Primordial perturbations in Type III hilltop inflation models
Chia-Min Lin, Harish Dhananjay Nalla, Chen-Pin Yeh, Da-Shin Lee
备注：
Accepted version to appear in JCAP. 15 pages, 7 figures. Added a subsection on PBH mass with a figure and references. Results remain unchanged. arXiv admin note: text overlap with arXiv:2311.13746
We analytically compute the power spectrum of primordial curvature perturbations in Type III hilltop inflation models under the slow-roll approximation. The model parameters are constrained using current Cosmic Microwave Background (CMB) data. The curvature perturbations that exit the horizon at small scales show sufficiently large amplitudes to produce primordial black holes (PBHs). We then consider the quantum one-loop corrections in these models from both the self-interaction of the inflaton and its interaction with the waterfall field. We show the loop corrections in both cases for 60 e-folds of inflation are negligible, ensuring the tree-level results are reliable within the chosen parameter regime.
A correction to the Quartic Hilltop inflationary model is proposed to account for stabilising terms in the potential. We derive analytical predictions for the spectral index $n_s$ and tensor-scalar ratio $r$ which lie within the Planck 2018 survey bounds. The reheating predictions of the corrected model are investigated and by considering the reheating temperature we further constrain the $(n_s,r)$ parameter space. It is shown that the correction terms are physically important during inflation and generally need to be accounted for when considering Hilltop models as a candidate for inflation.
In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framework of loop quantum cosmology. The initial conditions of inflaton field at the quantum bounce is categorized into two classes, first one is dominated by kinetic energy and second one by potential energy. In both cases, the physically viable initial values of inflaton field at the bounce are obtained numerically that generate the desired slow-roll inflation and also sufficient number of $e$-folds. To be consistent with observations at least 60 $e$-folds are required. In case of kinetic energy dominat…
Quartic hilltop inflation remains one of the most successful inflationary models. Yet, the expectations of early treatments of hilltop inflation would contradict the observations and render the model excluded. However, recent numerical treatment has demonstrated that quartic hilltop inflation actually fares well with observations. In this work, a fully analytic treatment of the model aims to dispel the mystery surrounding the behaviour of quartic hilltop inflation. The results obtained are in excellent agreement with numerical works on the subject, yet offer simple analytic formulas to calcula…
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.
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…
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 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, th…
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…
Primordial magnetic field generated in the inflationary era can act as a viable source for the present day intergalactic magnetic field of sufficient strength. We present a fundamental origin for such a primordial generation of the magnetic field, namely through anomaly cancellation of $U(1)$ gauge field in quantum electrodynamics in the context of hilltop inflation. We have analysed at length the power spectrum of the magnetic field, thus generated, which turns out to be helical in nature. We have also found that magnetic power spectrum has significant scale-dependence giving rise to a non-tr…
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…
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…
We implement a procedure by which the parameters present in the potential of Quartic Hilltop Inflation (QHI) are eliminated in favor of the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$. By doing this it is posible to obtain in a straightforward and simple way the equations of a previous analysis where an analytical treatment of QHI in the large field limit is given. This procedure also allows a more precise discussion of general properties of the model. Also, using a constraint from the reheating epoch it is possible to find bounds for the parameters of the model as well as f…
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 …
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…
We show explicitly how the T-model, E-model, and Hilltop inflations are obtained from the inflation models with a non-canonical kinetic term and an arbitrary potential. By this method, any attractor of observables $n_s$ and $r$ is possible. The presence of attractors poses a challenge to differentiate inflation models.
We show that the initial misalignment angle of the QCD axion (or axion-like particles) can be set very close to $π$, if the QCD axion has a mixing with another heavy axion which induces the phase shift $\approx π$ after inflation. In the simplest case, the heavy axion plays the role of the inflaton, and we call such inflation as "$π$nflation." The basic idea was first proposed by Daido and the present authors in Ref. [1702.03284] in 2017 and more recently discussed in Ref. [1903.00462]. We show that the QCD axion with a decay constant $f_a \gtrsim 3 \times 10^9\,$ GeV can explain dark matter b…
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…
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.
