Monodromy Inflation Research Articles

A cosmological bootstrap for resonant non-Gaussianity

Recent progress has revealed a number of constraints that cosmological correlators and the closely related field-theoretic wavefunction must obey as a consequence of unitarity, locality, causality and the choice of initial state. When combined with symmetries, namely homogeneity, isotropy and scale invariance, these constraints enable one to compute large classes of simple observables, an approach known as (boostless) cosmological bootstrap. Here we show that it is possible to relax the restriction of scale invariance, if one retains a discrete scaling subgroup. We find an infinite class of solutions to the weaker bootstrap constraints and show that they reproduce and extend resonant non-Gaussianity, which arises in well-motivated models such as axion monodromy inflation. We find no evidence of the new non-Gaussian shapes in the Planck data. Intriguingly, our results can be re-interpreted as a deformation of the scale-invariant case to include a complex order of the total energy pole, or more evocatively interactions with a complex number of derivatives. We also discuss for the first time IR-divergent resonant contributions and highlight an inconsequential inconsistency in the previous literature.

More on gravitational waves from double monodromy inflation

We further analyze phenomenological implications of double axion monodromy inflation proposed in Ref. (D'Amico et al. [13]), in gravitational wave physics. We show that in addition to chiral gravitational waves (GW) originating from gauge field instability, the model also predicts significant amount of non-chiral, scalar-induced gravitational waves, both peaking at around the same frequencies. We find that although chiral GW density has much larger peak, non-chiral GWs can dominate away from the peak as they decay at a slower rate. This provides an interesting GW signature to be probed by future space-based interferometers such as LISA and DECIGO.

CMB constraints on monodromy inflation at strong coupling

We carry out a thorough numerical examination of field theory monodromy inflation at strong coupling. We perform an MCMC analysis using a Gaussian likelihood, fitting multiparameter models using CMB constraints on the spectral index and the tensor to scalar ratio. We show that models with uniquely positive Wilson coefficients are ruled out. If there are coefficients that can take on both signs, there can be a cancellation of terms that flattens the potentials and allows one to satisfy current data, and forecasts with strong constraints on the tensor to scalar ratio. Models of field theory monodromy are naturally enhanced to include a mechanism for canceling off radiative corrections to vacuum energy, via vacuum energy sequestering (VES). Although they include a much larger parameter space, we find that a similar numerical examination yields no significant change in the Bayesian evidence for VES enhanced models, with naturalness considerations making them more attractive from a theoretical perspective.

Spectral distortions from axion monodromy inflation

With the advent of new missions to probe spectral distortions of the cosmic microwave background with unprecedented precision, the study of theoretical predictions of these signals becomes a promising avenue to test our description of the early Universe. Meanwhile, axion monodromy still offers a viable framework to describe cosmic inflation. In order to explore new constraints on inflationary models based on axion monodromy while aiming at falsifying this scenario, we compute the spectral distortions predicted by this model, revealing oscillatory features that are compatible with Planck data. Further, the predicted distortions are up to 10% larger than the signals obtained from the fiducial ΛCDM model and are observable in principle. However, contrasting with the predictions of the simplest power-law inflationary potentials challenges the falsifiability of axion monodromy as it would require to reduce at least 100 times the current forecast error of the PIXIE satellite, which shall be possible at some projected observational setups.

General double monodromy inflation

We revisit the roller-coaster cosmology based on multiple stages of monodromy inflation. Working within the framework of effective flux monodromy field theory, we include the full range of strong coupling corrections to the inflaton sector. We find that flattened potentials $V\ensuremath{\sim}{\ensuremath{\phi}}^{p}+\ensuremath{\cdots}$ with $p\ensuremath{\lesssim}1/2$, limited to $N\ensuremath{\lesssim}25\ensuremath{-}40$ $e$-folds in the first stage of inflation, continue to fit the cosmic microwave background. They yield $0.96\ensuremath{\lesssim}{n}_{s}\ensuremath{\lesssim}0.97$ and produce relic gravity waves with $0.006\ensuremath{\lesssim}r\ensuremath{\lesssim}0.035$, in full agreement with the most recent bounds from BICEP/Keck. The nonlinear derivative corrections generated by strong dynamics in effective field theory (EFT) also lead to equilateral non-Gaussianity ${f}_{\mathrm{NL}}^{\mathrm{eq}}\ensuremath{\simeq}\mathcal{O}(1)\ensuremath{-}\mathcal{O}(10)$, close to the current observational bounds. Finally, in the multistage roller coaster, an inflaton--hidden sector $U(1)$ coupling can produce a tachyonic chiral vector background, which converts rapidly into tensors during the short interruption by matter domination. The produced stochastic gravity waves are chiral, and so they may be clearly identifiable by gravity wave instruments like LISA, Big Bang Observer, Einstein Telescope, NANOgrav, or SKA, depending on the precise model realization. We also point out that the current attempts to resolve the ${H}_{0}$ tension using early dark energy generically raise ${n}_{s}$. This might significantly alter the impact of BICEP/Keck data on models of inflation.

