We propose a model of inflation with a suitable potential for a single scalar field which falls in the wide class of hilltop inflation. We derive the analytical expressions for most of the physical quantities related to inflation and show that all of them represent the true behavior as required from a model of inflation. We further subject the results to observational verification by formulating the theory of perturbations based on our model followed by an estimation for the values of those observable parameters. Our model is found to be in excellent agreement with observational data. Thus, the features related to the model leads us to infer that this type of hilltop inflation may be a natural choice for explaining the early universe.
We study cosmological perturbations and observational aspects for mutated hilltop model of inflation. Employing mostly analytical treatment, we evaluate observable parameters during inflation as well as post-inflationary perturbations. This further leads to exploring observational aspects related to Cosmic Microwave Background (CMB) radiation. This semi-analytical treatment reduces complications related to numerical computation to some extent for studying the different phenomena related to CMB angular power spectrum for mutated hilltop inflation.
In this work we re-investigate pros and cons of mutated hilltop inflation. Applying Hamilton-Jacobi formalism we solve inflationary dynamics and find that inflation goes on along the ${\cal W}_{-1}$ branch of the Lambert function. Depending on the model parameter mutated hilltop model renders two types of inflationary solutions: one corresponds to small inflaton excursion during observable inflation and the other describes large field inflation. The inflationary observables from curvature perturbation are in tune with the current data for a wide range of the model parameter. The small field br…
We present $\mathcal{N}=1$ supergravity models of mutated hilltop inflation (MHI) for both large and small field sectors. Models with canonical kinetic terms are developed based on a shift symmetric Kähler potential in inflaton superfield, and with a superpotential linear in Goldstino superfield. We also construct models with non-canonical kinetic terms for MHI by generalizing the shift symmetry. We found that a good fraction of the models can address the entire branch of MHI in a single framework.
Here we test the predictions of the theory of the origin of the universe from the landscape multiverse, against the 2015 Planck data, for the case of the Hilltop class of inflationary models, for $p=4$ and $p=6$. By considering the quantum entanglement correction of the multiverse, we can place just a lower limit on the local 'SUSY-breaking' scale, respectively $b>8.7\times10^6 GeV$ at $95 \%$ c.l. and $b>1.3\times10^8 GeV$ at $95 \%$ c.l. from Planck TT+lowP, so the case with multiverse correction is statistically indistinguishable from the case with an unmodified inflation. We find that the …
We study inflation with the non-minimally coupled Standard Model Higgs in the case when quantum corrections generate a hilltop in the potential. We consider both the metric and the Palatini formulation of general relativity. We investigate hilltop inflation in different parts of the Higgs potential and calculate predictions for CMB observables. We run the renormalization group equations up from the electroweak scale and down from the hilltop, adding a jump in-between to account for unknown corrections in the intermediate regime. Within our approximation, no viable hilltop inflation is possible…
The swampland criteria put significant constraints on inflation models. In this paper, I show that hilltop inflation on the brane may provide an initial condition for hilltop inflation and produce topological eternal inflation without violating the swampland distance and refined de Sitter criteria. This shows a way that string theory may not be incompatible with eternal inflation.
A reformulation of inflationary model analyses appeared recently, in which inflationary observables are determined by the structure of a pole in the inflaton kinetic term rather than the shape of the inflaton potential. We comprehensively study this framework with an arbitrary order of the pole taking into account possible additional poles in the kinetic term or in the potential. Depending on the setup, the canonical potential becomes the form of hilltop or plateau models, variants of natural inflation, power-law inflation, or monomial/polynomial chaotic inflation. We demonstrate attractor beh…
Starting from Einstein-Yang-Mills in higher dimensions with an instanton on a compact sphere, we dimensionally reduce to find an effective four-dimensional action describing "hilltop" inflation. Using recent CMB data, we analyse the parameter space of this model to search for viable set-ups. One unique feature of this class of inflationary models is that the value of the inflaton field, or alternatively, the size of the compact sphere, is stabilised dynamically during the inflationary process.
