Natural Inflation Research Articles

Study in the noncanonical domain of Goldstone inflation

Recent observations of the cosmic microwave background (CMB) indicate that a successful theory of cosmological inflation needs to have flat potential of the inflaton scalar field. Realizing the inflaton to be a pseudo-Nambu Goldstone boson (pNGB) could ensure the flatness and the sub-Planckian scales related to the dynamics of the paradigm. In this work, we have taken the most general form of such a scenario: Goldstone inflation, and studied the model in the noncanonical domain. Natural inflation is a limiting case of this model, which is also studied here in the noncanonical regime. Our result is compared with the recent release by Planck collaboration and it is shown that for some combination of the model parameters, a Goldstone inflationary model in the noncanonical realisation obeys the current observational bounds. Then, we studied the era of reheating after the end of inflation. For different choice of model parameters, constraints on the reheating temperature ($T_{\rm re}$) and number of e-folds during reheating($N_{\rm re}$) for the allowed inflationary observables (e.g. scalar spectral index($n_s$) and tensor to scalar ratio($r$)) are predicted for this model.

Rare Disasters, the Natural Interest Rate and Monetary Policy

This paper evaluates the impact of rare disasters on the natural interest rate and macroeconomic conditions by simulating a nonlinear New-Keynesian model. The model is calibrated using data on natural disasters in OECD countries. From an ex-ante perspective, disaster risk behaves as a negative demand shock and lowers the natural rate and inflation, even if disasters hit only the supply side of the economy. These effects become larger and nonlinear if extreme natural disasters become more frequent, a scenario compatible with climate change projections. From an ex-post perspective, a disaster realization leads to temporarily higher natural rate and inflation if supply-side effects prevail. If agents' risk aversion increases temporarily, disasters may generate larger demand effects and lead to a lower natural rate and inflation. If supply-side effects dominate, the central bank could mitigate output losses at the cost of temporarily higher inflation in the short run. Conversely, under strict inflation targeting, inflation is stabilized at the cost of larger output losses.

Fat inflatons, large turns and the η-problem

It is commonly believed that a successful period of inflation driven by a single or several scalar fields requires a specific hierarchy of masses given by Minf≪ H ≪ Mheavy, where Minf can correspond to several or a single light field and Mheavy corresponds to any heavy field that might be integrated out if it satisfies suitable conditions. This is at the heart of the so called η-problem in inflation, since large contributions to the masses of the inflatons might spoil the slow-roll conditions required for inflation. We show that, while this is an unavoidable conclusion in single field inflation, in multifield inflation, heavy fields as defined above, may be fully responsible for a successful period of what we call fat slow-roll inflation. Moreover we show that in this scenario, the turning rate of the inflationary trajectory, Ω/H, is larger than one. Thus, the η-problem is evaded with large turns in fat inflation. Depending on the perturbations' mass spectra, cosmological predictions will differ either slightly or largely with respect to those of the single field case. We illustrate this scenario in a concrete example in Type IIB string flux compactifications, where a probe D5-brane moving along the angular and radial directions in a warped throat drives fat D5-brane natural inflation. An instantaneous superplanckian decay constant can be defined, consistent with our low energy approximations. We compute the cosmological observables, which are consistent with Planck data, ameliorating the tension of single field natural inflation with observations. We also discuss fat inflation in the context of recently proposed swampland de Sitter conjectures.

Natural Rate Chimera and Bond Pricing Reality

Incorporating arbitrage-free term-structure dynamics into a semi-structural macro-model, we jointly estimate the real equilibrium interest rate (r), trend inflation, and term premia for the United States and the euro area, using a Bayesian approach. The natural real rate and trend inflation are cornerstones determining equilibrium yields across maturities and macroeconomic trends. Taking into account the secular decline in equilibrium rates, term premia exhibit cyclical behavior over the business cycle, rather than the commonly reported trend. Our estimates suggest a fall in r from a pre-crisis level of about 3% to around zero, but estimates are subject to sizeable uncertainty. Including survey expectations can lift r estimates for recent quarters by a margin.

Super-Planckian axions from near-conformality

We present a novel framework for obtaining large hierarchies in axion decay constants as well as trans-Planckian field excursions, with no need for tuning or a large number of fields. We consider a model with two or more CFTs with a common cutoff, that are linked by a gauged diagonal symmetry. This construction is dual to the geometry of a warped space with two or more throats glued at a common brane, allowing for calculability. Many applications of our setup are possible,such as ultra-light axions, natural inflation, and relaxion models.

