Inflationary Models Research Articles

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.

Inflation, Unemployment, and Inequality: Beyond the Traditional Phillips Curve

ABSTRACT This article undertakes a theoretical post-Keynesian analysis to explore the relationship between inflation, unemployment, and inequality. Firstly, we show the compatibility of the inequality-augmented Phillips curve, which first appeared in Rolim, Carvalho, and Lang (2023), with the post-Keynesian macroeconomic theory. The curve combines the Phillips curve, which relates unemployment and inflation and can be derived from the conflicting-claims inflation model, with the positive relation between unemployment and inequality due to the heterogeneous impact of unemployment on workers. The unemployment rate thus connects the inflation rate to income inequality in a three-dimensional relationship described by the inequality-augmented Phillips curve, which indicates a possible trade-off between low inflation and low inequality. Secondly, we consider the profits inflation case: when inflation is simultaneous with markup increases. Increases in the ex-ante markup rate shift the curve upwards, thus increasing the inflation rate and inequality. In this context, if monetary policy aims to control inflation by increasing unemployment, it will operate along the inequality-augmented Phillips curve and will further increase inequality.

Kaleckian Models of Conflict Inflation, Distribution and Employment: A Comparative Analysis

ABSTRACT This paper conducts a systematic comparison of two main textbook variants within the Kaleckian tradition of post-Keynesian conflict inflation and distribution theory: the Blecker and Setterfield (2019) and Lavoie (1992; 2022) (BSL) model based on Dutt (1987), and the Hein (2023a) and Hein and Stockhammer (2011) (HS) model founded on Rowthorn (1977). Focusing on a basic closed economy framework sans government, we explore various iterations of each approach. Our analysis reveals that disparities chiefly centre around the treatment of price inflation expectations (‘indexation’) and the incorporation of bargaining power in wage- and price-inflation equations. BSL variants generally yield stable price Phillips curves, stable distribution and employment curves, and hence stable equilibria. Only the BSL-3 variant with complete indexation and complete pass-through generates shifting Phillips and employment curves, implying instability. It is thus similar to the HS-0 approach, which has bargaining power and complete indexation representing adaptive expectations in wage inflation and incomplete pass-through in price inflation. Introducing a workers’ wage share target directly into the wage-inflation equation, but keeping full indexation/adaptive expectations in wage inflation and incomplete pass-through in price inflation, allows for stable and even flat Phillips curves, stable distribution and employment curves, and hence stable equilibria in the HS approach.

A Latticework of Inflation Models

A Latticework of Inflation Models

Statistical Anisotropy of Primordial Gravitational Waves from Generalized δN Formalism.

In this Letter, we demonstrate how to use the generalized δN formalism, which enables us to compute the evolution of all the large-scale fluctuations, including gravitational waves, solely by solving the evolution of the background homogeneous Universe. Using the Noether charge density, we derive an analytic formula which describes the mapping between the fluctuations at the horizon crossing and the sourced gravitational waves at the end of inflation. This formula can apply also to an inflation model with an anisotropic background. Using this formula, we discuss the condition for the nonvanishing linear polarization and the qualitative difference between single- and multigauge field models.

Forecast Cosmological Constraints with the 1D Wavelet Scattering Transform and the Lyman-α Forest.

We make forecasts for the constraining power of the 1D wavelet scattering transform when used with a Lyman-α forest cosmology survey. Using mock simulations and a Fisher matrix, we show that there is considerable cosmological information in the scattering transform coefficients not captured by the flux power spectrum. We estimate mock covariance matrices assuming uncorrelated Gaussian pixel noise for each quasar at a level drawn from a simple log-normal model. The extra information comes from a smaller estimated covariance in the first-order wavelet power and from second-order wavelet coefficients that probe non-Gaussian information in the forest. Forecast constraints on cosmological parameters from the wavelet scattering transform are more than an order of magnitude tighter than for the power spectrum, shrinking a 4D parameter space by a factor of 10^{6}. Should these improvements be realized with the Dark Energy Spectroscopic Instrument, inflationary running would be constrained to test common inflationary models predicting α_{s}=-6×10^{-4} and neutrino mass constraints would be improved enough for a 5-σ detection of the minimal neutrino mass.