We study `hilltop' inflation, in which inflation takes place near a maximum of the potential. Viewed as a model of inflation after the observable Universe leaves the horizon (observable inflation) hilltop inflation is rather generic. If the potential steepens monotonically, observable hilltop inflation gives a tiny tensor fraction (r< 0.002). The usual F- and D-term models may easily be transmuted to hilltop models by Planck-suppressed terms, making them more natural. The only commonly-considered model of observable inflation which is definitely not hilltop is tree-level hybrid inflation. View…
In this work, we consider a hilltop version of the (supersymmetric) sneutrino hybrid inflation where the right-handed sneutrino field plays the role of the inflaton field. This model is a type III hilltop inflation that can produce a spectral index $n_s=0.96$ which fits perfectly to experimental observations without fine-tuning of parameters. We also briefly consider nonthermal leptogenesis via the decay of the right-handed sneutrino inflaton field after inflation.
In this paper, I show that type I hilltop inflation under the current observational constaints could have $M_P^2 \frac{V^{\prime\prime}}{V} \sim -\mathcal{O}(10^{-2})$ in the parameter space which is in tension with the refined swampland criteria. On the other hand, $M_P^2 \frac{V^{\prime\prime}}{V} \sim -\mathcal{O}(1)$ can be achieved if type I hilltop inflation on the brane is considered.
The scale of small-field inflation cannot be constrained via primordial gravitational waves through measurement of tensor-to-scalar ratio $r$. In this study, I show that if cosmic strings are produced after symmetry breaking at the end of hilltop supernatural inflation, this small-field inflation model can be tested through the production of gravitational waves from cosmic strings. Future experiments of gravitational wave detectors will determine or further constrain the parameter space in the model.
Hilltop inflation models are often described by potentials $V = V_{0}(1-{ϕ^{n}\over m^{n}}+...)$. The omitted terms indicated by ellipsis do not affect inflation for $m \lesssim 1$, but the most popular models with $n =2$ and $4$ for $m \lesssim 1$ 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 $V = V_{0}(1-{ϕ^{n}\over m^{n}})$, for all $n$, converge to $r= 4/N \lesssim 0.07$, as in chaotic inflation with $V \sim ϕ$, suggesting a reasonably good fit to the Planck data. We show, however, that t…
In this paper, we investigate the parameter space in the framework of hilltop supernatural inflation in which the inflaton field can play the role of Affleck-Dine field to produce successful baryogenesis. The suitable value of reheating temperature could coincide with the reheating temperature required to produce lightest supersymmetric particle dark matter. The baryon isocurvature perturbation is shown to be negligible. We consider $p=3$, $p=4$, and $p=6$ type III hilltop inflation and discuss how to connect the models to supersymmetric theories.
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 $α$. The measurement of $α$ 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.
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 …
We study the low-temperature limit of warm inflation in a hilltop model. This limit remains valid up to the end of inflation, allowing an analytic description of the entire inflationary stage. In the weak dissipative regime, if the kinetic density of the inflaton dominates after inflation, low scale inflation is attained with Hubble scale as low as 1 GeV. In the strong dissipative regime, the model satisfies the observational requirements for the spectral index with a mild tuning of the model parameters, while also overcoming the $η$-problem of inflation. However, there is some danger of gravi…
In this paper, we explore the parameter space of hilltop supernatural inflation model and show the regime within which there is no gravitino problem even if we consider both thermal and nonthermal production mechanisms. We make plots for the allowed reheating temperature as a function of gravitino mass by constraints from big-bang nucleosynthesis. We also plot the constraint when gravitino is assumed to be stable and plays the role of dark matter.
