We study the axion-type curvaton model, with emphasis on the large field regime where analytic results are very difficult to obtain. We evaluate the tensor-scalar ratio $r$ using WMAP normalization and the non-linearity parameters $f_{NL}$ and $g_{NL}$ by solving the equations numerically using the $δN$ formalism. We compare them with results for the curvaton with quadratic potential. We find that $r$ is much smaller for the axion-type case compared to the result from the quadratic potential, with the difference increasingly more pronounced at larger field values. $g_{NL}$ is found to be positive, unlike the quadratic case where it is negative, and the amplitude of $g_{NL}$ is much larger. Moreover, there is a nearly linear scaling between $g_{NL}$ and $f_{NL}$, with small deviation from linearity at large field values. The slope between $g_{NL}$ and $f_{NL}$ depends on the parameters characterizing the axion-type curvaton model. We further consider a mixed scenario where both the inflaton and the curvaton contribute to the primordial power spectrum and the non-Gaussianity parameters are found to be much larger than those in the case with quadratic potential.
We derive the spectral index of $f_{NL}$ and its running from isocurvature single field and investigate the curvaton models with a negative spectral index of $f_{NL}$ in detail. In particular, a numerical study of the axion-type curvaton model is illustrated, and we find that the spectral index of $f_{NL}$ is negative and its absolute value is maximized around $σ_*=πf/2$ for the potential $V(σ)=m^2f^2(1-\cos{σ\over f})$. The spectral index of $f_{NL}$ can be ${\cal O}(-0.1)$ for the axion-type curvaton model. A convincing detection of a positive $n_{f_{NL}}$ will rule out the axion-type curvat…
We revisit the generation of dark matter isocurvature perturbations in the curvaton model in greater detail, both analytically and numerically. As concrete examples, we investigate the cases of thermally decoupled dark matter and axionic dark matter. We show that the radiation produced by the decay of the curvaton, which has not been taken into account in previous analytical studies, can significantly affect the amplitude of isocurvature perturbations. In particular, we find that they are drastically suppressed even when the dark matter freeze-out (or the onset of the axion oscillations for ax…
We discuss a possible connection between the recent NANOGrav results and the primordial black holes (PBHs) for the LIGO-Virgo events. In particular, we focus on the axion-like curvaton model, which provides a sizable amount of PBHs and GWs induced by scalar perturbations around the NANOGrav frequency range. The inevitable non-Gaussianity of this model suppresses the induced GWs associated with PBHs for the LIGO-Virgo events to be compatible with the NANOGrav results. We show that the axion-like curvaton model can account for PBHs for the LIGO-Virgo events and the NANOGrav results simultaneousl…
Considering the curvaton field that follows dissipative slow-roll equation, we show that the field can lead to entropy production and generation of curvature perturbation after reheating. Spectral index is calculated to discriminate warm and thermal scenarios of dissipative curvatons from the standard curvaton model. In contrast to the original curvaton model, quadratic potential is not needed in the dissipative scenario, since the growth in the oscillating period is not essential for the model.
We argue that the existence of the cold dark matter is explained by primordial black holes.We show that a significant number of primordial black holes can be formed in an axion-like curvaton model, in which the highly blue-tilted power spectrum of primordial curvature perturbations is achieved.It is found that the produced black holes with masses $\sim 10^{20} -10^{38} \mathrm{g}$ account for the present cold dark matter.We also argue the possibility of forming the primordial black holes with mass $\sim 10^5 M_{\odot}$ as seeds of the supermassive black holes.
