Multi-field Inflation Research Articles

Gravitational production of completely dark photons with nonminimal couplings to gravity

Dark photons are a theorized massive spin-1 particle which can be produced via various mechanisms, including cosmological gravitational particle production (GPP) in the early universe. In this work, we extend previous results for GPP of dark photons to include nonminimal couplings to gravity. We find that nonminimal couplings can induce a ghost instability or lead to runaway particle production at high momentum and discuss the constraints on the parameter space such that the theory is free of instabilities. Within the instability-free regime we numerically calculate the particle production and find that the inclusion of nonminimal couplings can lead to an enhancement of the particle number. As a result, GPP of nonminimally coupled dark photons can open the parameter space for production of a cosmological relevant relic density (constituting all or part of the dark matter) as compared to the minimally-coupled theory. These results are independent of the choice of inflation model, which we demonstrate by repeating the analysis for a class of rapid-turn multi-field inflation models.

Enhanced power spectra from multi-field inflation

We investigate the enhancement of the power spectra largeenough to produce primordial black holes in models with multiple scalar fields. We present analytic solutions for the perturbations in the case of constant turns without the need for an effective field theory for the first time and clarify the role of the Hubble friction that has been overlooked previously. We derive the criteria for an arbitrary number of fields that can lead to an exponential amplification of the curvature perturbation on subhorizon scales, while leaving the perturbations stable on superhorizon scales. Finally, we apply our results to a three-field generalization of the “ultra-light” scenario and show how the presence of field-space torsion can yield distinct observables compared to the two-field case.

Positivity from Cosmological Correlators

Effective field theories in flat space and in anti-de Sitter space are constrained by causality and unitarity, often in the form of positivity bounds. Similar bounds have been harder to demonstrate in cosmological backgrounds, where the roles of unitarity and causality are more obscure. Fortunately, the expansion of the universe ensures that late-time cosmological correlators are effectively classical and the role of unitarity is played by classical statistical inequalities. For multi-field inflation, the resulting positivity constraints have long been known in terms of the Suyama-Yamaguchi inequality. In this paper, we demonstrate that similar statistical bounds imply nontrivial constraints for massive fields in the early universe. We show that any real anomalous dimensions for principal series fields in de Sitter space must be positive. We also derive a limit on the amplitude of particular oscillatory signals from inflation, including those arising in cosmological collider physics. Finally, we demonstrate that these constraints manifest themselves directly in the two-point statistics of matter and galaxies that will be measured in upcoming surveys.

Spectral distortions from promising single and multifield inflationary models

Forthcoming missions probing the absolute intensity of the CMB are expected to be able to measurespectral distortions, which are deviations from its blackbody distribution. As cosmic inflation can induce spectraldistortions, these experiments offer a possibility to further test the various promising inflationaryproposals, whose predictions need to be carefully determined. After numerically fitting all inflationaryobservables to match current observations, we compute the predicted spectral distortions ofvarious promising single and multifield inflationary models. The predictions of single-fieldinflationary models display deviations between 0.5% and 20% with respect to the standard cosmologicalmodel in the observable window, where multi-natural and axion-monodromy inflation stand out in this respect.In the case of multifield inflation, we observe a richer structure of the power spectrum, which, inthe case of so-called hybrid attractors, yields spectral distortions about 100 times more intense thanthe standard signal. These observations open up questions about the relation among our resultsand other cosmological observables that are also to be probed soon, such as the production ofprimordial black holes and gravitational waves.

Supermassive primordial black holes from inflation

There is controversy surrounding the origin and evolution of our universe's largest supermassive black holes (SMBHs). In this study, we consider the possibility that some of these black holes formed from the direct collapse of primordial density perturbations. Since the mass of a primordial black hole is limited by the size of the cosmological horizon at the time of collapse, these SMBHs must form rather late, and are naively in conflict with constraints from CMB spectral distortions. These limits can be avoided, however, if the distribution of primordial curvature perturbations is highly non-Gaussian. After quantifying the departure from Gaussianity needed to evade these bounds, we explore a model of multi-field inflation — a non-minimal, self-interacting curvaton model — which has all the necessary ingredients to yield such dramatic non-Gaussianities. We leave the detailed model building and numerics to a future study, however, as our goal is to highlight the challenges associated with forming SMBHs from direct collapse and to identify features that a successful model would need to have. This study is particularly timely in light of recent observations of high-redshift massive galaxy candidates by the James Webb Space Telescope as well as evidence from the NANOGrav experiment for a stochastic gravitational wave background consistent with SMBH mergers.