We consider the basic supersymmetric (SUSY) models of F-term hybrid inflation (FHI). We show that a simple class of Kaehler potentials ensures a resolution to the ηproblem and allows for inflation of hilltop type. As a consequence, observationally acceptable values for the spectral index, ns, can be achieved constraining the coefficient c4k of the quartic supergravity correction to the inflationary potential. For about the central value of ns, in the case of standard FHI, the grand unification (GUT) scale turns out to be well below its SUSY value with the relevant coupling constant κin the ran…
It has been shown that black holes would have formed in the early Universe if, on any given scale, the spectral amplitude of the Cosmic Microwave Background (CMB) exceeds 10^(-4). This value is within the bounds allowed by astrophysical phenomena for the small scale spectrum of the CMB, corresponding to scales which exit the horizon at the end of slow-roll inflation. Previous work by Kohri et. al. (2007) showed that for black holes to form from a single field model of inflation, the slope of the potential at the end of inflation must be flatter than it was at horizon exit. In this work we show…
In this paper, we consider high scale (100 TeV) supersymmetry (SUSY) breaking and realize the idea of hilltop supernatural inflation in concrete particle physics models based on flipped-SU(5) and Pati-Salam models in the framework of supersymmetric grand unified theories (SUSY GUTs). The inflaton can be a flat direction including right-handed sneutrino and the waterfall field is a GUT Higgs. The spectral index is $n_s=0.96$ which fits very well with recent data by PLANCK satellite. There is no both thermal and non-thermal gravitino problems. Non-thermal leptogenesis can be resulted from the de…
A new hybrid inflationary scenario in the context of $f(R,{\Box}R)$-gravity is proposed. Demanding the waterfall field to 'support the potential from below' [unlike the original proposal by Stewart in Phys. Lett. B345, 414 (1995)], we demonstrate that the scalar potential is similar to that of the large-field chaotic inflation model proposed by Linde in Phys. Lett. B129, 177 (1983). Inflationary observables are used to constrain the parameter space of our model; in the process, an interesting limit on the number of e-folds N is found.
Using analytic expressions, we explore the parameter space for hilltop inflation models with a potential of the form $V_0\pm m^2ϕ^2 -aϕ^p$. With the positive sign and p>2 this converts the original hybrid inflation model into a hilltop model, allowing the spectral index to agree with the observed value n=0.95. In some cases the observed value is theoretically favored, while in others there is only the generic prediction $|n-1|\lsim 1$.
We investigate the rich nonlinear dynamics during the end of hilltop inflation by numerically solving the coupled Klein-Gordon-Friedmann equations in a 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 …
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 …
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 …
In this work, we studied the slow-roll approximation of cosmic inflation within the context of $f(R,T)$ gravity, where $R$ is the scalar curvature, and $T$ is the trace of the energy-momentum tensor. By choosing a minimal coupling between matter and gravity, we obtained the modified slow-roll parameters, the scalar spectral index ($n_s$), the tensor spectral index ($n_{\textrm{T}}$), and the tensor-to-scalar ratio ($r$). We computed these quantities for a general power-law potential, Natural & Quartic Hilltop inflation, and the Starobinsky model, plotting the trajectories on the $(n_s,r)$ plan…
F-term hybrid inflation (FHI) of the hilltop type can generate a scalar spectral index, ns, in agreement with the fitting of the seven-year Wilkinson microwave anisotropy probe data by the standard power-law cosmological model with cold dark matter and a cosmological constant, LambdaCDM. We investigate the realization of this type of FHI by using quasi-canonical Kahler potentials with or without the inclusion of extra hidden-sector fields. In the first case, acceptable results can be obtained by constraining the coefficients of the quadratic and/or quartic supergravity correction to the inflat…
We show explicitly how the T model, E model, and Hilltop inflations are obtained from the general scalar-tensor theory of gravity with arbitrary conformal factors in the strong coupling limit. We argue that $ξ$ attractors can give any observables $n_s$ and $r$ by this method. The existence of attractors imposes a challenge to distinguish different models.