We revise primordial black hole (PBH) formation in the axion-like curvaton model and investigate whether PBHs formed in this model can be the origin of the gravtitational wave (GW) signals detected by the Advanced LIGO. In this model, small-scale curvature perturbations with large amplitude are generated, which is essential for PBH formation. On the other hand, large curvature perturbations also become a source of primordial GWs by their second-order effects. Severe constraints are imposed on such GWs by pulsar timing array (PTA) experiments. We also check the consistency of the model with the…
The recent report of NANOGrav is gathering attention since its signal can be explained by the stochastic gravitational waves (GWs) with $Ω_{\rm GW}\sim 10^{-9}$ at $f\sim 10^{-8}$Hz. The PBH formation scenario is one of the candidates for the NANOGrav signal, which can simultaneously explain the observed $30 M_\odot$ black holes in the binary merger events in LIGO-Virgo collaboration. We focus on the type II axion-like curvaton model of the PBH formation. In type II model the complex field whose phase part is the axion rolls down from the origin of the potential. It is found that type II model…
We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay approximation, we obtain an analytical expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the cu…
We study a ghost-free model of massive vector curvaton proposed in the literature, where the quick decrease of the vector background expectation value is avoided by a suitable choice of kinetic and mass functions. The curvaton perturbations of this model have been so far computed assuming that these functions are external classical quantities, and it was found that some special time evolution of these functions leads to scale invariant and statistically isotropic perturbations of the vector curvaton. However, external functions should be understood as originating from the expectation value of …
In this paper, we study a curvaton model where the curvaton is acted by Galileon field. We calculate the power spectrum of fluctuation of G-curvaton during inflation and discuss how it converts to the curvature perturbation after the end of inflation. We estimate the bispectrum of curvature perturbation induced, and show the dependence of non-Gaussianity on the parameters of model. It is found that our model can have sizable local and equilateral non-Gaussianities to up to ${\cal O}(10^2)$, which is illustrated by an explicit example.
Inflating curvaton can create curvature perturbation when the curvaton density is slowly varying. Using the delta-N formalism, we discuss the evolution of the curvature perturbation during curvaton inflation and find analytic formulation of the non-Gaussianity parameter. We first consider the inflating curvaton with sufficiently long inflationary expansion. Then we compare the result with short curvaton inflation.
We consider a novel cosmological scenario in which a curvaton is long-lived and plays the role of cold dark matter (CDM) in the presence of a short, secondary inflation. Non-trivial evolution of the large scale cosmological perturbation in the curvaton scenario can affect the duration of the short term inflation, resulting in the inhomogeneous end of inflation. Non-linear parameters of the curvature perturbation are predicted to be fNL ~ 5/4 and gNL ~ 0. The curvaton abundance can be well diluted by the short-term inflation and accordingly, it does not have to decay into the Standard Model par…
We investigate the non-perturbatively generated axion-like particle (ALP) potential, involving fermions in the dark sector that couple to the ALP, in an early cosmological inflationary stage with the ALP being a spectator field. The potential here deviates from the standard cosine nature due to the presence of the two fermion masses $m_u$ and $m_d$ which couple to the ALP. The ALP is a spectator field during inflation but it starts to oscillate and dominates the energy density of the universe after inflation ends, thereby sourcing isocurvature perturbations, while standard curvature fluctuatio…
Some inflationary models predict the existence of isocurvature primordial fluctuations, in addition to the well known adiabatic perturbation. Such mixed models are not yet ruled out by available data sets. In this paper we explore the possibility of obtaining better constraints on the isocurva- ture contribution from future astronomical data. We consider the axion and curvaton inflationary scenarios, and use Planck satellite experimental specifications together with SDSS galaxy survey to forecast for the best parameter error estimation by means of the Fisher information matrix formal- ism. In …
Massless scalar fields originating in a quantum vacuum state acquire a scale-invariant spectrum of fluctuations in a matter-dominated contracting universe. We show that these isocurvature fluctuations transfer to a scale-invariant spectrum of curvature fluctuations during a non-singular bounce phase. This provides a mechanism for enhancing the primordial adiabatic fluctuations and suppressing the ratio of tensor to scalar perturbations. Moreover, this mechanism leads to new sources of non-Gaussianity of curvature perturbations.
The evolution of the curvature perturbation after multi-field inflation is studied in the light of the curvaton mechanism. Past numerical studies show that many-field inflation causes significant evolution of the curvature perturbation after inflation, which generates significant non-Gaussianity at the same time. We reveal the underlying mechanism of the evolution and show that the evolution is possible in a typical two-field inflation model.