Chromonatural warm inflation

Chromonatural inflation is a model where non-Abelian gauge fields are sustained by the coupling of the axion with the gauge field through the Chern-Simons term, while minimal warm inflation is a model where the axion produces a thermal bath of non-Abelian gauge particles through the Chern-Simons term. Since both axion inflation models are based on the same action, a natural question is if they are compatible or not. We study axion inflation with the Chern-Simons term and find that chromonatural inflation can accommodate radiation with a temperature much larger than the Hubble parameter during inflation, which is a characteristic feature of warm inflation. Thus, we conclude that chromonatural warm inflation exists, which must have phenomenologically interesting consequences. Published by the American Physical Society 2024

Inflation and reheating predictions in polynomial inflation with small and large fields

We explore the inflationary dynamics and reheating predictions of the fourth-order generalized polynomial inflation model featuring adjustable saddle-point position and flatness near the saddle point for both small and large field cases, based on the latest Planck 2018 Cosmic Microwave Background (CMB) and BICEP/Keck data. We observe that the small field case, with saddle points proximate to the origin, exhibits a significantly lower tensor-to-scalar ratio compared to the large field case. Additionally, the spectral index of the curvature perturbation increases as the flatness near the potential saddle point decreases. Through an analysis of the interplay between inflation and reheating parameters derived from the expansion history of the pivot CMB scale, we establish a permissible range for the reheating parameters. We find that both the small and large cases of polynomial inflation can be consistent with the latest observations due to potential flatness reduction, except for the case where the saddle point deviates significantly from the origin, and the reheating process accentuates the disparities in parameter space between small and large field inflationary scenarios.

Bayesian inference methodology for primordial power spectrum reconstructions from Large Scale Structure

We use Bayesian inference to develop a non-parametric method to reconstruct the primordial power spectrum Pℛ (k) from Large Scale Structure (LSS) data. The performance of the method is assessed by testing it against simulations of the clustering of high-z (QSOs) objects. Their clustering is derived from different templates of the primordial power spectrum motivated by models of inflation: the Standard Model power law characterized by the two parameters As and ns ; a local feature template; and a global oscillatory template. The primordial power spectrum is reconstructed using N knots in the log {k, Pℛ (k)} plane while sampling the cosmological parameters {H 0, Ω b , Ω c }. We use two statistical tests to examine the reconstructions for signs of primordial features: a global test comparing the evidences and a novel local test quantifying the power of the hypothesis test between the power law model and the marginalized probability over N model. We also discuss results of an application to low-z (ELGs) objects with two different photometric errors keeping the cosmology fixed. The method shows good performance in all scenarios considered. In particular, the tests show no feature detection for the standard power-law primordial power spectrum; yet, the method is able to detect power spectrum deviations at a percent level for all considered features, combining either the low-z or the high-z redshift bins. In addition, we include a test proof-of-concept application to real data from the Sloan Digital Sky Survey Luminous Red Galaxy Data Release 4 (SDSS LRG 04), finding no preference for deviations from the primordial power law. The method is flexible, model independent, and suitable for its application to existing and future LSS surveys.

Loop corrections in the separate universe picture

In inflationary models that produce a spike of power on short scales, back-reaction of small-scale substructure onto large-scale modes is enhanced. Loop corrections that quantify this back-reaction have been evaluated by a number of authors. We argue that the separate universe framework provides a highly convenient tool for such computations. Each loop of interest is characterized by large hierarchies in wavenumber and horizon exit time. The separate universe framework highlights important factorizations involving these hierarchies. We interpret each loop correction in terms of a simple, classical, back-reaction model, and clarify the meaning of the different volume scalings that have been reported in the literature. We argue that significant back-reaction requires both short-scale nonlinearities and long-short couplings that modulate the short-scale power spectrum. In the absence of long-short couplings, only incoherent “shot noise”-like effects are present, which are volume-suppressed. Dropping the shot noise, back-reaction from a particular scale is controlled by a product of f NL-like parameters: an equilateral configuration measuring the nonlinearity of the short-scale modes, and a squeezed configuration measuring the long-short coupling. These may carry important scale dependence controlling the behaviour of the loop in the decoupling limit where the hierarchy of scales becomes large. In single-field models the long-short coupling may be controlled by this hierarchy, in which case the net back-reaction would be safely suppressed. We illustrate our framework using explicit computations in a 3-phase ultra-slow-roll scenario. Our analysis differs from earlier treatments of this model, which did not consistently include the effect of small-scale modes. Finally, we discuss different choices for the smoothing scale used in the separate universe framework and argue the effect can be absorbed into a renormalization of local operators. This complicates interpretation of the loop, because the analytic part of each loop integral is degenerate with unknown, ultraviolet-sensitive contributions.

Inflation and reheating in quadratic metric-affine gravity with derivative couplings

Within the framework of metric-affine theories of gravity, where both the metric and connection are treated as independent variables, we consider actions quadratic in the Ricci scalar curvature coupled non-minimally to a scalar field through derivative couplings. Our analysis delves into the inflationary predictions, revealing their consistency with the latest observational constraints across a wide range of parameters. This compatibility permits adjustments such as an increase in the spectral index and a reduction in the tensor-to-scalar ratio. While we do not propose a specific reheating mechanism, our analysis demonstrates that within the quadratic model of inflation, the maximum reheating temperature can reach ∼ 3 × 1015 GeV.

