D-brane Inflation Research Articles

Cosmological dynamics of string theory axion strings

The quantum chromodynamics (QCD) axion may solve the strong CP problem and explain the dark matter (DM) abundance of our Universe. The axion was originally proposed to arise as the pseudo-Nambu-Goldstone boson of global U(1)PQ Peccei-Quinn (PQ) symmetry breaking, but axions also arise generically in string theory as zero modes of higher-dimensional gauge fields. In this work we show that string theory axions behave fundamentally differently from field theory axions in the early Universe. Field theory axions may form axion strings if the PQ phase transition takes place after inflation. In contrast, we show that string theory axions do not generically form axion strings. In special inflationary paradigms, such as D-brane inflation, string theory axion strings may form; however, their tension is parametrically larger than that of field theory axion strings. We then show that such QCD axion strings overproduce the DM abundance for all allowed QCD axion masses and are thus ruled out, except in scenarios with large warping. A loop-hole to this conclusion arises in the axiverse, where an axion string could be composed of multiple different axion mass eigenstates; a heavier eigenstate could collapse the network earlier, allowing for the QCD axion to produce the correct DM abundance and also generating observable gravitational wave signals. Published by the American Physical Society 2024

B-mode targets

The CMB-S4 Science Book [1], Simons Observatory report [2], Astro2020 Science White Paper on gravitational waves [3], and PICO report [4] contain an extensive discussion of many ongoing and planned efforts in the search for gravitational waves produced by inflation. Here we give a short executive summary of the results obtained in our papers [5–7], which specify the simplest available inflationary models providing physically motivated targets for these searches. Our conclusions are specific for the 10−3≲r≲10−2 range, where we present the B-mode benchmarks of the U-duality symmetric class of α-attractors, and for r≲10−3, where we present B-mode targets, for which the future precision measurements of ns will be decisive. We show that a combination of the simplest α-attractors and KKLTI models of D-brane inflation covers most of the area favored by Planck 2018.

On hilltop and brane inflation after Planck

Hilltop inflation models are often described by potentials V = V0 (1−ϕn/mn+… ). The omitted terms indicated by ellipsis do not affect inflation for m ≲ 1, but the most popular models with n = 2 and 4 for m ≲ 1 are ruled out observationally. Meanwhile in the large m limit the results of the calculations of the tensor to scalar ratio r in the models with V = V0 (1−ϕn/mn), for all n, converge to r = 4/N ≲ 0.07, as in chaotic inflation with V ∼ ϕ, suggesting a reasonably good fit to the Planck data. We show, however, that this is an artifact related to the inconsistency of the model V = V0 (1−ϕn/mn) at ϕ > m. Consistent generalizations of this model in the large m limit typically lead to a much greater value r = 8/N, which negatively affects the observational status of hilltop inflation. Similar results are valid for D-brane inflation with V = V0(1−mn/ϕn), but consistent generalizations of D-brane inflation models may successfully complement α-attractors in describing most of the area in the (ns, r) space favored by Planck 2018.

Planck 2018 and brane inflation revisited

We revisit phenomenological as well as string-theoretical aspects of D-brane inflation cosmological models. Phenomenologically these models stand out on par with α-attractors, as models with Planck-compatible values of ns, moving down to the sweet spot in the data with decreasing value of r. On the formal side we present a new supersymmetric version of these models in the context of de Sitter supergravity with a nilpotent multiplet and volume modulus stabilization. The geometry of the nilpotent multiplet is evaluated in the framework of string theory.

Sharp predictions from eternal inflation patches in D-brane inflation

We numerically generate the six-dimensional landscape of D3-brane inflation and identify patches of eternal inflation near sufficiently flat inflection points of the potential. We show that reasonable measures that select patches of eternal inflation in the landscape yield sharp predictions for the spectral properties of primordial perturbations on observable scales. These include a scalar tilt of .936, a running of the scalar tilt −.00103, undetectably small tensors and non-Gaussianity, and no observable spatial curvature. Our results explicitly demonstrate that precision cosmology probes the combination of the statistical properties of the string landscape and the measure implied by the universe's quantum state.