We present a curvaton model from type IIB string theory compactified on a warped throat with approximate isometries. Considering an (anti-)D3-brane sitting at the throat tip as a prototype standard model brane, we show that the brane's position in the isometry directions can play the role of curvatons. The basic picture is that the fluctuations of the (anti-)D3-brane in the angular isometry directions during inflation eventually turns into the primordial curvature perturbations, and subsequently the brane's oscillation excites other open string modes on the brane and reheat the universe. We fi…
We investigate the gravitational wave background induced by the first order scalar perturbations in the curvaton models. We consider the quadratic and axion-like curvaton potential which can generate the blue-tilted power spectrum of curvature perturbations on small scales and derive the maximal amount of gravitational wave background today. We find the power spectrum of the induced gravitational wave background has a characteristic peak at the frequency corresponding to the scale reentering the horizon at the curvaton decay, in the case where the curvaton does not dominate the energy density …
In this paper, we will use $δ\mathcal{N}$-formalism to calculate the primordial curvature perturbation for the curvaton model with a Lagrange multiplier field. We calculate the non-linearity parameters $f_{NL}$ and $g_{NL}$ in the sudden-decay approximation in this kind of model, and we find that one could get a large non-Gaussinity even if the curvaton dominates the total energy density before it decays, and this property will make the curvaton model much richer. We also calculate the probability density function of the primordial curvature perturbation in the sudden-decay approximation, as w…
We calculate curvature perturbations in the scenario in which the curvaton field decays into another scalar field via parametric resonance. As a result of a nonlinear stage at the end of the resonance, standard perturbative calculation techniques fail in this case. Instead, we use lattice field theory simulations and the separate universe approximation to calculate the curvature perturbation as a nonlinear function of the curvaton field. For the parameters tested, the generated perturbations are highly non-Gaussian and not well approximated by the usual fNL parameterisation. Resonant decay pla…
The vector curvaton paradigm is reviewed. The mechanism allows a massive vector boson field to contribute to or even generate the curvature perturbation in the Universe. Contribution of vector bosons is likely to generate statistical anisotropy in the spectrum and bispectrum of the curvature perturbation, which will soon be probed observationally. Two specific models for the generation of superhorizon spectra for the components of an Abelian vector field are analysed. Emphasis is put on the observational signatures of the models when the vector fields play the role of vector curvatons. If futu…
If more than one curvaton dominate the Universe at different epochs from each other, curvature perturbations can be temporarily enhanced to a value much larger than the observed one 10^{-5}. The traces of the enhancement may be left as higher order correlation functions, that is, as non-Gaussianity, the stochastic gravitational waves that are sourced by scalar-scalar mode couplings, as well as the primordial black holes that are formed by the gravitational collapse of the enhanced curvature perturbations. We first confirm that such a temporal enhancement indeed occurs by solving the linearized…
A vector curvaton model with a Maxwell kinetic term and varying kinetic function and mass during inflation is studied. It is shown that, if light until the end of inflation, the vector field can generate statistical anisotropy in the curvature perturbation spectrum and bispectrum, with the latter being predominantly anisotropic. If by the end of inflation the vector field becomes heavy, then particle production is isotropic and the vector curvaton can alone generate the curvature perturbation. The model does not suffer from instabilities such as ghosts and is the only concrete model, to date, …
We revisit the dynamics of the curvaton in detail taking account of effects from thermal environment, effective potential and decay/dissipation rate for general field values and couplings. We also consider the curvature perturbation generated through combinations of various effects: large scale modulation of the oscillation epoch, the effective dissipation rate and the timing at which the equation of state changes. In particular, we find that it tends to be difficult to explain the observed curvature perturbation by the curvaton mechanism without producing too large non-Gaussianity if the curv…
We consider the mixed inflaton-curvaton scenario in which quantum fluctuations of the curvaton field during inflation lead to a relatively large curvature perturbation spectrum at small scales. We use the model of chaotic inflation with quadratic potential including supergravity corrections leading to a large positive tilt in the power spectrum of the curvaton field. The model is characterized by the strongly inhomogeneous curvaton field in the Universe and large non-Gaussianity of curvature perturbations at small scales. We obtained the constraints on the model parameters considering the proc…
