Inflationary Models Research Articles

Primordial monopoles, black holes and gravitational waves

We show how topologically stable superheavy magnetic monopoles and primordial black holes can be generated at observable levels by the waterfall field in hybrid inflation models based on grand unified theories. In SU(5) ×U(1) χ grand unification, the monopole mass is of order 4 × 1017 GeV, and it carries a single unit (2 π /e) of Dirac magnetic charge as well as screened color magnetic charge. The monopole density is partially diluted to an observable value, and accompanied with the production of primordial black holes with mass of order 1017–1019 g which may make up the entire dark matter in the universe. The tensor to scalar ratio r is predicted to be of order 10-5–10 -4 which should be testable in the next generation of CMB experiments such as CMB-S4 and LiteBIRD. The gravitational wave spectrum generated during the waterfall transition is also presented. The observed baryon asymmetry can be explained via leptogenesis.

Loop blow-up inflation

We present a new model of string inflation driven by a blow-up Kähler modulus of type IIb compactifications with a potential generated by string loops. Slow-roll is naturally realized thanks to the fact that the blow-up mode is a leading-order flat direction lifted by string loops which are unavoidable and generate a plateau at large field values. We check that throughout the whole inflationary dynamics the effective field theory is under control. We perform a phenomenological analysis determining the exact number of efoldings by studying the post-inflationary evolution. We determine the values of the microscopic parameters which lead to agreement with CMB data, together with the prediction of a tensor-to-scalar ratio of order r ∼ 10−5.

Primordial non-Gaussianity as a saviour for PBH overproduction in SIGWs generated by pulsar timing arrays for Galileon inflation

We investigate the explicit role of negative local non-Gaussianity, fNL, in suppressing the abundance of primordial black holes (PBHs) in the single-field model of Galileon inflation. PBH formation requires significantly enhancing the scalar power spectrum, which greatly affects their abundance. The associated frequencies in the nHz regime are also sensitive to the generation of scalar-induced gravitational waves (SIGWs) which may explain the current data from the pulsar timing arrays (PTAs). Our analysis using the threshold statistics on the compaction function demonstrates that Galileon theory not only avoids PBH overproduction using the curvature perturbation enhancements that give fNL∼O(−6), but also generates SIGWs that conform well with the PTA data.

Ward identities under the frame transformations in curved space-time

Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity, as they are used to build feasible models for cosmic inflation. These theories can be formulated both in the Jordan and Einstein frame, which are related by a Weyl transformation with a field transformation, known together as a frame transformation. These theories formulated in the above two frames are often considered to be equivalent from the point of view of classical theory. However, this is no longer true from the quantum field theoretical perspective. In the present article, we show that the Ward identities derived in the above two frames are not connected through the frame transformation. This shows that the quantum field theories formulated in these two frames are not equivalent to each other. Moreover, this inequivalence is also shown by comparing the effective actions derived in these two frames.

Swampland program for hypergeometric inflation scenarios in rescaled gravity

In this paper, we investigate hypergeometric stringy corrections in the swampland program for rescaled gravity. Precisely, we study inflationary models from Gauss–Bonnet hypergeometric scalar couplings via the falsification scenario. We first derive generalized exponential potentials from such hypergeometric behaviors. Then, we examine certain selected scalar potentials by computing the relevant cosmological quantities using the slow-roll mechanism. Choosing specific points in the corresponding moduli space, we provide viable findings corroborated by Planck observational data and checked by the swampland criteria.

Starobinsky inflation in the swampland

We argue that the Starobinsky model of inflation, realised via an R2 term in the Lagrangian, can originate from quantum effects due to a tower of light species. By means of two separate arguments, we show how this implies that the scale of the R2 term must be of order of the species scale Λs, namely the energy at which gravity becomes strongly coupled. We discuss the implications and challenges of this scenario for inflation, inflationary reheating, and string theory embeddings. In this context, we collect strong evidence to conclude that Starobinsky inflation lies in the Swampland.