Hyperbolic compactification of M-theory and de Sitter quantum gravity

We present a mechanism for accelerated expansion of the universe in the generic case of negative-curvature compactifications of M-theory, with minimal ingredients. M-theory on a hyperbolic manifold with small closed geodesics supporting Casimir energy -- along with a single classical source (7-form flux) -- contains an immediate 3-term structure for volume stabilization at positive potential energy. Hyperbolic manifolds are well-studied mathematically, with an important rigidity property at fixed volume. They and their Dehn fillings to more general Einstein spaces exhibit explicit discrete parameters that yield small closed geodesics supporting Casimir energy. The off-shell effective potential derived by M. Douglas incorporates the warped product structure via the constraints of general relativity, screening negative energy. Analyzing the fields sourced by the localized Casimir energy and the available discrete choices of manifolds and fluxes, we find a regime where the net curvature, Casimir energy, and flux compete at large radius and stabilize the volume. Further metric and form field deformations are highly constrained by hyperbolic rigidity and warping effects, leading to calculations giving strong indications of a positive Hessian, and residual tadpoles are small. We test this via explicit back reacted solutions and perturbations in patches including the Dehn filling regions, initiate a neural network study of further aspects of the internal fields, and derive a Maldacena-Nunez style no-go theorem for Anti-de Sitter extrema for a range of parameters. A simple generalization incorporating 4-form flux produces axion monodromy inflation. As a relatively simple de Sitter uplift of the large-N M2-brane theory, the construction applies to de Sitter holography as well as to cosmological modeling, and introduces new connections between mathematics and the physics of string/M theory compactifications.

Double monodromy inflation: Gravitational wave factory for CMB-S4, LiteBIRD, and LISA

We consider a short rollercoaster cosmology based on two stages of monodromy inflation separated by a stage of matter domination, generated after the early inflaton falls out of slow roll. If the first stage is controlled by a flat potential, $V \sim \phi^p$ with $p < 1$ and lasts ${\cal N} \sim 30 - 40$ efolds, the scalar and tensor perturbations at the largest scales will fit the CMB perfectly, and produce relic gravity waves with $0.02 \lesssim r \lesssim 0.06$, which can be tested by LiteBIRD and CMB-S4 experiments. If in addition the first inflaton is strongly coupled to a hidden sector $U(1)$, there will be an enhanced production of vector fluctuations near the end of the first stage of inflation. These modes convert rapidly to tensors during the short epoch of matter domination, and then get pushed to superhorizon scales by the second stage of inflation, lasting another $20-30$ efolds. This band of gravity waves is chiral, arrives today with wavelengths in the range of $10^8$ km, and with amplitudes greatly enhanced compared to the long wavelength CMB modes by vector sources. It is therefore accessible to LISA. Thus our model presents a rare early universe theory predicting several simultaneous signals testable by a broad range of gravity wave searches in the very near future.

Universal axion backreaction in flux compactifications

We study the backreaction effect of a large axion field excursion on the saxion partner residing in the same mathcal{N} = 1 multiplet. Such configurations are relevant in attempts to realize axion monodromy inflation in string compactifications. We work in the complex structure moduli sector of Calabi-Yau fourfold compactifications of F-theory with four-form fluxes, which covers many of the known Type II orientifold flux compactifications. Noting that axions can only arise near the boundary of the moduli space, the powerful results of asymptotic Hodge theory provide an ideal set of tools to draw general conclusions without the need to focus on specific geometric examples. We find that the boundary structure engraves a remarkable pattern in all possible scalar potentials generated by background fluxes. By studying the Newton polygons of the extremization conditions of all allowed scalar potentials and realizing the backreaction effects as Puiseux expansions, we find that this pattern forces a universal backreaction behavior of the large axion field on its saxion partner.

Axion monodromy inflation, trapping mechanisms and the swampland

We study the effects of particle production on the evolution of the inflaton field in an axion monodromy model with the goal of discovering in which situations the resulting dynamics will be consistent with the swampland constraints. In the presence of a modulated potential the evolving background field (solution of the inflaton homogeneous in space) induces the production of long wavelength inflaton fluctuation modes. However, this either has a negligible effect on the inflaton dynamics (if the field spacing between local minima of the modulated potential is large), or else it traps the inflaton in a local minimum and leads to a graceful exit problem. On the other hand, the production of moduli fields at enhanced symmetry points can lead to a realization of trapped inflation consistent with the swampland constraints, as long as the coupling between the inflaton and the moduli fields is sufficiently large.

