Hilltop Inflation Models Research Articles

Swampland, trans-Planckian censorship and fine-tuning problem for inflation: tunnelling wavefunction to the rescue

The trans-Planckian censorship conjecture implies that single-field models of inflation require an extreme fine-tuning of the initial conditions due to the very low-scale of inflation. In this work, we show how a quantum cosmological proposal—namely the tunneling wavefunction—naturally provides the necessary initial conditions without requiring such fine-tunings. More generally, we show how the tunneling wavefunction can provide suitable initial conditions for hilltop inflation models, the latter being typically preferred by the swampland constraints.

On hilltop and brane inflation after Planck

Hilltop inflation models are often described by potentials V = V0 (1−ϕn/mn+… ). The omitted terms indicated by ellipsis do not affect inflation for m ≲ 1, but the most popular models with n = 2 and 4 for m ≲ 1 are ruled out observationally. Meanwhile in the large m limit the results of the calculations of the tensor to scalar ratio r in the models with V = V0 (1−ϕn/mn), for all n, converge to r = 4/N ≲ 0.07, as in chaotic inflation with V ∼ ϕ, suggesting a reasonably good fit to the Planck data. We show, however, that this is an artifact related to the inconsistency of the model V = V0 (1−ϕn/mn) at ϕ > m. Consistent generalizations of this model in the large m limit typically lead to a much greater value r = 8/N, which negatively affects the observational status of hilltop inflation. Similar results are valid for D-brane inflation with V = V0(1−mn/ϕn), but consistent generalizations of D-brane inflation models may successfully complement α-attractors in describing most of the area in the (ns, r) space favored by Planck 2018.

QCD axion window and low-scale inflation

We show that the upper bound of the classical QCD axion window can be significantly relaxed for low-scale inflation. If the Gibbons-Hawking temperature during inflation is lower than the QCD scale, the initial QCD axion misalignment angle follows the Bunch-Davies distribution. The distribution is peaked at the strong CP conserving minimum if there is no other light degree of freedom contributing to the strong CP phase. As a result, the axion overproduction problem is significantly relaxed even for an axion decay constant larger than $10^{12}$GeV. We also provide concrete hilltop inflation models where the Hubble parameter during inflation is comparable to or much smaller than the QCD scale, with successful reheating taking place via perturbative decays or dissipation processes.

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.

Observable induced gravitational waves from an early matter phase

Assuming that inflation is succeeded by a phase of matter domination, which correspondsto a low temperature of reheating Tr < 109GeV, we evaluate the spectraof gravitational waves induced in the post-inflationary universe. We work with models of hilltop-inflation with an enhancedprimordial scalar spectrum on small scales, which can potentially lead to the formation of primordial black holes.We find that a lower reheat temperature leads to the production of gravitational waves with energy densitieswithin the ranges of both space and earth based gravitational wave detectors.

Non-Gaussianity in AxionN-flation Models

We study perturbations in the multifield axion N-flation model, taking account of the full cosine potential. We find significant differences from previous analyses which made a quadratic approximation to the potential. The tensor-to-scalar ratio and the scalar spectral index move to lower values, which nevertheless provide an acceptable fit to observation. Most significantly, we find that the bispectrum non-Gaussianity parameter f{NL} may be large, typically of order 10 for moderate values of the axion decay constant, increasing to of order 100 for decay constants slightly smaller than the Planck scale. Such a non-Gaussian fraction is detectable. We argue that this property is generic in multifield models of hilltop inflation.

More hilltop inflation models

Using analytic expressions, we explore the parameter space for hilltop inflation models with a potential of theform V0 ± m2ϕ2−aϕp. With thepositive sign and p>2 this converts the original hybrid inflation model into a hilltopmodel, allowing the spectral index to agree with the observed valuen = 0.95. In some cases the observed value is theoretically favored, while in others there is only thegeneric prediction .

Large non-Gaussianity from non-local inflation

We study the possibility of obtaining large non-Gaussian signaturesin the cosmic microwave background in a general class of single-fieldnon-local hilltop inflation models. We estimate the non-linearity parameterfNL which characterizes non-Gaussianity in such models and showthat large non-Gaussianity is possible. For the recently proposedp-adic inflationmodel we find that fNL∼120 when the string coupling is order unity. We show that large non-Gaussianity is alsopossible in a toy model with an action similar to those which arise in string fieldtheory.