Warm inflation in a Universe with a Weylian boundary

We investigate the influence of boundary terms in the warm inflationary scenario, by considering that in the Einstein–Hilbert action the boundary can be described in terms of a Weyl-type geometry. The gravitational action, as well as the field equations, are thus extended to include new geometrical terms, coming from the non-metric nature of the boundary, and depending on the Weyl vector, and its covariant derivatives. We investigate the effects of these new boundary terms by considering the warm inflationary scenario of the early evolution of the Universe, in the presence of a scalar field. We obtain the generalized Friedmann equations in the Universe with a Weylian boundary by considering the Friedmann–Lemaitre–Robertson–Walker metric. We consider the simultaneous decay of the scalar field, and of the creation of radiation, by appropriately splitting the general conservation equation through the introduction of the dissipation coefficient, which can depend on both the scalar field, and the Weyl vector. We consider three distinct warm inflationary models, in which the dissipation coefficients are chosen as different functions of the scalar field and of the Weyl vector. The numerical solutions of the cosmological evolution equations show that the radiation is created during the very early phases of expansion, and, after the radiation reaches its maximum value, the transition from an accelerating inflationary phase to a decelerating one takes place. Moreover, it turns out that the Weyl vector, describing the boundary effects on the cosmological evolution, plays a significant role during the process of radiation creation.

Constant-roll inflation with non-minimally derivative coupling

We investigate the constant-roll inflation with non-minimally kinetic coupling to the Einstein tensor. With the slow-roll parameter ηϕ=−ϕ̈/(Hϕ̇) being a constant, we calculate the power spectra for scalar and tensor perturbations, and derive the expressions for the scalar spectral tilt n s , the tensor spectral tilt n T , and the tensor-to-scalar ratio r. We find that the expressions for n s are different with different ordering of taking the derivative of the scalar power spectrum with respect to the scale k and the horizon crossing condition c s k = aH in the constant-roll inflation, the consistency relation r = − 8n T does not hold if ∣η ϕ ∣ is not small, and the duality of the tensor-to-scalar ratio between the slow-roll inflation and ultra-slow-roll inflation does not exist in inflationary models with non-minimally derivative coupling. The result offers a fresh perspective on the understanding of the inflationary models with non-minimally derivative coupling and is helpful for the production of scalar induced gravitational waves in the framework of ultra-slow-roll inflation with non-minimally derivative coupling.

Connecting Cosmic Inflation to Particle Physics with LiteBIRD, CMB-S4, EUCLID, and SKA.

We show that next generation Cosmic Microwave Background (CMB) experiments will be capable of the first ever measurement of the inflaton coupling to other particles, opening a new window to probe the connection between cosmic inflation and particle physics. This sensitivity is based on the impact that the reheating phase after cosmic inflation has on the redshifting of cosmic perturbations. For our analysis we introduce a simple analytic method to estimate the sensitivity of future CMB observations to the reheating temperature and the inflaton coupling. Applying our method to LiteBIRD and CMB-S4 we find that, within a given model of inflation, these missions have the potential to impose both an upper and a lower bound on the inflaton coupling. Further improvement can be achieved if CMB data are combined with optical and 21cm surveys. Our results demonstrate the potential of future observations to constrain microphysical parameters that can provide an important clue to understand how a given model of inflation may be embedded in a more fundamental theory of nature.

Multifield stochastic dynamics in GUT hybrid inflation without monopole problem and with gravitational wave signatures of GUT Higgs representation

We revisit the hybrid inflation model within the framework of the Grand Unified Theory (GUT), focusing on cases where the waterfall phase transition extends over several e-foldings to dilute monopoles. Considering the stochastic effects of quantum fluctuations, we demonstrate that the waterfall fields (i.e., GUT Higgs) maintain a nonzero vacuum expectation value around the waterfall phase transition. By accurately accounting for the number of degrees of freedom of the GUT Higgs field, we establish that these fluctuations can produce observable gravitational waves without leading to an overproduction of primordial black holes. The amplitude of these gravitational waves is inversely proportional to the degrees of freedom of the waterfall fields, thereby providing a unique method to probe the representation of the GUT Higgs.

Scalar fields, localized structures and the Starobinsky model

This work deals with the presence of localized static structures in the real line, described by relativistic real scalar fields in two spacetime dimensions. We consider models featuring both standard and modified kinematics, where we employ two intriguing potentials supporting defect solutions. The first potential can transform kink into compacton in the standard framework, while the second one is based on the inflationary Starobinsky model. Interesting possibilities unseen in previous investigations are described, in particular, for the case related to the Starobinsky potential. The addressed potentials are inserted into a broader framework, and so the extended models are described by a wider set of solutions. This investigation also reveals the presence of the twinlike behaviour for a specific compact configuration, which solves two distinct models.