Monodromy charge in D7-brane inflation

In axion monodromy inflation, traversing N axion periods corresponds to discharging N units of a quantized charge. In certain models with moving D7-branes, such as Higgs-otic inflation, this monodromy charge is D3-brane charge induced on the D7-branes. The stress-energy of the induced charge affects the internal space, changing the inflaton potential and potentially limiting the field range. We compute the backreaction of induced D3-brane charge in Higgs-otic inflation. The effect on the nonperturbative superpotential is dramatic even for N = 1, and may preclude large-field inflation in this model in the absence of a mechanism to control the backreaction.

Potential-driven inflation with disformal coupling to gravity

In this paper, we investigate the potential-driven inflation models with a disformal coupling to Einstein Gravity, to find out the effects of such a coupling on these models. We consider a simple coupling form which introduces only one parameter, and three inflation models, namely the chaotic inflation, the Higgs inflation, and the monodromy inflation. We find that the disformal coupling can have some modifications to the observational variables of these models such as the power spectrum, the spectral index as well as the tensor/scalar ratio, although not too large due to the constraints on the disformal coupling parameter. With these modifications, one has the opportunity of improving models that lie on the edge of the favorable regions of Planck observational data, such as monodromy inflation. Moreover, the non-trivial sound speed of tensor perturbations (gravitational waves) may come out, due to the coupling of gravity and kinetic terms of the field.

Observable quantum loop effects in the sky

Expanding on [1], we analyze in detail the single field chaotic inflationary models plus a cosine modulation term, augmented by a light scalar field with inflaton dependent oscillatory mass term. We work out in detail the Feynman diagrams and compute one, two and in general estimate higher loop two and three point functions in the in-in formulation. We explicitly establish how the oscillatory mass term can amplify one-loop effects to dominate over the tree as well as the higher loop contributions. The power spectrum of curvature perturbations of this model is hence enhanced compared to the simple single field chaotic model. As a consequence, one can suppress the tensor to scalar ratio r and have a different expression for scalar spectral tilt and the running of the tilt, opening the way to reconcile chaotic models with convex potential and the Planck data. As in monodromy inflation models, we also have a cosine modulation in the spectral tilt. We also analyze the bispectrum, which can be dominated by the amplified one-loop effects, yielding a new shape in non-Gaussianity. We discuss the bounds on parameter space from all available CMB observables and possible implications for reheating.

Flattened axion monodromy beyond two derivatives

We study string inspired two-field models of large-field inflation based on axion monodromy in the presence of an interacting heavier modulus. This class of models has enough structure to approximate at least part of the backreaction effects known in full string theory, such as kinetic mixing with the axion, and flattening of the scalar potential. Yet, it is simple enough to fully describe the structure of higher-point curvature perturbation interactions driven by the adjusting modulus backreaction dynamics. We find that the presence of the heavy modulus can be described via two equivalent effective field theories, both of which can incorporate reductions of the speed of sound. Hence, the presence of heavier moduli in axion monodromy inflation constructions will necessarily generate some amount of non-Gaussianity accompanied by changes to $n_s$ and $r$ beyond what results from just from the well known adiabatic flattening backreaction.

Resonant reconciliation of convex-potential inflation models and the Planck data

We consider single field chaotic inflationary models plus a cosine modulation term, as in axion monodromy models, and augment it by a light scalar field with similar cosine coupling. We show the power spectrum of curvature perturbations of this model is dominated by the one-loop contribution to inflaton two-point function which is enhanced due to resonant interactions. This allows to disentangle the scale of scalar and tensor perturbations and hence to suppress the ratio of tensor-to-scalar power spectra and alters the expression of scalar spectral tilt from the simple chaotic models, thus opening the way to reconcile chaotic models with convex potential and the Planck data. As in monodromy inflation models, we also have a cosine modulation in spectral tilt. We mention that contribution of resonance effects on non-Gaussianty is small and it remains within the current bounds. Resonant production of light particles toward the end of inflation may set the stage for a successful reheating model.

Stochastic gravitational-wave background from axion-monodromy oscillons in string theory during preheating

Axion monodromy is a generic phenomenon in string compactifications. We investigate the production of gravitational-wave background from axion monodromy inflation during preheating. By performing lattice simulations using pseudo-spectral methods, we find that significant single-peak stochastic gravitational-wave backgrounds are generated during preheating for asymptotic linear $|\phi|$ and $\phi^{2/3}$ potentials in axion monodromy inflation and cuspy potentials. This may allow us to explore string compactifications through gravitational waves.