Constraining non-minimally coupled squared-Quartic Hilltop Inflation in light of ACT observations
Faculty of Science and Technology, Nakhon Si Thammarat Rajabhat University（那空沙他马拉差帕大学理学院）；Urgench State University（乌尔根奇国立大学）；School of Science & College of Graduate Studies, Walailak University（瓦莱拉克大学理学院及研究生院）
We examine the theoretical possibility for the heavy QCD axion to induce slow-roll inflation while solving the strong CP problem through the Peccei-Quinn mechanism. If the cancellation between contributions from a small-size instanton and another Peccei-Quinn symmetry breaking occurs with high accuracy, the potential can be flattened enough near its maximum to achieve hilltop inflation. This comes at the cost of severe fine-tuning of their relative size and phase, but it also allows us to relate the high quality problem of the Peccei-Quinn symmetry to the fine-tuning problem of the hilltop inf…
In this work we determine the power spectrum of the gravitational potential of the primordial fluctuations for an inflationary model whose \emph{inflaton} is a non-canonical scalar field of the tachyon-type. The respective background field equations for an inverse-square potential produce a power-law inflation, and it is explicitly shown that for such a potential the power spectrum tends to be scale-independent for highly accelerated regimes in the inflationary expansion.
We investigate the origin and evolution of primordial electric and magnetic fields in the early universe, when the expansion is governed by a cosmological constant $Λ_0$. Using the gravitoelectromagnetic inflationary formalism with $A_0=0$, we obtain the power of spectrums for large-scale magnetic fields and the inflaton field fluctuations during inflation. A very important fact is that our formalism is {\em naturally non-conformally invariant}.
I consider a semiclassical expansion of the scalar field in the warm inflation scenario. I study the evolution for the fluctuations of the metric around the Friedmann-Robertson-Walker one. The formalism predicts that, in the power-law expansion universe, the fluctuations of the metric decreases with time.
The gravitationally enhanced friction can reduce the speed of the inflaton to realize an ultra-slow-roll inflation, which will amplify the curvature perturbations. The amplified perturbations can generate a sizable amount of primordial black holes (PBHs) and induce simultaneously a significant background gravitational waves (SIGWs). In this paper, we investigate the primordial non-Gaussianity of the curvature perturbations in the inflation with gravitationally enhanced friction. We find that when the gravitationally enhanced friction plays a role in the inflationary dynamics, the non-Gaussiani…
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.
It is shown that in a number of scalar potentials with an unstable local maximum at the origin chaotic inflation is followed by new inflation if model parameters are appropriately chosen. In this model density fluctuation can have a large-amplitude peak on the comoving Hubble scale at the onset of the slow-roll new inflation and can result in formation of appreciable amount of primordial black holes on astrophysically interesting mass scales.
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…
In this study, we investigate the consequence of the constant-roll condition and examine the role of $f(Q,T)$ gravity in the cosmological inflation process. We analyze the inflationary scenario by calculating modified Friedmann equations, and giving an alternative technique that enables relating modified slow-roll parameters to the constant roll parameter $β$. Considering both chaotic and hilltop models, we calculate the spectral index and the tensor-to-scalar ratio and compare their compatibility with Planck's data for different choices of the constant roll parameter $β$. We examine the evolu…
We propose a new single field inflation model in which the usual slow-roll inflation is joined to a new period of slow-climb and slow-roll inflation through a short intermediate non-inflationary phase. We then show that primordial curvature perturbations can be enhanced at small scales, a sizable amount of primordial black holes (PBHs) can be produced which make up most of dark matter, the gravitational waves (GWs) induced by scalar metric perturbations that accompany with the formation of PBHs can be detectable by future GW experiments, and last but not least, our model is compatible with the…
Enormous information about interactions is contained in the non-Gaussianities of the primordial curvature perturbations, which are essential to break the degeneracy of inflationary models. We study the primordial bispectra for G-inflation models predicting both sharp and broad peaks in the primordial scalar power spectrum. We calculate the non-Gaussianity parameter $f_{\mathrm{NL}}$ in the equilateral limit and squeezed limit numerically, and confirm that the consistency relation holds in these models. Even though $f_{\mathrm{NL}}$ becomes large at the scales before the power spectrum reaches …
There are at least three cosmic backgrounds of primordial gravitational waves coming from inflation: those produced during inflation and associated with the stretching of quantum modes; those produced at the violent stage of preheating after inflation; and those associated with the self-ordering of Goldstone modes if inflation ends via a global symmetry breaking scenario, like in hybrid inflation. Each background has its own characteristic spectrum with specific features. We describe in detail the origin of extra peaks in the PGW background from preheating in the case in which inflation ends w…
We study a hilltop inflation model where an axion-like particle (ALP) plays the role of the inflaton. We find that, for a broad class of potentials, the decay constant and the mass at the potential minimum satisfy the relation, $m_ϕ\sim 10^{-6} f$, to explain the CMB normalization. The ALP is necessarily coupled to the standard model particles for successful reheating. The ALP with the above relation can be searched at beam dump experiments, e.g., the SHiP experiment, if the inflation scale is sufficiently low. In this case, the ALP decays through the interactions that led to the reheating of …