(Multi-field) natural inflation and gravitational waves

We provide a detailed study of natural inflation with a periodic non-minimal coupling, which is a well-motivated inflationary model that admits an explicit UV completion. We demonstrate that this construction can satisfy the most recent observational constraints from Planck and the BICEP/Keck collaborations. We also compute the corresponding relic gravitational wave background due to tensor perturbations and show that future space-borne interferometers, such as DECIGO, BBO and ALIA, may be able to detect it. Next, we extend this analysis and establish the validity of these results in a multi-field model featuring an additional R 2 term in the action, which allows us to interpolate between natural and scalaron (a.k.a. Starobinsky) inflation. We investigate the conditions under which the aforementioned future interferometers will have the capability to differentiate between pure natural inflation and natural-scalaron inflation. The latter analysis could open the door to distinguishing between single-field and multi-field inflation through gravitational wave observations in more general contexts.

Testing multi-field inflation with LiteBIRD

We investigate expected constraints on the primordial tensor power spectrum from the future cosmic microwave background polarization experiment LiteBIRD as a test of multi-field inflation, where we specifically consider spectator models as representative examples. We argue that the measurements of the tensor-to-scalar ratio and the tensor spectral index, in combination with the constraints on the scalar spectral index from the Planck observation, are useful in testing multi-field inflation models. We also discuss implications for multi-field inflationary model building.

Non-Gaussianity in rapid-turn multi-field inflation

We show that theories of inflation with multiple, rapidly turning fields can generate large amounts of non-Gaussianity. We consider a general theory with two fields, an arbitrary field-space metric, and a potential that supports sustained, rapidly turning field trajectories. Our analysis accounts for non-zero field cross-correlation and does not fix the power spectra of curvature and isocurvature perturbations to be equal at horizon crossing. Using the δN formalism, we derive a novel, analytical formula for bispectrum generated from multi-field mixing on super-horizon scales. Rapid-turn inflation can produce a bispectrum with several potentially large contributions that are not necessarily of the local shape. We exemplify the applicability of our formula with a fully explicit model and show that the new contributions indeed can generate a large amplitude of local non-Gaussianity, f NL loc ∼ 𝒪(1). These results will be important when interpreting the outcomes of future observations.

Tracking the multifield dynamics with cosmological data: a Monte Carlo approach

We introduce a numerical method specifically designed for investigating generic multifield models of inflation where a number of scalar fields ϕ K are minimally coupled to gravity and live in a field space with a non-trivial metric 𝒢> IJ (ϕ K ). Our algorithm consists of three main parts. Firstly, we solve the field equations through the entire inflationary period, deriving predictions for observable quantities such as the spectrum of scalar perturbations, primordial gravitational waves, and isocurvature modes. We also incorporate the transfer matrix formalism to track the behavior of adiabatic and isocurvature modes on super-horizon scales and the transfer of entropy to scalar modes after the horizon crossing. Secondly, we interface our algorithm with Boltzmann integrator codes to compute the subsequent full cosmology, including the cosmic microwave background anisotropies and polarization angular power spectra. Finally, we develop a novel sampling algorithm able to efficiently explore a large volume of the parameter space and identify a sub-region where theoretical predictions agree with observations. In this way, sampling over the initial conditions of the fields and the free parameters of the models, we enable Monte Carlo analysis of multifield scenarios. We test all the features of our approach by analyzing a specific model and deriving constraints on its free parameters. Our methodology provides a robust framework for studying multifield inflation, opening new avenues for future research in the field.

Multifield positivity bounds for inflation

Positivity bounds represent nontrivial limitations on effective field theories (EFTs) if those EFTs are to be completed into a Lorentz-invariant, causal, local, and unitary framework. While such positivity bounds have been applied in a wide array of physical contexts to obtain useful constraints, their application to inflationary EFTs is subtle since Lorentz invariance is spontaneously broken during cosmic inflation. One path forward is to employ a Breit parameterization to ensure a crossing-symmetric and analytic S-matrix in theories with broken boosts. We extend this approach to a theory with multiple fields, and uncover a fundamental obstruction that arises unless all fields obey a dispersion relation that is approximately lightlike. We then apply the formalism to various classes of inflationary EFTs, with and without isocurvature perturbations, and employ this parameterization to derive new positivity bounds on such EFTs. For multifield inflation, we also consider bounds originating from the generalized optical theorem and demonstrate how these can give rise to stronger constraints on EFTs compared to constraints from traditional elastic positivity bounds alone. We compute various shapes of non-Gaussianity (NG), involving both adiabatic and isocurvature perturbations, and show how the observational parameter space controlling the strength of NG can be constrained by our bounds.