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 study non-Gaussianity of density perturbations generated by an axionic curvaton, focusing on the case that the curvaton sits near the hilltop of the potential during inflation. Such hilltop curvatons can generate a red-tilted density perturbation spectrum without invoking large-field inflation. We show that, even when the curvaton dominates the Universe, the non-Gaussianity parameter fNL is positive and mildly increases towards the hilltop of the curvaton potential, and that fNL = O(10) is a general and robust prediction of such hilltop axionic curvatons. In particular, we find that the non…
We present constraints on inflationary dynamics and features in the primordial power spectrum of scalar perturbations using the Cosmic Microwave Background temperature, polarization data from Planck 2018 data release and updated likelihoods. We constrain the slow-roll dynamics using Hilltop Quartic Potential and Starobinsky $R+R^2$ model in the Einstein frame using the Planck 2018 binned Plik likelihood. Using the Hilltop as base potential we construct Whipped Inflation potential to introduce suppression in the scalar power spectrum at large angular scales. We notice marginal (68% C.L.) prefer…
In this paper, we investigate complex-valued Euclidean wormholes in the Starobinsky inflation. Due to the properties of the concave inflaton potential, the classicality condition at both ends of the wormhole can be satisfied, as long as the initial condition of the inflaton field is such that it is located sufficiently close to the hilltop. We compare the probabilities of classicalized wormholes with the Hartle-Hawking compact instantons and conclude that the Euclidean wormholes are probabilistically preferred than compact instantons, if the inflation lasts more than 50 e-foldings. Our result …
We study ``hilltop'' curvatons that evolve on a convex potential. Hilltop curvatons evolving on the Hubble-induced potential are generic if supergravity is assumed in the theory. We do not consider curvatons whose potential is protected from $O(H)$ corrections, where $H$ is the Hubble parameter. We assume that the effective mass of a curvaton is expressed as $m_σ= c H$, where the coefficient varies within $0.2 \le c \le 5$ depending on the circumstances. A negative mass term may lead to enhancement of curvaton fluctuation, which has a significant impact on the energy bound for low-scale inflat…
We propose a novel scenario of inflation, in which the inflaton is identified as the lightest mode of an angular field in a compactified fifth dimension. The periodic effective potential exhibits exponentially flat plateaus, so that a sub-Planckian field excursion without hilltop initial conditions is naturally realized. We can obtain consistent predictions with observations on the spectral index and the tensor-to-scalar ratio.
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 par…
Oscillons are spatially localised strong fluctuations of a scalar field. They can e.g. form after inflation when the scalar field potential is shallower than quadratic away from the minimum. Although oscillons are not protected by topology, they can be remarkably stable and have a significant impact on the (p)reheating phase. In this work we investigate the properties of oscillons in hilltop-shaped potentials, in particular the typical energies, shapes and lifetimes. In the first part of the paper, we simulate oscillon creation and stabilization with (3+1)-dimensional classical lattice simulat…
We study cosmological inflation and its dynamics in the framework of the Randall-Sundrum II brane model. In particular, we analyze in detail four representative small-field inflationary potentials, namely Natural inflation, Hilltop inflation, Higgs-like inflation, and Exponential SUSY inflation, each characterized by two mass scales. We constrain the parameters for which a viable inflationary Universe emerges using the latest PLANCK results. Furthermore, we investigate whether or not those models in brane cosmology are consistent with the recently proposed Swampland Criteria, and give predicti…
We investigate all single-field, slow-roll inflationary models whose slow-roll parameters scale as 1/N in the limit of a large number of e-folds N. We proof that all such models belong to two universality classes, characterised by a single parameter. One class contains small field models like hilltop inflation, while the other class consists of large field models like chaotic inflation. We give the leading expressions for the spectral index and tensor-to-scalar ratio r, which are universal for each class, plus subleading corrections for a number of models. This predicts r either to be unobserv…
We consider scalar field inflation in the Palatini formulation of general relativity. The covariant derivative of the metric is then non-zero. From the effective theory point of view it should couple to other fields. We write down the most general couplings between it and a scalar field that are quadratic in derivatives. We consider both the case when the torsion is determined by the field equations and the case when it is assumed to be zero a priori. We find the metric derivative terms can significantly modify inflationary predictions. We specialise to Higgs inflation and terms of only up to …
What new physics can we extract from inflation using the ACT DR6 and DESI DR2 Observations?
SGT University（SGT大学）；Institute of Theoretical Physics, Faculty of Physics, University of Warsaw（华沙大学物理学院理论物理研究所）；Center for Theoretical Physics, L.N. Gumilyov Eurasian National University（L.N. 古米廖夫欧亚国立大学理论物理中心）；B.M.S. College of Engineering（B.M.S.工程学院）
Matrix inflation, or M-flation, is a string theory motivated inflationary model with three scalar field matrices and gauge fields in the adjoint representation of the $\mathbf{U}(N)$ gauge group. One of these $3N^2$ scalars appears as the effective inflaton while the rest of the fields (scalar and gauge fields) can play the role of isocurvature fields during inflation and preheat fields afterwards. There is a region in parameter space and initial field values, "the hilltop region," where predictions of the model are quite compatible with the recent Planck data. We show that in this hilltop reg…
Assuming that inflation is succeeded by a phase of matter domination, which corresponds to a low temperature of reheating $T_r<10^9\rm{GeV}$, we evaluate the spectra of gravitational waves induced in the post-inflationary universe. We work with models of hilltop-inflation with an enhanced primordial 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 densities within the ranges of both space and earth based gravitational wave detectors.
