Hilltop Inflation Research Articles

The ALP miracle: unified inflaton and dark matter

We propose a scenario where both inflation and dark matter are described by a single axion-like particle (ALP) in a unified manner. In a class of the minimal axion hilltop inflation, the effective masses at the maximum and mimimum of the potential have equal magnitude but opposite sign, so that the ALP inflaton is light both during inflation and in the true vacuum. After inflation, most of the ALPs decay and evaporate into plasma through a coupling to photons, and the remaining ones become dark matter. We find that the observed CMB and matter power spectrum as well as the dark matter abundance point to an ALP of mass mϕ = \U0001d4aa(0.01) eV and the axion-photon coupling gϕ γ γ = \U0001d4aa(10−11) GeV−1: the ALP miracle. The suggested parameter region is within the reach of the next generation axion helioscope, IAXO, and high-intensity laser experiments in the future. Furthermore, thermalized ALPs contribute to hot dark matter and its abundance is given in terms of the effective number of extra neutrino species, Δ Neff ≃ 0.03, which can be tested by the future CMB and BAO observations. We also discuss a case with multiple ALPs, where the coupling to photons can be enhanced in the early Universe by an order of magnitude or more, which enlarges the parameter space for the ALP miracle. The heavy ALP plays a role of the waterfall field in hybrid inflation, and reheats the Universe, and it can be searched for in various experiments such as SHiP.

Features from the non-attractor beginning of inflation

We study the effects of the non-attractor initial conditions for the canonical single-field inflation. The non-attractor stage can last only several e-folding numbers, and should be followed by hilltop inflation. This two-stage evolution leads to large scale suppression in the primordial power spectrum, which is favored by recent observations. Moreover we give a detailed calculation of primordial non-Gaussianity due to the ``from non-attractor to slow-roll'' transition, and find step features in the local and equilateral shapes. We conclude that a plateau-like inflaton potential with an initial non-attractor phase yields interesting features in both power spectrum and bispectrum.

Variants of kinetically modified non-minimal Higgs inflation in supergravity

We consider models of chaotic inflation driven by the real parts of a conjugate pair of Higgs superfields involved in the spontaneous breaking of a grand unification symmetry at a scale assuming its Supersymmetric (SUSY) value. Employing Kähler potentials with a prominent shift-symmetric part proportional to c− and a tiny violation, proportional to c+, included in a logarithm we show that the inflationary observables provide an excellent match to the recent Planck and BICAP2/Keck Array results setting, e.g., 6.4 · 10−3 ≲ r± = c+/c− ≲ 1/N where N = 2 or 3 is the prefactor of the logarithm. Deviations of these prefactors from their integer values above are also explored and a region where hilltop inflation occurs is localized. Moreover, we analyze two distinct possible stabilization mechanisms for the non-inflaton accompanying superfield, one tied to higher order terms and one with just quadratic terms within the argument of a logarithm with positive prefactor NS < 6. In all cases, inflation can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale.

Eternal hilltop inflation

We consider eternal inflation in hilltop-type inflation models, favored by current data, in which the scalar field in inflation rolls off of a local maximum of the potential. Unlike chaotic or plateau-type inflation models, in hilltop inflation the region of field space which supports eternal inflation is finite, and the expansion rate HEI during eternal inflation is almost exactly the same as the expansion rate H* during slow roll inflation. Therefore, in any given Hubble volume, there is a finite and calculable expectation value for the lifetime of the ``eternal'' inflation phase, during which quantum flucutations dominate over classical field evolution. We show that despite this, inflation in hilltop models is nonetheless eternal in the sense that the volume of the spacetime at any finite time is exponentially dominated by regions which continue to inflate. This is true regardless of the energy scale of inflation, and eternal inflation is supported for inflation at arbitrarily low energy scale.

The reconstruction of inflationary potentials

The observational data on the anisotropy of the cosmic microwave background constraints the scalar spectral tilt $n_s$ and the tensor to scalar ratio $r$ which depend on the first and second derivatives of the inflaton potential. The information can be used to reconstruct the inflaton potential in the polynomial form up to some orders. However, for some classes of potentials, $n_s$ and $r$ behave as $n_s(N)$ and $r(N)$ universally in terms of the number of e-folds $N$. The universal behaviour of $n_s(N)$ can be used to reconstruct a class of inflaton potentials. By parametrizing one of the parameters $n_s(N)$, $\epsilon(N)$ and $\phi(N)$, and fitting the parameters in the models to the observational data, we obtain the constraints on the parameters and reconstruct the classes of the inflationary models which include the chaotic inflation, T-model, hilltop inflation, s-dual inflation, natural inflation and $R^2$ inflation.