Inflation with derivative self-interaction and coupling to gravity

We consider a subclass of Horndeski theories for studying cosmic inflation. In particular, we investigate models of inflation in which the derivative self-interaction of the scalar field and the non-minimal derivative coupling to gravity are present in the action and equally important during inflation. In order to control contributions of each term as well as to approach the single-term limit, we introduce a special relation between the derivative interaction and the coupling to gravity. By calculating observable quantities including the power spectra and spectral tilts of scalar and tensor perturbation modes, and the tensor-to-scalar ratio, we found that the tensor-to-scalar ratio is suppressed by a factor of (1+1/gamma ), where gamma reflects the strength of the derivative self-interaction of the inflaton field with respect to the derivative coupling gravity. We placed observational constraints on the chaotic and natural inflation models and showed that the models are consistent with the current observational data mainly due to the suppressed tensor-to-scalar ratio.

Constant-roll inflation driven by a scalar field with nonminimal derivative coupling

In this work, we study constant-roll inflation driven by a scalar field with nonminimal derivative coupling to gravity, via the Einstein tensor. This model contains a free parameter, [Formula: see text], which quantifies the nonminimal derivative coupling and a parameter [Formula: see text] which characterizes the constant-roll condition. In this scenario, using the Hamilton–Jacobi-like formalism, an ansatz for the Hubble parameter (as a function of the scalar field) and some restrictions on the model parameters, we found new exact solutions for the inflaton potential which include power-law, de Sitter, quadratic hilltop and natural inflation, among others. Additionally, a phase-space analysis was performed and it is shown that the exact solutions associated to natural inflation and a “cosh-type” potential, are attractors.

Quasi-conformal models and the earlyuniverse

Extensions of the Standard Model and general relativity featuring a UVfixed point can leave observable implications at accessible energies. Although massparameters such as the Planck scale can appear through dimensional transmutation,all fundamental dimension-4 operators can (at least approximately) respect Weylinvariance at finite energy. An example is the Weyl-squared term, whose consistencyand observational consequences are studied. This quasi-conformal scenario emergesfrom the UV complete quadratic gravity and is a possible framework for inflation. Wefind two realizations. In the first one the inflaton is a fundamental scalar with aquasi-conformal non-minimal coupling to the Ricci scalar. In this case the fieldexcursion must not exceed the Planck mass by far. An example discussed in detail ishilltop inflation. In the second realization the inflaton is a pseudo-Goldstoneboson (natural inflation). In this case we show how to obtain an elegant UVcompletion within an asymptotically free QCD-like theory, in which the inflaton is acomposite scalar due to new strong dynamics. We also show how efficient reheatingcan occur. Unlike the natural inflation based on Einstein gravity, thetensor-to-scalar ratio is well below the current bound set by Planck. In bothrealizations mentioned above, the basic inflationary formulæ are computedanalytically and, therefore, these possibilities can be used as simple benchmarkmodels.

The Different Regimes of Axion Gauge Field Inflation

In axion gauge field inflation an axion-like particle driving cosmic inflation is coupled to the Chern-Simons density of an Abelian or non-Abelian gauge group. In the case of a non-Abelian gauge group, this can lead to the formation of a stable, homogeneous and isotropic gauge field background. We study the dynamics of the inflaton and gauge fields in terms of the two effective coupling parameters: the gauge coupling and the axion decay constant. Starting from the Bunch-Davies vacuum in the far past, we find that the non-trivial gauge field background arises only significantly after the cosmic microwave background (CMB) scales have left the horizon. At these scales, the model thus closely resembles Abelian axion inflation, thereby naturally reconciling the tension of non-Abelian axion gauge field inflation with the latest CMB observations. We further consider two exemplary UV-completions of this setup: multiple Peccei-Quinn axions and axion monodromy in string theory. In both cases we find that the majority of the parameter space is excluded by theoretical or observational constraints. The remaining parameter space can be divided into three regimes. (i) For small gauge couplings we recover natural inflation. For large gauge couplings the non-Abelian gauge theory either (ii) mimics the Abelian theory or (iii) non-linear interactions prohibit a linear analysis of the gauge field perturbations.

