Inflationary Trajectory Research Articles

Generalised conditions for rapid-turn inflation

Rapid-turn slow-roll inflationary trajectories have been shown to be an attractor in two-field models, provided the turn rate is near constant and larger than the slow-roll parameters. These trajectories can produce primordial spectra consistent with current observations on CMB scales. We present the generalized consistency condition for sustained rapid-turn inflationary trajectory with two fields, arbitrary field-space metric and potential valid for any value of the turn rate. This has to be supplemented by a second condition to ensure slow roll evolution. Both conditions together constitute a tool to identify inflationary trajectories with arbitrary values of the turning rate without having to solve the equations of motion. We present a Python package for the numerical identification of regions in field-space and parameter space that allow for rapid-turn trajectories.

Modular invariant hilltop inflation

In this paper we show that it is possible to achieve successful hilltop inflation in which the inflaton is identified as the modulus field in a modular invariant theory.The dilaton plays a crucial role in shaping the potential.Modular invariant gaugino condensation provides the mechanism for the modulus stabilisation after inflation. The inflationary trajectory lies on the lower boundary of the fundamental domain of the modulus field τ. Inflation starts near the fixed point τ = i, and ends at a point near τ = ω, which is the global de Sitter vacuum.We investigate the allowed parameter space for successful modular invariant hilltop inflation.

Sudden braking and turning with a two-field potential bump: primordial black hole formation

We investigate the amplification of curvature perturbations in a two-field inflation model featuring a Gaussian potential bump. When the inflaton encounters a potential bump along the inflationary trajectory, its rolling speed is generally reduced, potentially causing a violation of the slow-roll condition. Consequently, the original decaying modes of comoving curvature perturbations during the slow-roll phase start growing, and lead to enhanced small-scale density perturbations which can produce amounts of primordial black holes (PBHs) and associated scalar-induced gravitational waves. In addition, inflaton also undergoes sudden turnings at the encounter of the Gaussian potential bump, which is insignificant to the overall curvature power spectrum due to the short duration of these turns. Our paper offers a simple example of the extension of a bump-like potential for PBH formation in a single-field inflation to a two-field case, which helps alleviate the fine-tuning of initial conditions to some extent.

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

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

Discordances in Cosmology and the Violation of Slow-Roll Inflationary Dynamics.

We identify examples of single field inflationary trajectories beyond the slow-roll regime that improve the fit to Planck 2018 data compared to a baseline Λ cold dark matter model with power law form of primordial spectrum and at the same time alleviate existing tensions between different datasets in the estimate of cosmological parameters such as H_{0} and S_{8}. A damped oscillation in the first Hubble flow function-or equivalently a feature in the potential-and the corresponding localized oscillations in the primordial power spectrum partially mimic the improvement in the fit of Planck data due to A_{L} or Ω_{K}. Compared to the baseline model, this model can lead simultaneously to a larger value of H_{0} and a smaller value of S_{8}, a trend that can be enhanced when the most recent SH0ES measurement for H_{0} is combined with Planck and BICEP-Keck 2018 data. Large scale structure data and more precise cosmic microwave background polarization measurements will further provide critical tests of this intermediate fast-roll phase.

On the choice of entropy variables in multifield inflation

We discuss the usefulness and theoretical consistency of different entropy variables used in the literature to describe isocurvature perturbations in multifield inflationary models with a generic curved field space. We clarify which is the proper entropy variable to be used to match the evolution of isocurvature modes during inflation to the one after the reheating epoch in order to compare with observational constraints. In particular, we find that commonly used variables, as the relative entropy perturbation or the one associated to the decomposition in tangent and normal perturbations with respect to the inflationary trajectory, even if more useful to perform numerical studies, can lead to results which are wrong by several orders of magnitude, or even to apparent destabilisation effects which are unphysical for cases with light kinetically coupled spectator fields.

A fake instability in string inflation

In type IIB fibre inflation models the inflation is a Kähler modulus which is kinetically coupled to the corresponding axion. In this setup the curvature of the field space induces tachyonic isocurvature perturbations normal to the background inflationary trajectory. However we argue that the associated instability is unphysical since it is due to the use of ill-defined entropy variables. In fact, upon using the correct relative entropy perturbation, we show that in fibre inflation axionic isocurvature perturbations decay during inflation and the dynamics is essentially single-field.