Multi-field inflation with large scalar fluctuations: non-Gaussianity and perturbativity

Recently multi-field inflation models that can produce large scalar fluctuations on small scales have drawn a lot of attention, primarily because they could lead to primordial black hole production and generation of large second-order gravitational waves. In this work, we focus on models where the scalar fields responsible for inflation live on a hyperbolic field space. In this case, geometrical destabilisation and non-geodesic motion are responsible for the peak in the scalar power spectrum. We present new results for scalar non-Gaussianity and discuss its dependence on the model's parameters. On scales around the peak, we typically find that the non-Gaussianity is large and close to local in form. We validate our results by employing two different numerical techniques, utilising the transport approach, based on full cosmological perturbation theory, and the δN formalism, based on the separate universe approximation. We discuss implications of our results for the perturbativity of the underlying theory, focusing in particular on versions of these models with potentially relevant phenomenology at interferometer scales.

Planck constraints and gravitational wave forecasts for primordial black hole dark matter seeded by multifield inflation

Planck constraints and gravitational wave forecasts for primordial black hole dark matter seeded by multifield inflation

Large primordial fluctuations in gravitational waves from phase transitions

It is well-known that first-order phase transitions in the early universe can be a powerful source of observable stochastic gravitational wave backgrounds. Any such gravitational wave background must exhibit large-scale anisotropies at least as large as those seen in the CMB 10−5, providing a valuable new window onto the (inflationary) origins of primordial fluctuations. While significantly larger fractional anisotropies are possible (for example, in multi-field inflation) and would be easier to interpret, it has been argued that these can only be consistent with CMB bounds if the gravitational wave signal is correspondingly smaller. In this paper, we show that this argument, which relies on assuming radiation dominance of the very early universe, can be evaded if there is an era of early matter dominance of a certain robust type. This allows large gravitational wave anisotropies to be consistent with observable signals at proposed future gravitational wave detectors. Constraints from the CMB on large scales, as well as primordial black hole and mini-cluster formation on small scales, and secondary scalar-induced gravitational waves are all taken into account.

Bootstrapping multi-field inflation: non-Gaussianities from light scalars revisited

Primordial non-Gaussianities from multi-field inflation are a leading target for cosmological observations, because of the possible large correlations generated between long and short distances.These signatures are captured by the local shape of the scalar bispectrum. In this paper, we revisit the nonlinearities of the conversion process from additional light scalars into curvature perturbations during inflation.We provide analytic templates for correlation functions valid at any kinematical configuration, using the cosmological bootstrap as a main computational tool. Our results include the possibility of large breaking of boost symmetry, in the form of small speeds of sound for both the inflaton and the mediators.We consider correlators coming from the tree-level exchange of a massless scalar field.By introducing a late-time cutoff, we identify that the symmetry constraints on the correlators are modified. This leads to anomalous conformal Ward identities, and consequently the bootstrap differential equations acquire a source term that depends on this cutoff.The solutions to the differential equations are scalar seed functions that incorporate these late-time growth effects. Applying weight-shifting operators to auxiliary “seed” functions, we obtain a systematic classification of shapes of non-Gaussianity coming from massless exchange.For theories with de Sitter symmetry, we compare the resulting shapes with the ones obtained via the δN formalism, identifying missing contributions away from the squeezed limit. For boost-breaking scenarios, we derive a novel class of shape functions with phenomenologically distinct features in scale-invariant theories.Specifically, the new shape provides a simple extension of equilateral non-Gaussianity: the signal peaks at a geometric configuration controlled by the ratio of the sound speeds of the mediator and the inflaton.

Turning in the landscape: A new mechanism for generating primordial black holes

We propose a new model-independent mechanism for producing primordial black holes from a period of multi-field inflation. This requires an enhancement of primordial fluctuations at short scales compared to their value at CMB scales. We show that such an amplification naturally occurs when the inflationary trajectory exhibits a strong turn, that is a limited period during which the trajectory strongly deviates from a geodesic in field space, and is sufficient for subsequently producing primordial black holes with the abundance to be all or a fraction of dark matter. Our mechanism is generic to models of inflation realized in a multi-dimensional field space with an overlying potential and geometry, also referred to as the inflationary landscape, as arises in embeddings of inflation in high-energy theories. We study analytically and numerically how the duration and the strength of the turn impact the primordial fluctuation power spectrum and the abundance of primordial black holes. Our mechanism has the potential of exhibiting unique features accessible to observation through the primordial black hole spectrum and the stochastic background of gravitational waves, offering a precious glimpse at the dynamics of inflation.