We show that initial conditions for small-field inflation can be determined quantum mechanically by introducing a suitable flattened region in the scalar potential. The inflaton is then driven towards the slow-roll attractor solution exponentially fast, desensitising inflation from the initial velocity and partially evading the so-called overshoot problem. We give an explicit example in the context of hilltop inflation by introducing an ultra slow-roll plateau around the maximum of the potential and analyse its effect on the phase-space trajectories.
In this work, we study constant-roll inflation driven by a scalar field with non-minimal derivative coupling to gravity, via the Einstein tensor. This model contains a free parameter, $η$, which quantifies the non-minimal derivative coupling and a parameter $α$ which characterize 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 an…
We propose a multi-natural inflation model in which the single-field inflaton potential consists of two or more sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase. The model is versatile enough to realize both large-field and small-field inflation. We show that, in a model with two sinusoidal potentials, the predicted values of the spectral index and tensor-to-scalar ratio lie within the $1σ$ region of the Planck data. In particular, there is no lower bound on the decay constants in contrast to the original natural inflatio…
We show that the radion in a warped geometry bounded by two branes can have a potential suitable for inflation. Our construction is based upon a solution known in string theory as the linear dilaton, in which the back-reaction from a bulk scalar Φis exactly accounted for. The radion, stabilized by Φ, is much heavier than the TeV scale and its couplings to the standard model are much more suppressed than in the usual Randall-Sundrum solution. We present a new formalism for obtaining approximate time-dependent solutions, based on perturbing the exact solution to the coupled Einstein and scalar f…
We propose a solution to the eta-problem in supergravity (SUGRA) hybrid inflation using a Nambu-Goldstone-like shift symmetry within a new class of models. The flatness of the tree-level inflaton potential is ensured by shift symmetry invariance of the Kaehler potential, while a small symmetry breaking term in the superpotential gives rise to a slope of the potential at loop-level. In the proposed class of inflation models, potentially dangerous couplings between the inflaton and the moduli sector are avoided. We also discuss under which conditions the predicted spectral index can be in agreem…
We investigate how long wavelength inflationary fluctuations can cause the background field to deviate from classical dynamics. For generic potentials, we show that, in the Hartree approximation, the long wavelength dynamics can be encapsulated by a two-field model operating in an effective potential. The latter is given by a simple Gaussian integral transformation of the original inflationary potential. We use this new expression to study backreaction effects in quadratic, hilltop, flattened, and axion monodromy potentials. We find that the net result of the altered dynamics is to slightly mo…
We examine a wide class of multi-field inflationary models based on fields that decay or stabilize during inflation in a staggered fashion. The fields driving assisted inflation are on flat, short stretches, before they encounter a sharp drop; whenever a field encounters such a drop due to its slow roll evolution, its energy is transferred to other degrees of freedom, i.e. radiation. The rate at which fields decay is determined dynamically and it is not a free parameter in this class of models. To compute observables, we generalize the analytic framework of staggered inflation, allowing for mo…
We consider cosmological inflation generated by a scalar field slowly rolling off from a de Sitter maximum of its potential. The models belong to the class of hilltop models and represent the most general model of this kind in which the scalar potential can be written as the sum of two exponentials. The minimally coupled Einstein-scalar gravity theory obtained in this way is the cosmological version of a two-scale generalization of known holographic models, allowing for solitonic solutions interpolating between an AdS spacetime in the infrared and scaling solutions in the ultraviolet. We then …
We consider Supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the phi^n potential with n=2 or 4. We show that the coexistence of an exponential nonminimal coupling to gravity, fR=Exp(cR phi^p), with a kinetic mixing of the form fK=cK fR^m can accommodate inflationary observables favored by the Planck and Bicep2/Keck Array results for p=1 and 2, 1<=m<=15 and 2.6x10^(-3)<=rRK=cR/cK^(p/2)<=1, where the upper limit is not imposed for p=1. Inflation is of hilltop type and it can be attained for subplanckian inflaton values with the corresponding effective theories retaining th…