Large and small field inflation from hyperbolic sigma models

Long standing themes in inflation include the issue of large field vs. small field inflation as well as the question what fraction of phase space leads to sufficient inflation and furthermore is compatible with the experimental data. In the present paper, these issues are discussed in the context of modular inflation, a specialization of the framework of automorphic nonlinear $\ensuremath{\sigma}$ models associated to homogeneous spaces $G/K$ in which the continuous shift symmetry group $G$ is weakly broken to discrete subgroups $\mathrm{\ensuremath{\Gamma}}$. The target spaces of these theories inherit a curved structure from the group $G$, which in the case of modular invariant inflation leads to a hyperbolic field space geometry. It is shown that in this class of models the symmetry structure leads to both large and small field inflationary trajectories within a single modular inflation model. The present paper analyzes the concrete model of $j$-inflation, a hyperbolic model with nontrivial inflaton interactions. It describes in some detail the structure of the initial conditions, including a systematic analysis of several phenomenological functions on the target space, leading to constraints on the curvature scalar of the field space by upcoming experiments, as well as a discussion of the scaling behavior of the spectral index, the finite volume fraction of the field space leading to sufficient inflation, the attractor behavior of $j$-inflation, and a comparison of inflaton trajectories vs. target space geodesics. The tensor-ratio analysis shows that $j$-inflation is an interesting target for upcoming ground and satellite experiments.

Rapid-turn inflation in supergravity is rare and tachyonic

Strongly non-geodesic, or rapidly turning trajectories in multifield inflation have attracted much interest recently from both theoretical and phenomenological perspectives. Most models with large turning rates in the literature are formulated as effective field theories. In this paper we investigate rapid-turn inflation in supergravity as a first step towards understanding them in string theory. We find that large turning rates can be generated in a wide class of models, at the cost of high field space curvature. In these models, while the inflationary trajectories are stable, one Hessian eigenvalue is always tachyonic and large, in Hubble units. Thus, these models satisfy the de Sitter swampland conjecture along the inflationary trajectory. However, the high curvatures underscore the difficulty of obtaining rapid-turn inflation in realistic string-theoretical models.In passing, we revisit the η-problem in multifield slow-roll inflation and show that it does not arise, inasmuch as the inflatons, ϕi , can all be heavier (in absolute value) that the Hubble scale: |mi |/H>1, ∀i.

Primordial gravitational waves from excited states

We show that a scalar excited state with large occupation numbers during inflation leads to an enhancement of tensor modes and a characteristic pattern of order-one oscillations in the associated stochastic gravitational wave background (SGWB) sourced during inflation. An effective excited state, i.e. a departure from the Bunch-Davies vacuum, can emerge dynamically as the result of a transient non-adiabatic evolution, e.g. a sharp feature along the inflationary history. We provide an explicit example in a multifield context where the sharp feature triggering the excited state is identified with a strong turn in the inflationary trajectory. En passant, we derive a universal expression for the tensor power spectrum sourced at second order by an arbitrary number of scalar degrees of freedom during inflation, crucially taking into account the nontrivial structure of the Hilbert space in multifield setups. The SGWB sourced during inflation can overcome the standard scalar-induced SGWB sourced at horizon re-entry of the fluctuations after inflation, while being less constrained by perturbativity and backreaction bounds. In addition, one may entertain the possibility of detecting both since they peak at different frequencies exhibiting oscillations with distinct periods.

An exact solution approach to warm inflation using Tsallis and Barrow holographic dark energy entropy within Rastall gravity.

This paper studies the phenomena of warm inflation in a modified cosmological scenario within Rastall gravity. In this context, we modify the standard Friedmann equations using recently proposed Tsallis and Barrow holographic dark energy entropies, alternatively. For both entropies, the exact solutions including the inflaton field, potential required to produce inflation and the scale factor are obtained under slow-roll approximation for low- and high-dissipative regimes. We obtain exponentially growing scale factors for both dark energy models. To confront the theoretical predictions of these models with recent observational data, we calculate the slow-roll parameters, number of e-folds, scalar spectral index, running of scalar spectral index and the tensor-to-scalar ratio for both extremes of dissipation. The Planck bounds on inflationary trajectories are being used to constraint the free parameters. The results are interesting and physically viable up to 2sigma level.

