D7 and O7 planes. We work within the effective 4D supergravity describing how the mobile D3 interacts with the lightest bulk moduli of the compactification, including the effects of modulus-stabilizing fluxes. We seek inflationary solutions to the resulting equations, performing our search numerically in order to avoid resorting to approximate parameterizations of the low-energy potential. We consider uplifting from D-terms and from the supersymmetry-breaking effects of anti-D3 branes. We find examples of slow-roll inflation (with anti-brane uplifting) with the mobile D3 moving along the toroidal directions, falling towards a D7-O7 stack starting from the antipodal point. The inflaton turns out to be a linear combination of the brane position and the axionic partner of the K3 volume modulus, and the similarity of the potential along the inflaton direction with that of racetrack inflation leads to the prediction n_s \le 0.95 for the spectral index. The slow roll is insensitive to most of the features of the effective superpotential, and requires a one-in-10^4 tuning to ensure that the torus is close to square in shape. We also consider D-term inflation with the D3 close to the attractive D7, but find that for a broad (but not exhaustive) class of parameters the conditions for slow roll tend to destabilize the bulk moduli. In contrast to the axionic case, the best inflationary example of this kind requires the delicate adjustment of potential parameters (much more than the part-per-mille level), and gives inflation only at an inflection point of the potential (and so suffers from additional fine-tuning of initial conditions to avoid an overshoot problem).Comment: 29 pages, 5 figure

Kahler Moduli Inflation

We show that under general conditions there is at least one natural inflationary direction for the Kahler moduli of type IIB flux compactifications. This requires a Calabi-Yau which has h^{2,1}>h^{1,1}>2 and for which the structure of the scalar potential is as in the recently found exponentially large volume compactifications. We also need - although these conditions may be relaxed - at least one Kahler modulus whose only non-vanishing triple-intersection is with itself and which appears by itself in the non-perturbative superpotential. Slow-roll inflation then occurs without a fine tuning of parameters, evading the eta problem of F-term inflation. In order to obtain COBE-normalised density perturbations, the stabilised volume of the Calabi-Yau must be O(10^5-10^7) in string units, and the inflationary scale M_{infl} ~ 10^{13} GeV. We find a robust model independent prediction for the spectral index of 1 - 2/N_e = 0.960 - 0.967, depending on the number of efoldings.Comment: 17 pages, 1 figure; v2. references adde

Dirac Born Infeld (DBI) Cosmic Strings

Motivated by brane physics, we consider the non-linear Dirac-Born-Infeld (DBI) extension of the Abelian-Higgs model and study the corresponding cosmic string configurations. The model is defined by a potential term, assumed to be of the mexican hat form, and a DBI action for the kinetic terms. We show that it is a continuous deformation of the Abelian-Higgs model, with a single deformation parameter depending on a dimensionless combination of the scalar coupling constant, the vacuum expectation value of the scalar field at infinity, and the brane tension. By means of numerical calculations, we investigate the profiles of the corresponding DBI-cosmic strings and prove that they have a core which is narrower than that of Abelian-Higgs strings. We also show that the corresponding action is smaller than in the standard case suggesting that their formation could be favoured in brane models. Moreover we show that the DBI-cosmic string solutions are non-pathological everywhere in parameter space. Finally, in the limit in which the DBI model reduces to the Bogomolnyi-Prasad-Sommerfield (BPS) Abelian-Higgs model, we find that DBI cosmic strings are no longer BPS: rather they have positive binding energy. We thus argue that, when they meet, two DBI strings will not bind with the corresponding formation of a junction, and hence that a network of DBI strings is likely to behave as a network of standard cosmic strings.Comment: 25 pages, 12 figure

Warped Tachyonic Inflation in Type IIB Flux Compactifications and the Open-String Completeness Conjecture

We consider a cosmological scenario within the KKLT framework for moduli stabilization in string theory. The universal open string tachyon of decaying non-BPS D-brane configurations is proposed to drive eternal topological inflation. Flux-induced `warping' can provide the small slow-roll parameters needed for successful inflation. Constraints on the parameter space leading to sufficient number of e-folds, exit from inflation, density perturbations and stabilization of the Kahler modulus are investigated. The conditions are difficult to satisfy in Klebanov-Strassler throats but can be satisfied in T^3 fibrations and other generic Calabi-Yau manifolds. This requires large volume and magnetic fluxes on the D-brane. The end of inflation may or may not lead to cosmic strings depending on the original non-BPS configuration. A careful investigation of initial conditions leading to a phenomenologically viable model for inflation is carried out. The initial conditions are chosen on the basis of Sen's open string completeness conjecture. We find time symmetrical bounce solutions without initial singularities for k=1 FRW models which are correlated with an inflationary period. Singular big-bang/big-crunch solutions also exist but do not lead to inflation. There is an intriguing correlation between having an inflationary universe in 4 dimensions and 6 compact dimensions or a big-crunch singularity and decompactification.Comment: 43 pages, 9 figures. v3: Typos correcte