LiteBIRD science goals and forecasts. A case study of the origin of primordial gravitational waves using large-scale CMB polarization

We study the possibility of using the LiteBIRD satellite B-mode survey to constrain models of inflation producing specific features in CMB angular power spectra. We explore a particular model example, i.e. spectator axion-SU(2) gauge field inflation. This model can source parity-violating gravitational waves from the amplification of gauge field fluctuations driven by a pseudoscalar “axionlike” field, rolling for a few e-folds during inflation. The sourced gravitational waves can exceed the vacuum contribution at reionization bump scales by about an order of magnitude and can be comparable to the vacuum contribution at recombination bump scales. We argue that a satellite mission with full sky coverage and access to the reionization bump scales is necessary to understand the origin of the primordial gravitational wave signal and distinguish among two production mechanisms: quantum vacuum fluctuations of spacetime and matter sources during inflation. We present the expected constraints on model parameters from LiteBIRD satellite simulations, which complement and expand previous studies in the literature. We find that LiteBIRD will be able to exclude with high significance standard single-field slow-roll models, such as the Starobinsky model, if the true model is the axion-SU(2) model with a feature at CMB scales. We further investigate the possibility of using the parity-violating signature of the model, such as the TB and EB angular power spectra, to disentangle it from the standard single-field slow-roll scenario. We find that most of the discriminating power of LiteBIRD will reside in BB angular power spectra rather than in TB and EB correlations.

Exploring the NANOGrav signal and planet-mass primordial black holes through Higgs inflation

The data recently released by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) provides compelling evidence supporting the existence of a stochastic signal that aligns with a gravitational-wave background. We show that the scalar-induced gravitational waves from the Higgs inflation model with the parametric amplification mechanism can explain this signal. Such a gravitational-wave background naturally predicts the substantial existence of planet-mass primordial black holes, which can be planet 9 in our solar system and the lensing objects for the ultrashort-timescale microlensing events observed by the Optical Gravitational Lensing Experiment. Therefore, the NANOGrav signal, the potential Planet 9 in our solar system, and the Optical Gravitational Lensing Experiment can be explained within the framework of Higgs inflation.

Relationship between unemployment and inflation in Poland in the context of the Phillips curve — a time of pandemic and war in Ukraine

In this article we undertake a verification of the Phillips curve in Polish conditions during the pandemic and the war in Ukraine. The theoretical part introduces evolution of Phillips’s theory and the review of literature and its verification in the conditions of Polish economy. Additionally, theoretical aspects regarding crisis and exogenous shocks are discussed. The aim of the empirical part of the work was to investigate the existence of the Phillips curve in the Polish economy in 2013–2022. The direction and strength of the relationship between inflation and unemployment rates were tested based on monthly data on full period and the pandemic period. In the research econometric methods were used in order to estimate parameters of an autoregressive inflation model, including both the influence of unemployment on the inflation rate and exogenous shock that were caused by periods of economic disruption reflected by binary, sustained and interaction variables. It was concluded that in the pandemic time the effect of the Phillips curve was present and that was accentuated by the war. However, in the longer term, this effect was not perceived as a negative relationship between characteristics under study. Nevertheless, in the full period of the study, disruptions in inflation patterns which were caused by the pandemic and the period of Russian aggression against Ukraine were evident.

Bare mass effects on the reheating process after inflation

We consider the effects of a bare mass term for the inflaton, when the inflationary potential takes the form V(ϕ)=λϕk about its minimum with k≥4. We concentrate on k=4, but discuss general cases as well. Further, we assume λϕend2≫mϕ2, where ϕend is the inflaton field value when the inflationary expansion ends. We show that the presence of a mass term (which may be present due to radiative corrections or supersymmetry breaking) can significantly alter the reheating process, as the equation of state of the inflaton condensate changes from wϕ=13 to wϕ=0 when λϕ2 drops below mϕ2. We show that, for a mass mϕ≳3λ14TRH, the mass term will dominate at reheating. The value of λ is relatively model independent as it is normalized by the cosmic microwave background perturbation spectrum. For T models of inflation, this leads to mϕ≳TRH/250. We compute the effects on the reheating temperature for cases where reheating is due to inflaton decay (to fermions, scalars, or vectors) or to inflaton scattering (to scalars or vectors). For scattering to scalars and in the absence of a decay, there is always a residual inflaton background that acts as cold dark matter. In this case, we derive a strong upper limit to the inflaton bare mass which for T models is mϕ&lt;350 MeV(TRH/1010 GeV)3/5. We also consider the effect of the bare mass term on the fragmentation of the inflaton condensate. Published by the American Physical Society 2024