Inflationary Models Research Articles

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.

Numerical 1-loop correction from a potential yielding ultra-slow-roll dynamics

Single-field models of inflation might lead to amplified scalar fluctuations on small scales due, for example, to a transient ultra-slow-roll phase. It was argued by Kristiano & Yokoyama in ref. [1] that the enhanced amplitude of the scalar power spectrum on small scales has the potential to induce a sizeable 1-loop correction to the spectrum at large scales. In this work, we repeat the calculation for the 1-loop correction presented in ref. [1]. We closely follow their assumptions but evaluate the loop numerically. This allows us to consider both instantaneous and smooth transitions between the slow-roll and ultra-slow-roll phases. In particular, we generate models featuring realistic, smooth evolution from an analytic inflationary potential. We find that, upon fixing the amplitude of the peak in the power spectrum at short scales, the resulting 1-loop correction is not significantly reduced by considering a smooth evolution. In particular, for a power spectrum with a tree-level peak amplitude potentially relevant for small-scale phenomenology, e.g. primordial black hole production, the 1-loop correction on large scales is a few percent of the tree-level power spectrum.

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.

Primordial Black Holes in Scalar Field Inflation Coupled to the Gauss–Bonnet Term with Fractional Power-law Potentials

In this study, we investigate the formation of primordial black holes (PBHs) in a scalar field inflationary model coupled to the Gauss–Bonnet term with fractional power-law potentials. The coupling function enhances the curvature perturbations, then results in the generation of PBHs and detectable secondary gravitational waves (GWs). We identify three separate sets of parameters for the potential functions of the form ϕ 1/3, ϕ 2/5, and ϕ 2/3. By adjusting the model parameters, we decelerate the inflaton during the ultra-slow-roll phase and enhance curvature perturbations. Our calculations predict the formation of PBHs with masses of O(10)M⊙ , which are compatible with LIGO-Virgo observational data. Additionally, we find PBHs with masses around O(10−6)M⊙ and O(10−5)M⊙ , which can explain ultra-short-timescale microlensing events in OGLE data. Furthermore, our proposed mechanism could lead to the formation of PBHs in mass scales around O(10−14)M⊙ and O(10−13)M⊙ , contributing to approximately 99% of the dark matter in the Universe. We also study the production of secondary GWs in our model. In all cases of the model, the density parameter of secondary GWs ΩGW0 exhibits peaks that intersect the sensitivity curves of GW detectors, providing a means to verify our findings using data of these detectors. Our numerical results demonstrate a power-law behavior for the spectra of ΩGW0 with respect to frequency, given by ΩGW0(f)∼(f/fc)n . Additionally, in the infrared regime where f ≪ f c , the power index takes a log-dependent form, specifically n=3−2/ln(fc/f) .

Inflationary models constrained by reheating

The study of reheating in inflationary models is crucial to understand the early universe and obtain information about the dynamics and parameters of inflation. The reheating temperature Tre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{re}$$\\end{document} and the duration of the reheating phase, quantified by the number of e-folds Nre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{re}$$\\end{document}, have significant implications for particle production, thermalisation, and the primordial power spectrum. The duration of reheating affects the abundance of particles, including dark matter, and shapes the primordial power spectrum and the anisotropies of the cosmic microwave background. By combining cosmological observations and theoretical considerations, we can constrain both Tre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{re}$$\\end{document} and Nre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{re}$$\\end{document}, which in turn restrict the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r, and the parameters of the inflationary model. The use of consistency relations between observables, such as ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document} and r, provides additional constraints on inflationary models and determines limits for other observables, such as the running of the scalar spectral index. These limits are valuable for assessing the viability of models and can serve to specify priors in Bayesian analyses of specific models. As an example of how to proceed, we study in detail a particular case of a generalized α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-attractor model that accurately reproduces the observed quantities. We present equations for the conditions of instantaneous reheating, establish consistency relations, and explore the generalized α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-attractor model using cosmological data. We study the model defined by its potential as a given formula and, furthermore, considering its possible origin in supergravity theories, we impose constraints on the reheating temperature to avoid the overproduction of gravitinos.