Cosmic Inflation at the crossroads

The capability of Cosmic Inflation to explain the latest Cosmic Microwave Background and Baryonic Acoustic Oscillation data is assessed by performing Bayesian model comparison within the landscape of nearly three-hundred models of single-field slow-roll inflation. We present the first Bayesian data analysis based on the third-order slow-roll primordial power spectra. In particular, the fourth Hubble-flow function ε4 remains unbounded while the third function verifies, at two-sigma, ε3 ∈[-0.4,0.5], which is perfectly compatible with the slow-roll predictions for the running of the spectral index. We also observe some residual excess of B-modes within the BICEP/Keck data favoring, at a non-statistically significant level, non-vanishing primordial tensor modes: log(ε1) > -3.9, at 68% confidence level. Then, for 287 models of single-field inflation, we compute the Bayesian evidence, the Bayesian dimensionality and the marginalized posteriors of all the models' parameters, including the ones associated with the reheating era. The average information gain on the reheating parameter R reh reaches 1.3 ± 0.18 bits, which is more than a factor two improvement compared to the first Planck data release. As such, inflationary model predictions cannot meet data accuracy without specifying, or marginalizing over, the reheating kinematics. We also find that more than 40% of the scenarios are now strongly disfavored, which shows that the constraining power of cosmological data is winning against the increase of the number of proposed models. In addition, about 20% of all models have evidences within the most probable region and are all favored according to the Jeffreys' scale of Bayesian evidences.

First constraints on non-minimally coupled Natural and Coleman-Weinberg inflation and massive neutrino self-interactions with Planck+BICEP/Keck

In this work, for the first time in literature, we study the predictions of non-minimally coupled Natural and Coleman-Weinberg potentials in the ns -r plane, and an extended ΛCDM model where we include non-standard self-interactions among massive neutrinos, mediated by a heavy scalar or vector boson. Constraints were derived using the Planck 2018 + BICEP/Keck 2018 datasets along with other data. For the inflationary potentials, we consider two different formulations in gravity that are non-minimally coupled to the scalar field of the inflaton: Metric and Palatini. We only consider the self-interaction to be present among τ-neutrinos and only at moderate strengths. This is because strong interactions among τ-neutrinos, or any strength self-interaction among electron- and muon-neutrinos, as well as any strength flavor-universal interactions, are strongly disfavoured from particle physics experiments.In terms of cosmological data, we use the latest public CMB datasets from Planck 2018 and BICEP/Keck 2018 collaborations, along with other data from CMB lensing, BAO, RSD, and SNe Ia luminosity distance measurements. We find that there are some situations where predictions from the inflationary models are ruled out at more than 2σ by the minimal ΛCDM+r model, but they are allowed in the self-interacting neutrino scenario.

Inflation and Higgs phenomenology in a model unifying the DFSZ axion with the majoron

The Two-Higgs-Doublet-Standard Model-Axion-Seesaw-Higgs-Portal inflation (2hdSMASH) model consisting of two Higgs doublets, a Standard Model (SM) singlet complex scalar and three SM singlet right-handed neutrinos can embed axion dark matter, neutrino masses and address inflation. We report on an investigation of the inflationary aspects of 2hdSMASH and its subsequent impact on low energy phenomenology. In particular, we identify inflationary directions for which the parameter values required for successful inflation do not violate perturbative unitarity and boundedness-from-below conditions. By analyzing the renormalization-group flow of the parameters we identify the necessary and sufficient constraints for running all parameters perturbatively and maintaining stability from the electroweak to the PLANCK scale. We observe that stringent constraints arise on the singlet scalar self coupling from inflationary constraints, i.e., λS ∼ 10-10. Further, we find that all theoretical and experimental constraints are satisfied if the portal couplings are typically in the range (v/vS ) and (v/vS )2 (where v, vS refer to the electroweak and singlet scalar vacuum expectation value respectively). As a consequence, inflation is realized in a variety of field space directions in the effective single field regime. Finally we provide testable benchmark scenarios at colliders.

Development of generic no-scale inflation

We develop generalized no-scale supergravity models of inflation, and then study the corresponding cosmological predictions as well as the formation of primordial black holes (PBHs) and scalar-induced gravitational waves (SIGWs). With a new parameter 0 < a ≤ 1, the generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index ns , and tensor-to-scalar ratio r can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with a ≠ 1 give a smaller ratio r ≤ 10-3, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of PBHs with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.