Oscillations in the stochastic gravitational wave background from sharp features and particle production during inflation

We identify a characteristic pattern in the scalar-induced stochastic gravitational wave background from particle production during inflation.If particle production is sufficiently efficient, the scalar power spectrum exhibits \U0001d4aa(1) oscillations periodic in k, characteristic of a sharp feature, with an exponentially enhanced envelope. We systematically study the properties of the induced spectrum of gravitational waves sourced after inflation and find that this inherits the periodic structure in k, resulting in a peak in the gravitational wave energy density spectrum with \U0001d4aa(10 %) modulations. The frequency of the oscillation in the scalar power spectrum is determined by the scale of the feature during inflation and in turn sets the frequency of modulations in the gravitational wave signal. We present an explicit realisation of this phenomenon in the framework of multifield inflation, in the form of a strong sharp turn in the inflationary trajectory. The resulting stochastic background is potentially detectable in future gravitational wave observatories, and considerations of backreaction and perturbativity can be used to constrain the parameter space from the theoretical side. Our work motivates more extensive research linking primordial features to observable properties of the stochastic background of gravitational waves, and dedicated development in data analysis for their detection.

A solution to the de Sitter swampland conjecture versus inflation tension via supergravity

The methods of supergravity allow us to derive a multi-field F-term potential. Using this, we denote a generic and non-positive single-field F-term potential. We insert our theory into the scalar-gravity part of the (2,1|1) invariant superconformal action. That action leads us to a de Sitter solution at the inflationary trajectory. One can denote stabilization of fields in terms of the Kähler kinetic terms and single-field slow-roll inflation parameters. We combine these with the de Sitter swampland conjecture to generate a bounded conjecture. This approach allowed us to show that the single field slow-roll inflation works in harmony with bounded de Sitter conjecture for any concave inflation potential.

Shifted μ -hybrid inflation, gravitino dark matter, and observable gravity waves

We investigate supersymmetric hybrid inflation in a realistic model based on the gauge symmetry $SU(4)_c \times SU(2)_L \times SU(2)_R$. The minimal supersymmetric standard model (MSSM) $\mu$ term arises, following Dvali, Lazarides, and Shafi, from the coupling of the MSSM electroweak doublets to a gauge singlet superfield which plays an essential role in inflation. The primordial monopoles are inflated away by arranging that the $SU(4)_c \times SU(2)_L \times SU(2)_R$ symmetry is broken along the inflationary trajectory. The interplay between the (above) $\mu$ coupling, the gravitino mass, and the reheating following inflation is discussed in detail. We explore regions of the parameter space that yield gravitino dark matter and observable gravity waves with the tensor-to-scalar ratio $r \sim 10^{-4}-10^{-3}$.

Monetarna politika ECB u vreme pandemije

This paper aims to point out the monetary policy measures that the European This paper aims to point out the monetary policy measures that the European Central Bank has taken since the outbreak of the COVID-19 crisis. In the Eurozone, at the start of the COVID-19 crisis, financial conditions deteriorated sharply, potentially threatening to worsen the economic outlook, deepen market fragmentation, jeopardize monetary policy transmission, encourage a downward inflationary trajectory, weaken prices and undermine public and private stability. Aware of the new situation of the ECB, it responded quickly and efficiently with coordinated and ambitious measures to alleviate the perceived financial and economic difficulties. To maintain a flexible monetary policy stance, the ECB adopted an interim non-standard measured COVID-19 Asset Purchase Program (PEPP) to mitigate and improve financial conditions and restart an earlier Asset Purchase Program (APP) aimed at inflation expectations. At the same time, other measures have been strengthened and expanded, such as Targeted Long-Term Refinancing Operations (LTROs, TLTRO III, and PLTRO) aimed at providing liquidity ampleness to the real sector and collateral standards. The implementation of the adopted measures has influenced the stabilization of the economic and financial system of the EU and improved lending to corporate and household banks.

Origin of ultra-light fields during inflation and their suppressed non-Gaussianity

We study the structure of multi-field inflation models where the primordial curvature perturbation is able to vigorously interact with an ultra-light isocurvature field — a massless fluctuation orthogonal to the background inflationary trajectory in field space. We identify a class of inflationary models where ultra-light fields can emerge as a consequence of an underlying “scaling transformation” that rescales the entire system's action and keeps the classical equations of motion invariant. This scaling invariance ensures the existence of an ultra-light fluctuation that freezes after horizon crossing. If the inflationary trajectory is misaligned with respect to the scaling symmetry direction, then the isocurvature field is proportional to this ultra-light field, and becomes massless. In addition, we find that even if the isocurvature field interacts strongly with the curvature perturbation — transferring its own statistics to the curvature perturbation — it is unable to induce large non-Gaussianity. The reason is simply that the same mechanism ensuring a suppressed mass for the isocurvature field is also responsible for suppressing its self-interactions. As a result, in models with light isocurvature fields the bispectrum is generally expected to be slow-roll suppressed, but with a squeezed limit that differs from Maldacena's consistency relation.