Solution for cosmological observables in the Starobinsky model of inflation

This paper focuses on the Starobinsky model of inflation in the Einstein frame. We derive solutions for various cosmological observables, such as the scalar spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r and their runnings, as well as the number of e-folds of inflation, reheating, and radiation, with minimal assumptions. The impact of reheating on inflation is explored by constraining the equation of state parameter ωre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{re}$$\\end{document} at the end of reheating. An equation linking inflation with reheating is established, which is solved for the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}. Using consistency relations of the model, we determine the other observables while the number of e-folds during inflation Nk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_k$$\\end{document}, and the number of e-folds during reheating Nre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{re}$$\\end{document} are determined by their respective formulas involving ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}. We find remarkable agreement between the Starobinsky model and current measurements of the power spectrum of primordial curvature perturbations and the present bounds on the spectrum of primordial gravitational waves.

A coupled-fluid approach to explore bounce and inflationary cosmology with Barrow holographic as the driving dark fluid

Assuming that viscous fluid in the form of Barrow holographic dark energy (BHDE) (a particular case of more generalized version of HDE elaborated in Nojiri et al. in Phys Lett B 825:136844, 2022; Symmetry 13(6):928, 2021) and pressure-less dark matter are present across the flat Friedmann–Robertson–Walker universe, we find the precise solutions of viscous BHDE models in non-interacting and interacting scenarios for different choices of scale factor. We show the evolution of the EoS parameters in the viscous non-interacting and interacting situations together with the deceleration parameters for observing the transition time frame. Afterwards, we investigate a bounce inflation model using the analytical results of model’s slow-roll parameters, scalar spectral index, and tensor-to-scalar ratio. We investigated an association between BHDE and scalar field models since inflation is typically attributed to the existence of scalar fields. The evolution of the generated potential from the scalar fields are plotted against time. Finally, we investigated the GSL of the thermodynamics.

Searching for local features in primordial power spectrum using genetic algorithms

ABSTRACT We present a novel methodology for exploring local features directly in the primordial power spectrum using a genetic algorithm pipeline coupled with a Boltzmann solver and Cosmic Microwave Background data (CMB). After testing the robustness of our pipeline using mock data, we apply it to the latest CMB data, including Planck 2018 and CamSpec PR4. Our model-independent approach provides an analytical reconstruction of the power spectra that best fits the data, with the unsupervised machine learning algorithm exploring a functional space built off simple ‘grammar’ functions. We find significant improvements upon the simple power-law behaviour, by Δχ2 ≲ −21, consistently with more traditional model-based approaches. These best-fits always address both the low-ℓ anomaly in the TT spectrum and the residual high-ℓ oscillations in the TT, TE, and EE spectra. The proposed pipeline provides an adaptable tool for exploring features in the primordial power spectrum in a model-independent way, providing valuable hints to theorists for constructing viable inflationary models that are consistent with the current and upcoming CMB surveys.

Impact of the Hubble tension on the r − ns contour

The injection of early dark energy (EDE) before the recombination, a possible resolution of the Hubble tension, will not only shift the scalar spectral index ns towards ns=1, but also be likely to tighten the current upper limit on tensor-to-scalar ratio r. In this work, with the latest CMB datasets (Planck PR4, ACT, SPT and BICEP/Keck), as well as BAO and SN, we confirm this result, and discuss its implication on inflation. We also show that if we happen to live with EDE, how the different inflation models currently allowed would be distinguished by planned CMB observations, such as CMB-S4 and LiteBIRD.

Spontaneous baryogenesis and generation of gravitational waves in a new model of quintessential [formula omitted]-attractor

We study the role of α-parameter of the newly proposed model of quintessential α-attractor inflation (arXiv: 2305.00230 [gr-qc]) to the case of quintessential spontaneous baryogenesis and generation of relic gravitational waves in presence of a rolling scalar field during kination. An effective 4-Fermi construct technique has been employed to compute the freeze-out temperature and the baryon-to-entropy ratio, of which the obtained results conform to the experimental requirements for 0.28≤α≤0.30. This range of α is found to originate from the functional behavior of the end-value expression of the potential concerned. We also find a blue-tilted gravitational wave spectrum during a transition from inflation to kination. The amplitudes of the gravitational waves during radiation domination satisfy the constraint for nucleosynthesis and the characteristic strain of the ongoing gravitational wave detectors. Thus, the most important observation emerged from the present study is that, increasingly small fractional values of α are favorable for unification of inflation, baryogenesis, quintessence and gravitational waves within a single model. This could have an interesting connection with the fundamental origin of α-attractor.