Where does curvaton reside? Differences between bulk and brane frames

Some classes of inflationary models naturally introduce two distinct metrics/frames, and their equivalence in terms of observables has often been put in question. D-brane inflation proposes candidates for an inflaton embedded in the string theory and possesses descriptions on the brane and bulk metrics/frames, which are connected by a conformal/disformal transformation that depends on the inflaton and its derivatives. It has been shown that curvature perturbations generated by the inflaton are identical in both frames, meaning that observables such as the spectrum of cosmic microwave background (CMB) anisotropies are independent of whether matter fields---including those in the standard model of particle physics---minimally couple to the brane or the bulk metric/frame. This is true despite the fact that the observables are eventually measured by the matter fields and that the total action including the matter fields is different in the two cases. In contrast, in curvaton scenarios, the observables depend on the frame to which the curvaton minimally couples. Among all inflationary scenarios, we focus on two models motivated by the KKLMMT fine-tuning problem: a slow-roll inflation with an inflection-point potential and a model of a rapidly rolling inflaton that conformally couples to gravity. In the first model, the difference between the frames in which the curvaton resides is encoded in the spectral index of the curvature perturbations, depicting the nature of the frame transformation. In the second model, the curvaton on the brane induces a spectral index significantly different from that in the bulk and is even falsified by the observations. This work thus demonstrates that two frames connected by a conformal/disformal transformation lead to different physical observables such as CMB anisotropies in curvaton models.

Statistical anisotropy from vector curvaton in D-brane inflation

We investigate the possibility of embedding the vector curvaton paradigm in D-brane models of inflation in type IIB string theory in a simple toy model. The vector curvaton is identified with the U(1) gauge field that lives on the world volume of a D3-brane, which may be stationary or undergoing general motion in the internal space. The dilaton is considered as a spectator field which modulates the evolution of the vector field. In this set-up, the vector curvaton is able to generate measurable statistical anisotropy in the spectrum and bispectrum of the curvature perturbation assuming that the dilaton evolves as e−ϕ∝a2 where a(t) is the scale factor. Our work constitutes a first step towards exploring how such distinctive features may arise from the presence of several light fields that naturally appear in string theory models of cosmology.

Multifield consequences for D-brane inflation

We analyse the multifield behaviour in D-brane inflation when contributions from the bulk are taken into account. For this purpose, we study a large number of realisations of the potential; we find the nature of the inflationary trajectory to be very consistent despite the complex construction. Inflation is always canonical and occurs in the vicinity of an inflection point. Extending the transport method to non-slow-roll and to calculate the running, we obtain distributions for observables. The spectral index is typically blue and the running positive, putting the model under moderate pressure from WMAP7 constraints. The local fNL and tensor-to-scalar ratio are typically unobservably small, though we find approximately 0.5% of realisations to give observably large local fNL. Approximating the potential as sum-separable, we are able to give fully analytic explanations for the trends in observed behaviour. Finally we find the model suffers from the persistence of isocurvature perturbations, which can be expected to cause further evolution of adiabatic perturbations after inflation. We argue this is a typical problem for models of multifield inflation involving inflection points and renders models of this type technically unpredictive without a description of reheating.

Universality in D-brane inflation

We study the six-field dynamics of D3-brane inflation for a general scalar potential on the conifold, finding simple, universal behavior.We numerically evolve the equations of motion for an ensemble of more than 7·107 realizations, drawing the coefficients in the scalar potential from statistical distributions whose detailed properties have demonstrably small effects on our results.When prolonged inflation occurs, it has a characteristic form: the D3-brane initially moves rapidly in the angular directions, spirals down to an inflection point in the potential, and settles into single-field inflation.The probability of Ne e-folds of inflation is a power law, P(Ne)∝Ne−3, and wederivethe same exponent from a simple analytical model. The success of inflation is relatively insensitive to the initial position: we find attractor behavior in the angular directions, and the D3-brane can begin far above the inflection point without overshooting. Initial radial or angular velocities, on the other hand, can have a significant effect on the duration of inflation. In favorable regions of the spaces of initial velocities and of Lagrangian parameters, models yielding 60 e-folds of expansion arise approximately once in 103 trials. Realizations that are effectively single-field and give rise to a primordial spectrum of fluctuations consistent with WMAP, for which at least 120 e-folds are required, arise approximately once in 105 trials. The emergence of robust predictions from a six-field potential with hundreds of terms invites an analytic approach to multifield inflation.

Warm Dirac-Born-Infeld inflation

We propose a warm inflationary model in the context of relativistic D-brane inflation in a warped throat, which has Dirac-Born-Infeld (DBI) kinetic term and is coupled to radiation through a dissipation term. The perturbation freezes at the sound horizon and the power spectrum is determined by a combination of the dissipative parameter and the sound speed parameter. The thermal dissipation ameliorates the eta problem and softens theoretical constraints from the extra-dimensional volume and from observational bounds on the tensor-to-scalar ratio. The warm DBI model can lead to appreciable non-Gaussianity of the equilateral type. As a phenomenological model, ignoring compactification constraints, we show that large-field warm inflation models do not necessarily yield a large tensor-to-scalar ratio.