Certain models of cosmic inflation produce strong cosmological perturbations at short length scales, which may later collapse into primordial black holes. To find the statistics of these strong perturbations and the ensuing black holes, it is necessary to go beyond linear perturbation theory. Stochastic inflation provides a way to take the leading non-linear effects into account. In this contribution, I discuss recent progress in numerical computations of stochastic inflation. A numerical approach can include more of the non-linearities than an analytical calculation, and can be applied to sin…
The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it is consistent with many inflation models that can produce primordial black holes, such as nonminimal derivative coupling inflation, scalar-tensor inflation, Gauss-Bonnet inflation, and K/G inflation. The constraints from primordial black holes on the primordial curvature power spectrum with the broken power law form are obtained, where the fra…
We investigate the primordial power spectra for general kinetic inflation models that support a period of kinetic dominance in the case of curved universes. We present derivations of the Mukhanov-Sasaki equations with a nonstandard scalar kinetic Lagrangian which manifests itself through the inflationary sound speed $c_s^2$. We extend the analytical approximations exploited in Contaldi et al [1] and Thavanesan et al [2] to general kinetic Lagrangians and show the effect of $k$-inflation on the primordial power spectra for models with curvature. In particular, the interplay between sound speed …
We study the emission of neutral massless $(1, 2)\hbar$-spin bosons during power-law inflation using unified spinor field theory. We shows that during inflation gravitons and photons were emitted with wavelengths (on physical coordinates) that increase as the Hubble radius: $λ_{Ph} \sim a/H$. The quantised action related to these bosons is calculated and results to be a fraction of the Planck constant.
We compute the spectral index for scalar perturbations generated in a primordial inflationary model. In this model, the transition of the inflationary phase to the radiative era is achieved through the decay of the cosmological term leading a second order phase transition and the characteristics of the model allow to implement a set of initial conditions where the perturbations display a thermal spectrum when they emerge from the horizon. The obtained value for the spectral index is equal to 2, a result that depends very weakly on the various parameters of the model and on the initial conditio…
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…
The large-scale power deficit in the cosmic microwave background fluctuations might be relevant with the physics of pre-inflation, a bounce, or a superinflationary phase preceding slow-roll inflation, which can provide a singular-free realization of inflation. We investigate the primordial perturbations from such pre-inflationary evolutions, which generally may consist of multiple phases with different background dynamics, and give a universal formula for the power spectrum of primordial perturbations in terms of the recursive Bogoliubov coefficients. We also apply our formula to corresponding…
We study a double inflation model (a hybrid inflation + a new inflation) in supergravity and discuss the formation of primordial black holes (PBHs) with mass \sim 10^{-20}-10^{5}M_{\odot}. We find that in a wide range of parameter space, we obtain PBHs which amount to Ω\simeq 1, i.e., PBH dark matter. Also, we find a set of inflation parameters which produces PBHs evaporating now. Those PBHs may be responsible for antiproton fluxes observed by the BESS experiment.
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）
We consider the space-condensate inflation model to study the primordial gravitational waves generated in the early Universe. We calculate the energy spectrum of gravitational waves induced by the space-condensate inflation model for full frequency range with assumption that the phase transition between two consecutive regimes to be abrupt during evolution of the Universe. The suppression of energy spectrum is found in our model for the decreasing frequency of gravitational waves depending on the model parameter. To realize the suppression of energy spectrum of the primordial gravitational wav…
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-Guassianity 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 initia…
Measuring the primordial power spectrum on small scales is a powerful tool in inflation model building, yet constraints from Cosmic Microwave Background measurements alone are insufficient to place bounds stringent enough to be appreciably effective. For the very small scale spectrum, those which subtend angles of less than 0.3 degrees on the sky, an upper bound can be extracted from the astrophysical constraints on the possible production of primordial black holes in the early universe. A recently discovered observational by-product of an enhanced power spectrum on small scales, induced gravi…
We argue that primordial gravitational waves have a spectral break and its information is quite useful for exploring the early universe. Indeed, such a spectral break can be a fingerprint of the end of inflation, and the amplitude and the frequency at the break can tell us the energy scale of inflation and the reheating temperature simultaneously. In order to investigate the spectral break, we give an analytic formula for evolution of the Hubble parameter around the end of inflation where the slow roll approximation breaks down. We also evaluate the spectrum of primordial gravitational waves a…