Constraints on real scalar inflation from preheating using LATTICEEASY* *Wei Cheng was Supported by the Natural Science Foundation of Chongqing, China (CSTB2022NSCQ-MSX0432), the Science and Technology Research Project of Chongqing Education Commission (KJQN202200621), and the Chongqing Human Resources and Social Security Administration Program (D63012022005). Ruiyu Zhou was Supported by the Chongqing Natural Science Foundation (CSTB2022NSCQ-MSX0534). This work was supported in

In this paper, we undertake a detailed study of real scalar inflation using LATTICEEASY simulations to investigate preheating phenomena. Generally, the scalar inflation potential with non-minimal coupling can be approximated using a quartic potential. We observe that the evolutionary behavior of this potential remains unaffected by the coupling coefficient. Furthermore, the theoretical predictions for the scalar spectral index ( ) and tensor-to-scalar power ratio (r) are independent of this coefficient. Consequently, the coefficients of this model are not constrained by Planck observations. Fortunately, the properties of preheating after inflation provide a viable approach to examining these coefficients. Through LATTICEEASY simulations, we trace the evolution of particle number density, scale factor, and energy density during the preheating process. Subsequently, we derive the parameters, such as the energy ratio (γ) and the e-folding number of preheating ( ), which facilitate further predictions of and r. We successfully validate real scalar inflation model using preheating in LATTICEEASY simulations based on the analytical relationship between preheating and inflation models.

Inflation correlators with multiple massive exchanges

The most general tree-level boundary correlation functions of quantum fields in inflationary spacetime involve multiple exchanges of massive states in the bulk, which are technically difficult to compute due to the multi-layer nested time integrals in the Schwinger-Keldysh formalism. On the other hand, correlators with multiple massive exchanges are well motivated in cosmological collider physics, with the original quasi-single-field inflation model as a notable example. In this work, with the partial Mellin-Barnes representation, we derive a simple rule, called family-tree decomposition, for directly writing down analytical answers for arbitrary nested time integrals in terms of multi-variable hypergeometric series. We present the derivation of this rule together with many explicit examples. This result allows us to obtain analytical expressions for general tree-level inflation correlators with multiple massive exchanges. As an example, we present the full analytical results for a range of tree correlators with two massive exchanges.

Non-perturbative wavefunction of the universe in inflation with (resonant) features

We study the statistics of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential (resonant non-Gaussianity). We do so by deriving the wavefunction Ψ[ζ(x)] non-perturbatively in ζ, but at first order in the amplitude of the oscillations. The expression of the wavefunction of the universe (WFU) is explicit and does not require solving partial differential equations. One finds qualitative deviations from perturbation theory for |ζ| ≳ α−2, where α ≫ 1 is the number of oscillations per Hubble time. Notably, the WFU exhibits distinct behaviours for negative and positive values of ζ (troughs and peaks respectively). While corrections for ζ < 0 remain relatively small, of the order of the oscillation amplitude, positive ζ yields substantial effects, growing exponentially as eπα/2 in the limit of large ζ. This indicates that even minute oscillations give large effects on the tail of the distribution.

Inflation Driven by Nonlinear Electrodynamics in Anisotropic Spacetime

The well-known Big Bang theory has explained how the universe came into being. This extraordinary event caused the later universe to be accelerated by a scale factor a(t). However, standard Big Bang theory has had some problems that can’t be explained, such as monopoles, horizons, and flatness. To solve this problem, a model of inflation in the early universe is required. Recent studies show that nonlinear electrodynamics coupled with general relativity can describe the inflation of the universe. In this work, we consider a model of nonlinear electrodynamics in anisotropic spacetime. We derive the dynamical equation from Einstein’s field equation and the law of conservation of energy-momentum tensor. Then, we use the perturbation method to solve the dynamical equation of the universe and obtain the evolution of the non-singular scale factor with anisotropy parameter ϵ. Using a phase-space analysis of the inflationary model, we obtain a phase portrait in the presence of fixed points. Our result shows that in the model of nonlinear electrodynamics coupled to gravity in anisotropic spacetime, the universe can undergo an inflationary mechanism if ϵ < 1. We also show the absence of singularity in density and pressure using this model.