We calculate the power spectrum and hemispherical asymmetry of isocurvature and curvaton perturbations due to a complex field Φwhich is evolving along the tachyonic part of its potential. Using a semi-classical evolution of initially sub-horizon quantum fluctuations, we compute the power spectrum, mean field and hemispherical asymmetry as a function of the number of e-foldings of tachyonic growth ΔN and the tachyonic mass term cH^2. We find that a large hemispherical asymmetry due to the modulation of |Φ| can easily be generated via the spatial modulation of |Φ| across the horizon, with Delta …
We study the Affleck-Dine (AD) baryogenesis in the inflating curvaton scenario, when the curvaton is a moduli field with O($10-10^2$TeV) mass. A moduli field with such mass is known to be free from the Polonyi problem, and furthermore its decay products can explain the present cold dark matter abundance. In our scenario, it further explains the primordial curvature perturbation and the present baryon density all together. The current observational bound on the baryon isocurvature perturbation, which severely constrains the AD baryogenesis with the original oscillating moduli curvaton scenario,…
We study density perturbations, including their non-Gaussianity, in models in which the decay rate of the curvaton depends on another light scalar field, denoted the modulaton. Although this model shares some similarities with the standard curvaton and modulated reheating scenarios, it exhibits interesting predictions for f_NL and g_NL that are specific to this model. We also discuss the possibility that both modulaton and curvaton fluctuations contribute to the final curvature perturbation. Our results naturally include the standard curvaton and modulated reheating scenarios as specific limit…
Inspired by \cite{Jiang:2018uce}, we propose a similar curvaton mechanism whose realization occurs in preheating process, in which the effective mass is running (its potential consists of coupling part and exponential part whose contribution is subdominant comparing to the coupling part). The production of curvaton contains the cases of narrow resonance and broad resonances whose criteria comes via the spectral index of curvaton. Since the inflationary potential is chaotic inflation (quadratic potential), it could smoothly transit into the preheating process. Once the entropy perturbation tran…
We investigate two-field inflationary models in which scalar cosmological pertubations are generated via a spectator field nonminimally coupled to gravity, with the particular emphasis on curvaton scenarios. The principal advantage of these models is in the possibility to tune the spectator spectral index via the nonminimal coupling. Our models naturally yield red spectrum of the adiabatic perturbation demanded by observations. We study how the nonminimal coupling affects the spectrum of the curvature perturbation generated in the curvaton scenarios. In particular we find that for small, negat…
In this paper we study a curvaton model obtained by considering a probe anti-D3-brane with angular motion at the bottom of a KS throat with approximate isometries. We calculate the spectrum of curvature perturbations and the non-Gaussianities of this model. Specifically, we consider the limit of relativistic rotation of the curvaton brane which leads to a small sound speed, and thus it can be viewed as an implementation of the DBI-curvaton mechanism. We find that the primordial power spectrum is nearly scale-invariant while the non-Gaussianity of local type is sizable and that of equilateral t…
In the curvaton scenario, primordial curvature perturbations are produced by a second field that is sub-dominant during inflation. Depending on how the curvaton decays [possibly producing baryon number, lepton number, or cold dark matter (CDM)], mixtures of correlated isocurvature perturbations are produced, allowing the curvaton scenario to be tested using cosmic microwave background (CMB) data. Here, a full range of 27 curvaton-decay scenarios is compared with CMB data, placing limits on the curvaton fraction at decay, $r_D$, and the lepton asymmetry, $ξ_{\rm lep}$. If baryon number is gener…
We consider the presence of an axion like particle, $σ$, with a generic $CP$ violating axial coupling of the form $ (α\, σ/f) F \tilde{F}$, where $F_{μν}$ is the gauge field strength of a generic abelian $U(1)$ gauge group, not necessarily associated with the standard electromagnetism, and $f$ is the decay constant of the axion. It has previously been demonstrated that if the axion is identified with the inflaton, such an interaction can lead to measurable cosmological signatures (non-Gaussian modifications of the curvature perturbation spectrum) depending on the parameter $ξ= α\dotσ/ (f H)$. …