Volume Stabilization via α′\alpha^\prime Corrections in Type IIB Theory with Fluxes

We consider the Type IIB string theory in the presence of various extra $7/\bar 7$-brane pairs compactified on a warped Calabi-Yau threefold that admits a conifold singularity. We demonstrate that the volume modulus can be stabilized perturbatively at a non-supersymmetric $AdS_4/dS_4$ vacuum by the effective potential that includes the stringy $(\alpha^\prime)^3$ correction obtained by Becker {\it et al.} together with a combination of positive tension and anomalous negative tension terms generated by the additional 7-brane-antibrane pairs.Comment: 20 pages, 4 figures, parts of introduction and conclusions are modifie

An Inflationary Scenario in Intersecting Brane Models

We propose a new scenario for D-term inflation which appears quite straightforwardly in the open string sector of intersecting brane models. We take the inflaton to be a chiral field in a bifundamental representation of the hidden sector and we argue that a sufficiently flat potential can be brane engineered. This type of model generically predicts a near gaussian red spectrum with negligible tensor modes. We note that this model can very naturally generate a baryon asymmetry at the end of inflation via the recently proposed hidden sector baryogenesis mechanism. We also discuss the possibility that Majorana masses for the neutrinos can be simultaneously generated by the tachyon condensation which ends inflation. Our proposed scenario is viable for both high and low scale supersymmetry breaking.Comment: 30 pages, 2 figures; v2 references and comments adde

Multiple Inflation, Cosmic String Networks and the String Landscape

Motivated by the string landscape we examine scenarios for which inflation is a two-step process, with a comparatively short inflationary epoch near the string scale and a longer period at a much lower energy (like the TeV scale). We quantify the number of $e$-foldings of inflation which are required to yield successful inflation within this picture. The constraints are very sensitive to the equation of state during the epoch between the two inflationary periods, as the extra-horizon modes can come back inside the horizon and become reprocessed. We find that the number of $e$-foldings during the first inflationary epoch can be as small as 12, but only if the inter-inflationary period is dominated by a network of cosmic strings (such as might be produced if the initial inflationary period is due to the brane-antibrane mechanism). In this case a further 20 $e$-foldings of inflation would be required at lower energies to solve the late universe's flatness and horizon problems.Comment: 27 pages, 6 figures; v2: refences adde

Inflation in Realistic D-Brane Models

We find successful models of D-brane/anti-brane inflation within a string context. We work within the GKP-KKLT class of type IIB string vacua for which many moduli are stabilized through fluxes, as recently modified to include `realistic' orbifold sectors containing standard-model type particles. We allow all moduli to roll when searching for inflationary solutions and find that inflation is not generic inasmuch as special choices must be made for the parameters describing the vacuum. But given these choices inflation can occur for a reasonably wide range of initial conditions for the brane and antibrane. We find that D-terms associated with the orbifold blowing-up modes play an important role in the inflationary dynamics. Since the models contain a standard-model-like sector after inflation, they open up the possibility of addressing reheating issues. We calculate predictions for the CMB temperature fluctuations and find that these can be consistent with observations, but are generically not deep within the scale-invariant regime and so can allow appreciable values for $dn_s/d\ln k$ as well as predicting a potentially observable gravity-wave signal. It is also possible to generate some admixture of isocurvature fluctuations.Comment: 39 pages, 21 figures; added references; identified parameters combining successful inflation with strong warping, as needed for consistency of the approximation

Uplifting and Inflation with D3 Branes

Back-reaction effects can modify the dynamics of mobile D3 branes moving within type IIB vacua, in a way which has recently become calculable. We identify some of the ways these effects can alter inflationary scenarios, with the following three results: (1) By examining how the forces on the brane due to moduli-stabilizing interactions modify the angular motion of D3 branes moving in Klebanov-Strassler type throats, we show how previous slow-roll analyses can remain unchanged for some brane trajectories, while being modified for other trajectories. These forces cause the D3 brane to sink to the bottom of the throat except in a narrow region close to the D7 brane, and do not ameliorate the \eta-problem of slow roll inflation in these throats; (2) We argue that a recently-proposed back-reaction on the dilaton field can be used to provide an alternative way of uplifting these compactifications to Minkowski or De Sitter vacua, without the need for a supersymmetry-breaking anti-D3 brane; and (3) by including also the D-term forces which arise when supersymmetry-breaking fluxes are included on D7 branes we identify the 4D supergravity interactions which capture the dynamics of D3 motion in D3/D7 inflationary scenarios. The form of these potentials sheds some light on recent discussions of how symmetries constrain D term interactions in the low-energy theory.Comment: JHEP.cls, 35 pages, 3 .eps figure