Ricci reheating reloaded

A Hubble-induced phase transition is a natural spontaneous symmetry breaking mechanism allowing for explosive particle production in non-oscillatory models of inflation involving non-minimally coupled spectator fields. In this work, we perform a comprehensive characterisation of this type of transitions as a tachyonic Ricci-heating mechanism, significantly extending previous results in the literature. By performing 𝒪 (100) 3+1-dimensional classical lattice simulations, we explore the parameter space of two exemplary scenarios, numerically determining the main timescales in the process. Based on these results, we formulate a set of parametric equations that offer a practical approach for determining the efficiency of the heating process, the temperature at the onset of radiation domination, and the minimum number of e-folds of inflation needed to resolve the flatness and horizon problems in specific quintessential inflation scenarios. These parametric equations eliminate the need for additional lattice simulations, providing a convenient and efficient method for evaluating these key quantities.

(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.

Deblurring the early Universe: reconstruction of primordial power spectrum from Planck CMB using image analysis techniques

While the simplest inflationary models predict the primordial perturbations to be near scale-invariant, the primordial power spectrum (PPS) can exhibit oscillatory features in many physically well-motivated models. We search for hints of such features via free-form reconstructions of the PPS based on Planck 2018 CMB temperature and polarization anisotropies. In order to robustly invert the oscillatory integrals and handle noisy unbinned data, we draw inspiration from image analysis techniques. In previous works, the Richardson-Lucy deconvolution algorithm for deblurring images has been modified for reconstructing PPS from the CMB temperature angular power spectrum. We extensively develop the methodology by including CMB polarization and introducing two new regularization techniques, also inspired by image analysis and adapted for our cosmological context. Regularization is essential for improving the fit to the temperature and polarization channels (TT, TE and EE) simultaneously without sacrificing one for another. The reconstructions we obtain are consistent with previous findings from temperature-only analyses. We evaluate the statistical significance of the oscillatory features in our reconstructions using mock data and find the observations to be consistent with having a featureless PPS. The machinery developed here will be a complimentary tool in the search for features with upcoming CMB surveys. Our methodology also shows competitive performance in image deconvolution tasks, which have various applications from microscopy to medical imaging.

An exact model for enhancing/suppressing primordial fluctuations

Abstract Enhancements of primordial curvature fluctuations in single field inflation often involve departures from attractor trajectories in the phase space. We study enhancement/suppression of primordial fluctuations in one of the simplest models with exact background solutions for arbitrary initial conditions: a single field inflationary model with a piecewise exponential potential. We then present close to exact analytical solutions for primordial fluctuations in a general transition between two slow-roll attractors, valid whether the first slow parameter increases or decreases. The main features in the primordial spectrum are determined by the ratio of exponents of the potential. We also discuss the imprint of such features in the induced GW spectrum. Lastly, we apply the δN formalism to discuss non-Gaussianities and the tail of the probability distribution. We find that while non-Gaussianities are at most 𝒪(1) in the case of enhancement, they can be very large in the case of suppression. Our work can be easily generalized to multiple piecewise exponential potentials.

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.

Inflation, superheavy metastable strings and gravitational waves in non-supersymmetric flipped SU(5)

Motivated by the NANOGrav 15 year data and other recent investigations of stochastic gravitational background radiation based on pulsar timing arrays, we show how superheavy strings survive inflation but the slightly heavier monopoles do not in a non-supersymmetric hybrid inflation model based on flipped SU(5). With the dimensionless string tension parameter Gμ ∼ 10-6, the gravitational wave spectrum emitted by the strings, which are metastable due to breaking caused by monopole-antimonopole quantum mechanical tunneling, is compatible with the latest NANOGrav measurement as well as the advanced LIGO-VIRGO third run data. The string network undergoes about 30 e-foldings of inflation which suppresses the spectrum in the LIGO-VIRGO frequency range. With the symmetry breaking chain SU(5)×U(1) X → SU(3) c ×SU(2) L ×U(1) Z ×U(1) X → SU(3) c ×SU(2) L ×U(1) Y , the estimated proton lifetime is of order 1036-1037 yrs.