Dynamical fine-tuning of initial conditions for small field inflation

Small-field inflation (SFI) is widely considered to be unnatural because an extreme fine-tuning of the initial condition is necessary for sufficiently large e-folding. In this paper, we show that the unnaturally-looking initial condition can be dynamically realised without any fine-tuning if the SFI occurs after rapid oscillations of the inflaton field and particle creations by preheating. In fact, if the inflaton field $\phi$ is coupled to another scalar field $\chi$ through the interaction $g^2 \chi^2 \phi^2$ and the vacuum energy during the small field inflation is given by $\lambda M^4$, the initial value can be dynamically set at $(\sqrt{\lambda}/g) M^2/M_{\rm pl}$, which is much smaller than the typical scale of the potential $M.$ This solves the initial condition problem in the new inflation model or some classes of the hilltop inflation models.

Impact of other scalar fields on oscillons after hilltop inflation

Oscillons are spatially localized and relatively stable field fluctuations which can form after inflation under suitable conditions. In order to reheat the universe, the fields which dominate the energy density after inflation have to couple to other degrees of freedom and finally produce the matter particles present in the universe today. In this study, we use lattice simulations in 2+1 dimensions to investigate how such couplings can affect the formation and stability of oscillons. We focus on models of hilltop inflation, where we have recently shown that hill crossing oscillons generically form, and consider the coupling to an additional scalar field which, depending on the value of the coupling parameter, can get resonantly enhanced from the inhomogeneous inflaton field. We find that three cases are realized: without a parametric resonance, the additional scalar field has no effects on the oscillons. For a fast and strong parametric resonance of the other scalar field, oscillons are strongly suppressed. For a delayed parametric resonance, on the other hand, the oscillons get imprinted on the other scalar field and their stability is even enhanced compared to the single-field oscillons.

Parametric resonance after hilltop inflation caused by an inhomogeneous inflaton field

We study preheating after hilltop inflation where the inflaton couples to another scalar field, e.g. a right-handed sneutrino, which provides a mechanism for generating the correct initial conditions for inflation and also a decay channel for the inflaton that allows for reheating and non-thermal leptogenesis. In the presence of such a coupling, we find that after the phases of tachyonic preheating and tachyonic oscillations, during which the inflaton field becomes inhomogeneous, there can be a subsequent preheating phase where the fluctuations of the other field get resonantly enhanced, from initial vacuum fluctuations up to amplitudes of the same order (and even larger) as the ones of the inflaton field. This resonant enhancement differs from the usual parametric resonance as the inflaton field is inhomogeneous at the time the enhancement takes place. We study this effect using lattice simulations as well as semi-analytically with a generalized Floquet analysis for inhomogeneous background fields.

Disappearing inflaton potential via heavy field dynamics

We propose a possibility that the inflaton potential is significantly modified after inflation due to heavy field dynamics. During inflation such a heavy scalar field may be stabilized at a value deviated from the low-energy minimum. In extreme cases, the inflaton potential vanishes and the inflaton becomes almost massless at some time after inflation. Such transition of the inflaton potential has interesting implications for primordial density perturbations, reheating, creation of unwanted relics, dark radiation, and experimental search for light degrees of freedom. To be concrete, we consider a chaotic inflation in supergravity where the inflaton mass parameter is promoted to a modulus field, finding that the inflaton becomes stable after the transition and contributes to dark matter. Another example is a hilltop inflation (also called new inflation) by the MSSM Higgs field which acquires a large expectation value just after inflation, but it returns to the origin after the transition and finally rolls down to the electroweak vacuum. Interestingly, the smallness of the electroweak scale compared to the Planck scale is directly related to the flatness of the inflaton potential.

New type of hill-top inflation

We suggest a new type of hill-top inflation originating from the initial conditions in the form of the microcanonical density matrix for the cosmological model with a large number of quantum fields conformally coupled to gravity. Initial conditions for inflation are set up by cosmological instantons describing underbarrier oscillations in the vicinity of the inflaton potential maximum. These periodic oscillations of the inflaton field and cosmological scale factor are obtained within the approximation of two coupled oscillators subject to the slow roll regime in the Euclidean time. This regime is characterized by rapid oscillations of the scale factor on the background of a slowly varying inflaton, which guarantees smallness of slow roll parameters ϵ and η of the following inflation stage. A hill-like shape of the inflaton potential is shown to be generated by logarithmic loop corrections to the tree-level asymptotically shift-invariant potential in the non-minimal Higgs inflation model and R2-gravity. The solution to the problem of hierarchy between the Planckian scale and the inflation scale is discussed within the concept of conformal higher spin fields, which also suggests the mechanism bringing the model below the gravitational cutoff and, thus, protecting it from large graviton loop corrections.