Testing scale-invariant inflation against cosmological data

There is solid theoretical and observational motivation behind the idea of scale-invariance as a fundamental symmetry of Nature. We consider a recently proposed classically scale-invariant inflationary model, quadratic in curvature and featuring a scalar field non-minimally coupled to gravity. We go beyond earlier analytical studies, which showed that the model predicts inflationary observables in qualitative agreement with data, by solving the full two-field dynamics of the system — this allows us to corroborate previous analytical findings and set robust constraints on the model's parameters using the latest Cosmic Microwave Background (CMB) data from Planck and BICEP/Keck. We demonstrate that scale-invariance constrains the two-field trajectory such that the effective dynamics are that of a single field, resulting in vanishing entropy perturbations and protecting the model from destabilization effects. We derive tight upper limits on the non-minimal coupling strength, excluding conformal coupling at high significance. By explicitly sampling over them, we demonstrate an overall insensitivity to initial conditions. We argue that the model predicts a minimal level of primordial tensor modes set by r ≳ 0.003, well within the reach of next-generation CMB experiments. These will therefore provide a litmus test of scale-invariant inflation, and we comment on the possibility of distinguishing the model from Starobinsky and α-attractor inflation. Overall, we argue that scale-invariant inflation is in excellent health, and possesses features which make it an interesting benchmark for tests of inflation from future CMB data.

The cosmological collider in R 2 inflation

Starobinsky's R 2 inflation manifests a best-fit scenario for the power spectrum of primordial density fluctuations. Observables derived from the slow-roll picture of the R 2 model in the Einstein frame relies on the conformal transformation of the metric, which inevitably induces a unique exponential-type couplings of the rolling scalaron with all matter fields during inflation. The “large-field” nature of the R 2 model further invokes non-negligible time and scale dependence to the matter sector through such an exponential coupling, modifying not only the dynamics of matter perturbations on superhorizon scales but also their decay rates. In this work, we identify the simplest observable of the cosmological collider physics built in the background of R 2 inflation, focusing on the so-called “quantum primordial clock” signals created by the non-local propagation of massive scalar perturbations. Our numerical formalism based on the unique conformal coupling can have extended applications to (quasi-)single-field inflationary models with non-trivial couplings to gravity or models that originated from the f(R) modification of gravity.

One-loop power spectrum in ultra slow-roll inflation and implications for primordial black hole dark matter

We apply the in-in formalism to address the question of whether the size of the one-loop spectrum of curvature fluctuations in ultra-slow-roll inflation models designed for producing a large population of primordial black holes implies a breakdown of perturbation theory. We consider a simplified piece-wise description of inflation, in which the ultra-slow-roll phase is preceded and followed by slow-roll phases linked by transitional periods. We work in the δϕ-gauge, including all relevant cubic and quartic interactions and the necessary counterterms to renormalize the ultraviolet divergences, regularized by a cutoff. The ratio of the one-loop to the tree-level contributions to the spectrum of curvature perturbations is controlled by the duration of the ultra-slow-roll phase and of the transitions. Our results indicate that perturbation theory does not necessarily break in well-known models proposed to account for all the dark matter in the form of primordial black holes.

Seminal electromagnetic fields from preinflation

We investigate the geometric dynamics of the primordial electric and magnetic fields during the early stages of the universe by extending a recently introduced quantum algebra (Bellini et al., 2023). We work on an extended model of gravity that considers the boundary terms from the Einstein–Hilbert action as geometric quantum fluctuations of the spacetime. We propose that the extended Riemann manifold is generated by a new connection δΓˆαβμ. This connection contains geometric information about the fluctuations of gravitational and electromagnetic fields in the vacuum, which could have been crucial during the primordial stages of the universe’s evolution. We revisit a preinflationary cosmological model (Bellini, 2023) with a variable time scale and negative spatial curvature, such that the universe begins with a null initial background energy density. We observed the emergence of large scale magnetic fields starting from small values during the early phases of the universe’s evolution. Subsequently, these fields decrease to reach present day values on the order of δBˆ≃10−12G on cosmological scales (between 1024 and 1026 meters). This significant deviation from inflationary models eliminates the need to impose excessively large initial values on these fields.

The de Sitter Swampland Conjectures in the Context of Chaplygin-Inspired Inflation

In this work, we discuss the de Sitter swampland conjectures in the context of the generalized Chaplygin-inspired inflationary model. We demonstrate that these conjectures can be satisfied, but only in the region of the parameter space far away from the General Relativity limit. The cosmic microwave background data had already been found to restrict the allowed inflationary potentials of this model. Our results impose a further limitation on the possible potentials.