Towards multi-field D-brane inflation in a warped throat

We study the inflationary dynamics in a model of slow-roll inflation in warped throat. Inflation is realized by the motion of a D-brane along the radial direction of the throat, and at later stages instabilities develop in the angular directions. We closely investigate both the single field potential relevant for the slow-roll phase, and the full multi-field one including the angular modes which becomes important at later stages. We study the main features of the instability process, discussing its possible consequences and identifying the vacua towards which the angular modes are driven.

Effects of Compactification in D-brane Inflation

In D3-brane inflation, the inflaton potential receives important contributions from sources in the compact space, such as fluxes, other D-branes, and orientifold planes. Most previous analyses have considered only the effects of sources near to the inflationary D3-brane, but in fact distant sources do not generically decouple and can critically influence the dynamics during inflation. We provide a systematic method for incorporating the effects of arbitrary distant sources as perturbations to the local supergravity background. We use this approach to obtain the structure of the potential for a D3-brane in a warped throat geometry attached to a general compact space. A significant, and well-known, contribution to this potential arises from quantum effects involved in the stabilization of the compactification volume. Our method automatically captures these effects, encoding them in a suitable flux background.

Effects of light fields during inflation

In the inflationary universe, there can be light fields other than the inflaton. We explore a possibility that such light fields source the primordial perturbations, while minimally affecting the inflaton dynamics. We show that during inflation, fluctuations of the light fields can be converted to adiabatic curvature perturbations, which accumulate and become significant by the end of the inflationary era. An additional goal of this work is to distinguish between light fields which can/cannot be ignored during inflation. Such criteria become useful for examining cosmological scenarios with multiple fields. As concrete examples, our results are applied to D-brane inflation models. We consider effects from KK modes (oscillation modes) of wrapped branes in monodromy-driven large-field models, and angular directions of throat geometries in warped D-brane inflation.

Reheating the D-brane universe via instant preheating

We investigate a possibility of reheating in a scenario of D-brane inflation in a warped deformed conifold background which includes perturbative corrections to throat geometry sourced by chiral operator of dimension 3/2 in the CFT. The effective D-brane potential, in this case, belongs to the class of non-oscillatory models of inflation for which the conventional reheating mechanism does not work. We find that gravitational particle production is inefficient and leads to reheating temperature of the order of ${10^8} GeV$. We show that instant preheating is quite suitable to the present scenario and can easily reheat universe to a temperature which is higher by about three orders of magnitudes than its counter part associated with gravitational particle production. The reheating temperature is shown to be insensitive to a particular choice of inflationary parameters suitable to observations.

Inflationary potentials in DBI models

We study DBI inflation based upon a general model characterized by a power-law flow parameter ϵ(ϕ) ∝ ϕα and speed of sound cs(ϕ) ∝ ϕβ, where α and β are constants. We show that in the slow-roll limit this general model gives rise to distinct inflationary classes according to the relation between α and β and to the time evolution of the inflaton field, each one corresponding to a specific potential; in particular, we find that the well-known canonical polynomial (large- and small-field), hybrid and exponential potentials also arise in this non-canonical model. We find that these non-canonical classes have the same physical features as their canonical analogs, except for the fact that the inflaton field evolves with varying speed of sound; also, we show that a broad class of canonical and D-brane inflation models are particular cases of this general non-canonical model. Next, we compare the predictions of large-field polynomial models with the current observational data, showing that models with low speed of sound have red-tilted scalar spectrum with low tensor-to-scalar ratio, in good agreement with the observed values. These models also show a correlation between large non-gaussianity with low tensor amplitudes, which is a distinct signature of DBI inflation with large-field polynomial potentials.