Origin of inflation in CFT driven cosmology: $$R^2$$ R 2 -gravity and non-minimally coupled inflaton models

We present a detailed derivation of the recently suggested new type of hill-top inflation [arXiv:1509.07270] originating from the microcanonical density matrix initial conditions in cosmology driven by conformal field theory (CFT). The cosmological instantons of topology $S^1\times S^3$, which set up these initial conditions, have the shape of a garland with multiple periodic oscillations of the scale factor of the spatial $S^3$-section. They describe underbarrier oscillations of the inflaton and scale factor in the vicinity of the inflaton potential maximum, which gives a sufficient amount of inflation required by the known CMB data. We build the approximation of two coupled harmonic oscillators for these garland instantons and show that they can generate inflation consistent with the parameters of the CMB primordial power spectrum in the non-minimal Higgs inflation model and in $R^2$ gravity. In particular, the instanton solutions provide smallness of inflationary slow-roll parameters $\epsilon$ and $\eta<0$ and their relation $\epsilon\sim\eta^2$ characteristic of these two models. We present the mechanism of formation of hill-like inflaton potentials, which is based on logarithmic loop corrections to the asymptotically shift-invariant tree level potentials of these models in the Einstein frame. We also discuss the role of $R^2$-gravity as an indispensable finite renormalization tool in the CFT driven cosmology, which guarantees the non-dynamical (ghost free) nature of its scale factor and special properties of its cosmological garland type instantons. Finally, as a solution to the problem of hierarchy between the Planckian scale and the inflation scale we discuss the concept of a hidden sector of conformal higher spin fields.

Inflation with a constant rate of roll

We consider an inflationary scenario where the rate of inflaton roll defined by ̈ϕ/H ϕ̇ remains constant. The rate of roll is small for slow-roll inflation, while a generic rate of roll leads to the interesting case of ‘constant-roll’ inflation. We find a general exact solution for the inflaton potential required for such inflaton behaviour. In this model, due to non-slow evolution of background, the would-be decaying mode of linear scalar (curvature) perturbations may not be neglected. It can even grow for some values of the model parameter, while the other mode always remains constant. However, this always occurs for unstable solutions which are not attractors for the given potential. The most interesting particular cases of constant-roll inflation remaining viable with the most recent observational data are quadratic hilltop inflation (with cutoff) and natural inflation (with an additional negative cosmological constant). In these cases even-order slow-roll parameters approach non-negligible constants while the odd ones are asymptotically vanishing in the quasi-de Sitter regime.

Scale factor self-dual cosmological models

We implement a conformal time scale factor duality for Friedmann-Robertson-Walker cosmological models, which is consistent with the weak energy condition. The requirement for self-duality determines the equations of state for a broad class of barotropic fluids. We study the example of a universe filled with two interacting fluids, presenting an accelerated and a decelerated period, with manifest UV/IR duality. The associated self-dual scalar field interaction turns out to coincide with the “radiation-like” modified Chaplygin gas models. We present an equivalent realization of them as gauged Kähler sigma models (minimally coupled to gravity) with very specific and interrelated Kähler- and super-potentials. Their applications in the description of hilltop inflation and also as quintessence models for the late universe are discussed.

Hill crossing during preheating after hilltop inflation

In ``hilltop inflation'', inflation takes place when the inflaton field slowly rolls from close to a maximum of its potential (i.e. the ``hilltop'') towards its minimum. When the inflaton potential is associated with a phase transition, possible topological defects produced during this phase transition, such as domain walls, are efficiently diluted during inflation. It is typically assumed that they also do not reform after inflation, i.e. that the inflaton field stays on its side of the ``hill'', finally performing damped oscillations around the minimum of the potential. In this paper we study the linear and the non-linear phases of preheating after hilltop inflation. We find that the fluctuations of the inflaton field during the tachyonic oscillation phase grow strong enough to allow the inflaton field to form regions in position space where it crosses ``over the top of the hill'' towards the ``wrong vacuum''. We investigate the formation and behaviour of these overshooting regions using lattice simulations: rather than durable domain walls, these regions form oscillon-like structures (i.e. localized bubbles that oscillate between the two vacua) which should be included in a careful study of preheating in hilltop inflation.