Scaling behavior of observables as a model characteristic in multifield inflation

One of the fundamental questions in inflation is how to characterize the structure of different types of models in the field theoretic landscape. Proposals in this direction include attempts to directly characterize the formal structure of the theory by considering complexity measures of the potentials. An alternative intrinsic approach is to focus on the behavior of the observables that result from different models and to ask whether their behavior differs among models. This type of analysis can be applied even to nontrivial multifield theories where a natural measure of the complexity of the model is not obvious and the analytical evaluation of the observables is often impossible. In such cases one may still compute these observables numerically and investigate their behavior. One interesting case is when observables show a scaling behavior, in which case theories can be characterized in terms of their scaling amplitudes and exponents. Generically, models have nontrivial parameter spaces, leading to exponents that are functions of these parameters. In such cases we consider an iterative procedure to determine whether the exponent functions in turn lead to a scaling behavior. We show that modular inflation models can be characterized by families of simple scaling laws and that the scaling exponents that arise in this way in turn show scaling in dependence of the varying energy scales.

Sharp turns in axion monodromy: primordial black holes and gravitational waves

Large turns in multifield inflation can lead to a very rich phenomenology, but are difficult to realise in supergravity, and typically require large field space curvatures. In this work, we present a mechanism to realise multiple sharp turns, and therefore strong non-geodesic trajectories, from transient violations of slow-roll without the requirement of large field space curvatures in supergravity inflation. Such turning rates can strongly source the adiabatic fluctuations, resulting in an enhanced scalar power spectrum with resonant features and a large peak amplitude. If the growth of the scalar power spectrum at small scales is large enough, primordial black holes can be produced in abundance. These large scalar fluctuations induce a characteristic large spectrum of gravitational waves for a wide range of frequencies, which inherits the resonant features. We illustrate this mechanism in a supergravity model of axion monodromy, which provides the first concrete model to realise such resonant features.The model can sustain inflation for around 60 e-folds, leading to considerable production of very light primordial black holes, and large gravitational wave spectra, which could be detectable by multiple upcoming gravitational wave surveys. For the set of parameter we consider, large oscillations occur at all scales. This represents a challenge for the model at large scales and motivates further investigation to reconcile this class of models with Planck data.

Completely dark matter from rapid-turn multifield inflation

We study cosmological gravitational particle production as applied to “rapid-turn” models of inflation involving two scalar fields. We are interested in the production of massive spin-0 particles that only interact gravitationally and provide a candidate for the dark matter. Specifically, we study two models of rapid-turn multifield inflation, motivated in part by the de Sitter swampland conjecture, that are distinguished by the curvature of field space and the presence or absence of field space ‘angular momentum’ conservation. We find that one of these models leads to insufficient particle production and cannot explain the observed dark matter relic abundance. The second model is able to explain the origin of spin-0 dark matter via gravitational production, and we identify the relevant region of parameter space that is consistent with measurements of the dark-matter relic abundance, the dark-matter-photon isocurvature perturbations, and the spectrum of curvature perturbations that is probed by cosmological observations. Our work demonstrates the compatibility of the de Sitter swampland conjecture with completely dark matter.

Mimetic curvaton

In this paper, we investigate the primordial perturbations of inflation model induced from the multi-field mimetic gravity, where there are two field during inflation, and thus both adiabatic and isocurvature perturbation modes are generated. We show that although it is true that the original adiabatic perturbation mode loses the kinetic term due to the constraint equation, by applying the curvaton mechanism where one of the field is viewed as curvaton field, the adiabatic perturbation can actually be transferred from the isocurvature one at the end of inflation. Detailed calculations are performed for both inflationary and the consequent matter-dominant epochs. Therefore, the so-called "non-propagating problem" of the adiabatic mode will actually do no harm to the multi-field mimetic inflation models.

Sneutrinos as two inflatons and curvaton and leptogenesis

We argue that sneutrinos can be embedded in a multi-field inflation framework where two inflatons and a curvaton simultaneously contribute to primordial fluctuations, which is consistent with current constraints on the spectral index and the tensor-to-scalar ratio from Planck and BICEP/Keck 2018. We also show that the same framework can also explain the baryon asymmetry of the Universe via leptogenesis realized by the decay of the lightest sneutrino. We investigate the parameter range for the scenario to work such as that of sneutrino masses. In particular, we show that the tensor-to-scalar ratio should be larger than 10-4 for a successful scenario.