Holographic systematics of D-brane inflation

We provide a systematic treatment of possible corrections to the inflaton potential for D-brane inflation in the warped deformed conifold. We consider the D3-brane potential in the presence of the most general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. This corresponds to the potential on the Coulomb branch of the dual gauge theory, in the presence of arbitrary perturbations of the Lagrangian. The leading contributions arise from perturbations by the most relevant operators that do not destroy the throat geometry. We find a generic contribution from a non-chiral operator of dimension $\Delta=2$ associated with a global symmetry current, resulting in a negative contribution to the inflaton mass-squared. If the Calabi-Yau preserves certain discrete symmetries, this is the dominant correction to the inflaton potential, and fine-tuning of the inflaton mass is possible. In the absence of such discrete symmetries, the dominant contribution comes from a chiral operator with $\Delta=3/2$, corresponding to a $\phi^{3/2}$ term in the inflaton potential. The resulting inflationary models are phenomenologically similar to the inflection point scenarios arising from specific D7-brane embeddings, but occur under far more general circumstances. Our strategy extends immediately to other warped geometries, given sufficient knowledge of the Kaluza-Klein spectrum.

Inflation on an open racetrack

We present a variant of warped D-brane inflation by incorporating multiple sets of holomorphically-embedded D7-branes involved in moduli stabilization with extent into a warped throat. The resultant D3-brane motion depends on the D7-brane configuration and the relative position of the D3-brane in these backgrounds. The non-perturbative moduli stabilization superpotential takes the racetrack form, but the additional D3-brane open string moduli dependence provides more flexibilities in model building. For concreteness, we consider D3-brane motion in the warped deformed conifold with the presence of multiple D7-branes, and derive the scalar potential valid for the entire throat. By explicit tuning of the microphysical parameters, we obtain inflationary trajectories near an inflection point for various D7-brane configurations. Moreover, the open racetrack potential admits approximate Minkowski vacua before uplifting. We demonstrate with a concrete D-brane inflation model where the Hubble scale during inflation can exceed the gravitino mass. Finally, the multiple sets of D7-branes present in this open racetrack setup also provides a mechanism to stabilize the D3-brane to metastable vacua in the intermediate region of the warped throat.

Advances in Inflation in String Theory

We provide a pedagogical overview of inflation in string theory. We focus upon the sensitivity of inflation to Planck-scale physics, which we argue provides both the primary motivation and the central theoretical challenge for the subject. We illustrate these issues through two case studies of inflationary scenarios in string theory: warped d-brane inflation and axion monodromy inflation. Finally, we indicate how future observations can test scenarios of inflation in string theory.

Towards an explicit model of D-brane inflation

We present a detailed analysis of an explicit model of warped D-brane inflation,incorporating the effects of moduli stabilization. We consider the potential for D3-branemotion in a warped conifold background that includes fluxes and holomorphicallyembedded D7-branes involved in moduli stabilization. Although the D7-branes significantlymodify the inflaton potential, they do not correct the quadratic term in the potential, andhence do not cause a uniform change in the slow roll parameter eta. Nevertheless,we present a simple example based on the Kuperstein embedding of D7-branes,z1 = constant, in which the potential can be fine-tuned to be sufficiently flat for inflation. To derive thisresult, it is essential to incorporate the fact that the compactification volume changesslightly as the D3-brane moves. We stress that the compactification geometry dictatescertain relationships among the parameters in the inflaton Lagrangian, and thesemicroscopic constraints impose severe restrictions on the space of possible models. We notethat the shape of the final inflaton potential differs from projections given in earlier studies:in configurations where inflation occurs, it does so near an inflection point. Finally,we comment on the difficulty of making precise cosmological predictions in thisscenario. This is the companion paper to Baumann et al (2007 Phys. Rev. Lett. 99141601).

Phenomenology of D-brane inflation with general speed of sound

A characteristic of D-brane inflation is that fluctuations in the inflaton field can propagate at a speed significantly less than the speed of light. This yields observable effects that are distinct from those of single-field slow-roll inflation, such as a modification of the inflationary consistency relation and a potentially large level of non-Gaussianities. We present a numerical algorithm that extends the inflationary flow formalism to models with general speed of sound. For an ensemble of D-brane-inflation models parametrized by the Hubble parameter and the speed of sound as polynomial functions of the inflaton field, we give qualitative predictions for the key inflationary observables. We discuss various consistency relations for D-brane inflation, and compare the qualitative shapes of the warp factors we derive from the numerical models with analytical warp factors considered in the literature. Finally, we derive and apply a generalized microphysical bound on the inflaton field variation during brane inflation. While a large number of models are consistent with current cosmological constraints, almost all of these models violate the compactification constraint on the field range in four-dimensional Planck units. If the field range bound is to hold, then models with a detectable level of non-Gaussianity predict a blue scalar spectral index, and a tensor component that is far below the detection limit of any future experiment.