Pseudo-periodic natural Higgs inflation

Inflationary cosmology represents a well-studied framework to describe the expansion of space in the early universe, as it explains the origin of the large-scale structure of the cosmos and the isotropy of the cosmic microwave background radiation. The recent detection of the Higgs boson renewed research activities based on the assumption that the inflaton could be identified with the Higgs field. At the same time, the question whether the inflationary potential can be extended to the electroweak scale and whether it should be necessarily chosen ad hoc in order to be physically acceptable are at the center of an intense debate. Here, we propose and perform the slow-roll analysis of the so-called Massive Natural Inflation (MNI) model which has three adjustable parameters, the explicit mass term, a Fourier amplitude u, and a frequency parameter β, in addition to a constant term of the potential. This theory has the advantage to present a structure of infinite non-degenerate minima and is amenable to an easy integration of high-energy modes. We show that, using PLANCK data, one can fix, in the large β-region, the parameters of the model in a unique way. We also demonstrate that the value for the parameters chosen at the cosmological scale does not influence the results at the electroweak scale. We argue that other models can have similar properties both at cosmological and electroweak scales, but with the MNI model one can complete the theory towards low energies and easily perform the integration of modes up to the electroweak scale, producing the correct order-of-magnitude for the Higgs mass.

Spinodal solution to swampland inflationary constraints

We show how the inclusion of non-perturbative, {\em dynamical} quantum effects on the evolution of the inflaton can allow for an inflationary phase that is both consistent with cosmological constraints {\em and} avoids the problems associated with the so-called swampland conditions. In particular, for concave potentials such as those preferred by the Planck data, spinodal instabilities associated with tachyonic masses for long wavelength modes induce a second round of inflation, which in essence decouples the tree-level potential from the inflationary phase. We illustrate these points using natural inflation as an example.

Soliton model of dark matter and natural inflation

Axion-like scalar fields with their periodic potential are analyzed as a toy model of dark matter halos. Here, solitons collison of the well-known kinks in (1 + 1) spacetime dimensions are mapped to the localized lumps of the Lane-Emden (LE) truncation. Recent attempts to generalize this mapping to (2 + 1)D or even (3 + 1)D collision are related to an intrinsic inelastic effect during relativistic soliton collisions.An indirect method of determining the stability of (3 + 1)D soliton or boson stars (BSs) is displayed without resorting to explicit solutions. Instead, the scalar part of the Lagrangian is mapped into a function L(R) of the scalar curvature, such that a BS is effectively described by by a higher order gravity model. This higher order Lagrangian exhibits minima which are correlated with the transition point from stable to unstable configurations. In the case of an axion BS, the function L(R) exhibits a combination of swallow tail cusps well-known from catastrophe theory.

Thraxions: ultralight throat axions

We argue that a new type of extremely light axion is generically present in the type IIB part of the string theory landscape. Its mass is suppressed by the third power of the warp factor of a strongly warped region (Klebanov-Strassler throat), suggesting the name thraxion. Our observation is based on the generic presence of several throats sharing the same 2-cycle. This cycle shrinks to zero volume at the end of each throat. It is hence trivial in homology and the corresponding C2 axion is massive. However, the mass is warping-suppressed since, if one were to cut off the strongly warped regions, a proper 2-cycle would re-emerge. Since the kinetic term of the axion is dominated in the UV, an even stronger, quadratic mass suppression results. Moreover, if the axion is excited, the angular modes of the throats backreact. This gives our effective C2 axion a finite monodromy and flattens its potential even further. Eventually, the mass turns out to scale as the third power of the warp factor. We briefly discuss possible implications for phenomenology and potential violations of the Weak Gravity Conjecture for axions. Moreover we identify a mechanism for generating super-Planckian axionic field ranges which we call drifting monodromies. However, in the examples we consider, the potential oscillates on sub-Planckian distances in field space, preventing us from building a natural inflation model on the basis of this idea.

Rescuing quartic and natural inflation in the Palatini formalism

When considered in the Palatini formalism, the Starobinsky model does not provide us with a mechanism for inflation due to the absence of a propagating scalar degree of freedom. By (non)-minimally coupling scalar fields to the Starobinsky model in the Palatini formalism we can in principle describe the inflationary epoch. In this article, we focus on the minimally coupled quartic and natural inflation models. Both theories are excluded in their simplest realization since they predict values for the inflationary observables that are outside the limits set by the Planck data. However, with the addition of the R2 term and the use of the Palatini formalism, we show that these models can be rendered viable.

Clusters of Primordial Black Holes

The Primordial Black Holes (PBHs) are a well-established probe for new physics in the very early Universe. We discuss here the possibility of PBH agglomeration into clusters that may have several prominent observable features. The clusters can form due to closed domain walls appearance in the natural and hybrid inflation models whose subsequent evolution leads to PBH formation. The dynamical evolution of such clusters discussed here is of crucial importance. Such a model inherits all the advantages of uniformly distributed PBHs, like possible explanation of supermassive black holes existence (origin of the early quasars), the binary black hole mergers registered by LIGO/Virgo through gravitational waves, which could provide ways to test the model in future, the contribution to reionization of the Universe. If PBHs form clusters, they could alleviate or completely avoid existing constraints on the abundance of uniformly distributed to PBH, thus allowing PBH to be a viable dark matter candidate. Most of the existing constraints on uniform PBH density should be re-considered to the case of PBH clustering. Furthermore, unidentified cosmic gamma-ray point-like sources could be (partially) accounted. We conclude that models leading to PBH clustering are favored compared to models predicting the uniform distribution of PBHs.