Inflation from gravitino condensates

We review work on the formation of gravitino condensates via the super-Higgs effect in the early Universe. This is a scenario for both inflating the early universe and breaking local supersymmetry(supergravity), entirely independent of any coupling to external matter. The goldstino mode associated with the breaking of (global) supersymmetry is “eaten” by the gravitino field, which becomes massive (via its own vacuum condensation) and breaks supergravity dynamically. The most natural association of gravitino condensates with inflation proceeds in an indirect way, via a Starobinsky-type inflation, in the massive gravitino phase. This inflationary phase is associated with scalar modes hidden in the higher order curvature corrections of the effective action arising from integrating out massive gravitino degrees of freedom. The scenario is in agreement with Planck data phenomenology in a natural and phenomenologically-relevant range of parameters, namely Grand-Unified-Theory values for the supersymmetry breaking energy scale and dynamically-induced gravitino mass. A hill-top inflation, on the other hand, which could also occur in the model, whereby the role of the inflaton field is played by the gravitino condensate itself, would require significant fine tuning in the inflaton's wave function renormalisation and thus may be discarded on naturalness grounds.

Getting inflationary models using the deformation method

In this paper we show that the dynamics associated with slow-roll models of inflation can be investigated through a method called the deformation procedure. Using the latter, we explicitly derive an expression linking two slow-roll inflationary potentials, applying the resulting framework to show how to construct an eternal inflation from chaotic inflation, or even, a natural inflation from hilltop inflation, easily.

Consistency relations for large-field inflation

Consistency relations for chaotic inflation with a monomial potential and natural inflation and hilltop inflation are given which involve the scalar spectral index $n_s$, the tensor-to-scalar ratio $r$ and the running of the spectral index $\alpha$. The measurement of $\alpha$ with $O(10^{-3})$ and the improvement in the measurement of $n_s$ could discriminate monomial model from natural/hilltop inflation models. A consistency region for general large field models is also presented.

Hilltop inflation with preinflation from coupling to matter fields

We propose a class of models of supersymmetric hilltop inflation (also called ``new inflation'') where the initial conditions of the inflaton close to the hilltop are generated through ``matter field preinflation''. This is achieved via a coupling term between the inflaton and matter fields (i.e. Standard Model fields or a right-handed neutrino). The same coupling also opens up a decay channel for the inflaton into Standard Model fields, which allows efficient reheating of the universe. We discuss the multifield dynamics of the inflaton and matter fields during inflation using the δN formalism and show under which conditions the model effectively reduces to single-field hilltop inflation during the last 60 e-folds. We also study perturbative reheating through the matter-inflaton coupling for a specific example where the matter field is identified with a right-handed (s)neutrino, and demonstrate that in this case the model can generate the observed baryon asymmetry through nonthermal leptogenesis.

Multi-natural inflation in supergravity

We show that the recently proposed multi-natural inflation can be realized within the framework of 4D ${\cal N}=1$ supergravity. The inflaton potential mainly consists of two sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase. For a sub-Planckian decay constant, the multi-natural inflation model is reduced to axion hilltop inflation. We show that, taking into account the effect of the relative phase, the spectral index can be increased to give a better fit to the Planck results, with respect to the hilltop quartic inflation. We also consider a possible UV completion based on a string-inspired model. Interestingly, the Hubble parameter during inflation is necessarily smaller than the gravitino mass, avoiding possible moduli destabilization. Reheating processes as well as non-thermal leptogenesis are also discussed.

Transition to order after hilltop inflation

We investigate the rich nonlinear dynamics during the end of hilltop inflation by numerically solving the coupled Klein-Gordon-Friedmann equations in an expanding universe. In particular, we search for coherent, nonperturbative configurations that may emerge due to the combination of nontrivial couplings between the fields and resonant effects from the cosmological expansion. We couple a massless field to the inflaton to investigate its effect on the existence and stability of coherent configurations and the effective equation of state at reheating. For parameters consistent with data from the Planck and WMAP satellites, and for a wide range of couplings between the inflaton and the massless field, we identify a transition from disorder to order characterized by emergent oscillonlike configurations. We verify that these configurations can contribute a maximum of roughly 30% of the energy density in the universe. At late times their contribution to the energy density drops to about 3%, but they remain long lived on cosmological time scales, being stable throughout our simulations. Cosmological oscillon emergence is described using a new measure of order in field theory known as relative configurational entropy.