Monodromy inflation and an emergent mechanism for stabilising the cosmological constant

We show that a pair of field theory monodromies in which the shift symmetry is broken by small, well motivated deformations, naturally incorporates a mechanism for cancelling off radiative corrections to the cosmological constant. The lighter monodromy sector plays the role of inflation as well as providing a rigid degree of freedom that acts as a dynamical counterterm for the cosmological constant. The heavier monodromy sector includes a rigid dilaton that forces a global constraint on the system and the cancellation of vacuum energy loops occurs at low energies via the sequestering mechanism. This suggests that monodromy constructions in string theory could be adapted to incorporate mechanisms to stabilise the cosmological constant in their low energy descriptions.

Initial conditions for inflation in an FRW universe

We examine the class of initial conditions which give rise to inflation. Our analysis is carried out for several popular models including: Higgs inflation, Starobinsky inflation, chaotic inflation, axion monodromy inflation and non-canonical inflation. In each case we determine the set of initial conditions which give rise to sufficient inflation, with at least $60$ e-foldings. A phase-space analysis has been performed for each of these models and the effect of the initial inflationary energy scale on inflation has been studied numerically. This paper discusses two scenarios of Higgs inflation: (i) the Higgs is coupled to the scalar curvature, (ii) the Higgs Lagrangian contains a non-canonical kinetic term. In both cases we find Higgs inflation to be very robust since it can arise for a large class of initial conditions. One of the central results of our analysis is that, for plateau-like potentials associated with the Higgs and Starobinsky models, inflation can be realised even for initial scalar field values which lie close to the minimum of the potential. This dispels a misconception relating to plateau potentials prevailing in the literature. We also find that inflation in all models is more robust for larger values of the initial energy scale.

Qualitative dynamics and inflationary attractors in loop cosmology

Qualitative dynamics of three different loop quantizations of spatially flat isotropic and homogeneous models is studied using effective spacetime description of the underlying quantum geometry. These include the standard loop quantum cosmology (LQC), its recently revived modification (referred to as mLQC-I), and another related modification of LQC (mLQC-II) whose dynamics is studied in detail for the first time. Various features of LQC, including quantum bounce and pre-inflationary dynamics, are found to be shared with the mLQC-I and mLQC-II models. We study universal properties of dynamics for chaotic inflation, fractional monodromy inflation, Starobinsky potential, non-minimal Higgs inflation, and an exponential potential. We find various critical points and study their stability, which reveal various qualitative similarities in the post-bounce phase for all these models. The pre-bounce qualitative dynamics of LQC and mLQC-II turns out to be very similar, but is strikingly different from that of mLQC-I. In the dynamical analysis, some of the fixed points turn out to be degenerate for which center manifold theory is used. For all these potentials, non-perturbative quantum gravitational effects always result in a non-singular inflationary scenario with a phase of super-inflation succeeded by the conventional inflation. We show the existence of inflationary attractors, and obtain scaling solutions in the case of the exponential potential. Since all of the models agree with general relativity at late times, our results are also of use in classical theory where qualitative dynamics of some of the potentials has not been studied earlier.

Monodromy Inflation in the Strong Coupling Regime of the Effective Field Theory.

We present a simple effective field theory formulation of a general family of single-field flux monodromy models for which strong coupling effects at large field values can flatten the potential and activate higher-derivative operators. Both of these effects can suppress the tensor amplitude. These models are radiatively and nonperturbatively stable and can sustain ≳60 e folds of inflation. The dynamics combines features of both large-field chaotic inflation and k inflation. Reducing the tensor-scalar ratio below the observational bound r≲0.1 while keeping the scalar spectral index n_{s} within experimental bounds either yields equilateral non-Gaussianity f_{NL}^{eq}≃O(1), close to the current observational bounds, or gives very small r.

Primordial black holes and associated gravitational waves in axion monodromy inflation

In the axion monodromy inflation, the inflation is driven by the axion with super-Planckian field values in a monomial potential with superimposed sinusoidal modulations. The coupling of the axion to massless gauge fields can induce copious particle production during inflation, resulting in large non-Gaussian curvature perturbation that leads to the formation of primordial black holes. In this paper, we explore the parameter space in the axion monodromy inflation model that favors the formation of primordial black holes with masses ranging from 108 grams to 20 solar masses. We also study the associated gravitational waves and their detection in pulsar timing arrays and interferometry experiments.