Seeding Primordial Black Holes in Multifield Inflation.

The inflationary origin of primordial black holes (PBHs) relies on a large enhancement of the power spectrum Δ_{ζ} of the curvature fluctuation ζ at wavelengths much shorter than those of the cosmic microwave background anisotropies. This is typically achieved in models where ζ evolves without interacting significantly with additional (isocurvature) scalar degrees of freedom. However, quantum gravity inspired models are characterized by moduli spaces with highly curved geometries and a large number of scalar fields that could vigorously interact with ζ (as in the cosmological collider picture). Here we show that isocurvature fluctuations can mix with ζ inducing large enhancements of its amplitude. This occurs whenever the inflationary trajectory experiences rapid turns in the field space of the model leading to amplifications that are exponentially sensitive to the total angle swept by the turn, which induce characteristic observable signatures on Δ_{ζ}. We derive accurate analytical predictions and show that the large enhancements required for PBHs demand noncanonical kinetic terms in the action of the multifield system.

Consistent inflationary cosmology from quadratic gravity with dynamical torsion

The idea of gauge theories of gravity predicts that there should exist not only the massless graviton but also massive particles carrying the gravitational force. We study the cosmology in a quadratic gravity with dynamical torsion where gravity may be interpreted as a gauge force associated with the Poincaré group. In addition to the massless spin-2 graviton, the model contains four non-ghost massive particle species: a couple of spin-0, a spin-1 and a spin-2. Supposing the restoration of the local Weyl invariance in the UV limit and the parity invariance, we find the most general minisuperspace action describing a homogeneous and isotropic universe with a flat spatial geometry. We then transform the minisuperspace action to a quasi-Einstein frame in which the field space is a hyperboloid and the field potential is a combination of those of a Starobinsky-like inflation and a natural inflation. Remarkably, thanks to the multi-field dynamics, the Starobinsky-like inflationary trajectory can be realized even if the initial condition is away from the top of the Starobinsky-like potential. We also study linear tensor perturbations and find qualitatively different features than the Starobinsky inflation, spontaneous parity violation and mixing of the massless and massive spin-2 modes, which might reveal the underlying nature of gravity through inflationary observables.

A gigaparsec-scale local void and the Hubble tension

We explore the possibility of using a gigaparsec-scale local void to reconcile the Hubble tension. Such a gigaparsec-scale void can be produced by multi-stream inflation where different parts of the observable universe follow different inflationary trajectories. These trajectories become different parts of the observable universe after inflation, when these scales return to the horizon. If these trajectories have different e-folding numbers, these parts of the universe have different energy densities, possibly creating a local large void. The impacts of such a void for cosmological observations are studied, especially those involving supernovae, Baryon Acoustic Oscillations (BAO) and the kinetic Sunyaev-Zel’dovich (kSZ) effect. We show that with the presence of the void, supernovae observations may be more consistent with the CMB. We also estimate the impacts of a local large void on BAO observations. In addition, we show that a local large void and hence its capabilities to ease the Hubble tension is limited by the kSZ effect. As a benchmark model, a 1.7 Gpc scale void with boundary width 0.7 Gpc and density contrast −0.14 may ease the Hubble tension, evading the kSZ limit.

Superconformal generalizations of auxiliary vector modified polynomial f(R) theories

We present the supersymmetric completion of the auxiliary vector modified polynomial f(R) theories in their dual scalar-tensor theory formulation that interpolate between the auxiliary vector modified polynomial f(R) theories and chaotic inflation with the power-law potential V(ϕ) ∝ ϕp. The supersymmetrization is achieved in two steps: first, we introduce a superconformal theory for three chiral multiplets by choosing a conformal Kähler potential and a conformal superpotential. In the second step, we use one of the chiral multiplets to compensate for the superconformal symmetries and achieve the Kähler potential and the superpotential while the other two are used to realize inflation with a stable inflationary trajectory. The stability of the inflationary trajectory requires certain deformations to the Kähler potential which we discuss their compatibility against the inflationary observables from the latest Planck data.