Energy Consumption and Inflation Dynamics in Nigeria: An ARDL Cointegration Approach

This paper investigated the dynamic relationship between energy consumption and inflation in Nigeria using time series data obtained for the period 1980 to 2017. Applying Autoregressive Distributed Lag (ADL) technique on the variables, the study found that Premium Motor Spirit (PMS), Dual Purpose Kerosene (DPK) and Natural gas were noninflationary in Nigeria both in consumption and prices over the period. Also, Automotive Gas Oil (AGO) consumption produces strong evidence of positive inflationary pressure but not in prices throughout the study period. Further, we found a strong causality link between natural gas consumption and inflation in Nigeria. We concluded that inflation in Nigeria is not majorly a demand-pull phenomenon, pulled by energy consumption. We provide both subjective and evidence-based reasons for the economic trend and recommend a bridge in the degrading systemic informality in the energy sector that will deliver real time effect of energy consumption-inflation proposition in Nigeria.

Gauss–Bonnet Chern–Simons gravitational wave leptogenesis

The gravitational Chern–Simons term coupled to an evolving axion is known to generate lepton number through the gravitational anomaly. We examine this leptogenesis scenario in the presence of the Gauss–Bonnet term over and above the gravitational Chern–Simons term. We find that the lepton production can be exponentially enhanced. The Gauss–Bonnet term creates CP-violating instability of gravitational waves that may appear transiently after inflation, and during the period of instability elliptically polarized gravitational waves are exponentially amplified at sub-horizon scales. This instability does not affect the spectrum of the cosmic microwave background as it occurs at much shorter length scales. In a typical scenario based on natural inflation, the observed baryon asymmetry of the Universe corresponds to the UV cutoff scale at 1014–16 GeV.

Natural Inflation with a periodic non-minimal coupling

Natural inflation is an attractive model for primordial inflation, since the potential for the inflaton is of the pseudo Nambu-Goldstone form, V(ϕ)=Λ4 [1+cos (ϕ/f)], and so is protected against radiative corrections. Successful inflation can be achieved if f ≳ few MP and Λ ∼ mGUT where Λ can be seen as the strong coupling scale of a given non-abelian gauge group. However, the latest observational constraints put natural inflation in some tension with data. We show here that a non-minimal coupling to gravity γ2(ϕ) R, that respects the symmetry ϕ→ ϕ+2 π f and has a simple form, proportional to the potential, can improve the agreement with cosmological data. Moreover, in certain cases, satisfactory agreement with the Planck 2018 TT, TE, EE and low P data can be achieved even for a periodicity scale of approximately Mp.

Slow-roll analysis of double-field axion inflation

We adopt the double field natural inflation model motivated by the non-perturbative effects of supergravity and superstring theory to do the slow roll analysis. We show that when the parameters are suitably chosen, there exist ranges of initial values of fields that can satisfy the constraints of Planck observations. This implies less fine tuning of field values can be allowed with tolerance of $4 {M}_{\text{pl}}$ for ${\phi}_{1}$ and $5 {M}_{\text{pl}}$ for ${\phi}_{2}$ respectively, which become more physical for field fluctuation in quantum era. We also show that the spectral index ${n}_{\mathcal{RR}}$, the fraction of entropic power spectrum and the fraction of power spectra (so-called ${\beta}_{\text{iso}}$) and $\cos{\Delta}$ can satisfy the constraints of Planck observation. This implies that double field natural inflation is a valid model to describe cosmological inflation.

Strong dynamics and natural inflation

We continue our investigation of the 4d effective field theory for closed string axions in Type II compactifications with D-branes. The inclusion of St\"uckelberg couplings for the axions requires the presence of chiral fermions at D-brane intersections, whose interactions at strong non-Abelian gauge coupling induce mass terms for the axions and scalar chiral condensate excitations, dubbed infladrons. The set-up allows for a realization of natural-like inflation with a closed string axion as inflaton and a flattened scalar potential due to the back-reaction of the more massive infladrons. We further point out that this large field inflationary model is not compromised by axionic wormhole corrections.