During inflationary preheating, the energy stored in the inflaton field is rapidly converted into excitations of other entropy fields. This stage is characterized by exponential particle production due to parametric resonance and is notoriously difficult to analyze using analytic methods. We develop a detailed numerical simulation to investigate inflationary preheating when the potential of the inflaton is a power-law function with arbitrary power index. To achieve a successful graceful exit from a primordial inflationary phase to a smooth, oscillatory phase during preheating, we assume the in…
A new model realisation of the vector curvaton paradigm is presented and analysed. The model consists of a single massive Abelian vector field, with a Maxwell type kinetic term. By assuming that the kinetic function and the mass of the vector field are appropriately varying during inflation, it is shown that a scale invariant spectrum of superhorizon perturbations can be generated. These perturbations can contribute to the curvature perturbation of the Universe. If the vector field remains light at the end of inflation it is found that it can generate substantial statistical anisotropy in the …
We investigate how the background evolution affects the curvature perturbations generated by the curvaton, assuming a curvaton potential that may deviate slightly from the quadratic one, and parameterizing the background fluid density as ρ\propto a^{-α}, where a is the scale factor, and αdepends on the background fluid. It turns out that the more there is deviation from the quadratic case, the more pronounced is the dependence of the curvature perturbation on α. We also show that the background can have a significant effect on the nonlinearity parameters f_NL and g_NL. As an example, if at the…
We consider the possibility that the primordial curvature perturbation was generated through the curvaton mechanism from a scalar field with an electric charge, or precisely the Standard Model U(1) weak hypercharge. This links the dynamics of the very early universe concretely to the Standard Model of particle physics, and because the coupling strength is known, it reduces the number of free parameters in the curvaton model. The gauge coupling also introduces several new physical effects. Charge fluctuations are generated during inflation, but they are screened by electron-positron pairs there…
Primordial magnetic fields of cosmologically interesting field strengths can be generated from gravitationally coupled electrodynamics during inflation. As the cosmological constraints require this to be power law inflation it is not possible to generate at the same time the curvature perturbation from inflation. Therefore here a completion is considered whereby the large scale magnetic field is generated during inflation and the primordial curvature mode in a subsequent era from a curvaton field. It is found that constraints on the model to obtain strong magnetic fields and those to suppress …
We analyse the situation where the primordial curvature perturbations are produced by the joint effects of an inflaton field and two curvaton fields. We present general equations which allow the reader to obtain f_NL for several different scenarios which differ in the order in which fields decay into radiation after inflation. In order to investigate the physics of these equations we analyse some simplified situations where the fields are harmonic and both curvatons are frozen at the same expectation value during inflation. We find quite complex behaviour - for a given situation where the infl…
In this paper, the curvature perturbation generated by the modulated curvaton decay is studied by a direct application of $δN$-formalism. Our method has a sharp contrast with the {\it non-linear formalism} which may be regarded as an indirect usage of $δN$-formalism. We first show that our method can readily reproduce results in previous works of modulation of curvaton. Then we move on to calculate the case where the curvaton mass (and hence also the decay rate) is modulated. The method can be applied to the calculation of the modulation in the freezeout model, in which the heavy species are c…
Some classes of inflationary models naturally introduce two distinct metrics/frames, and their equivalence in terms of observables has often been put in question. D-brane inflation proposes candidates for an inflaton embedded in the string theory and possesses descriptions on the brane and bulk metrics/frames, which are connected by a conformal/disformal transformation that depends on the inflaton and its derivatives. It has been shown that curvature perturbations generated by the inflaton are identical in both frames, meaning that observables such as the spectrum of cosmic microwave backgroun…
We consider the early Universe scenario which allows for production of non-Gaussian curvature perturbations at small scales. We study the peculiarities of a formation of primordial black holes (PBHs) connected with the non-Gaussianity. In particular, we show that PBH constraints on the values of curvature perturbation power spectrum amplitude are strongly dependent on the shape of perturbations and can significantly (by two orders of magnitude) deviate from the usual Gaussian limit ${\cal P}_ζ\lesssim 10^{-2}$. We give examples of PBH mass spectra calculations and PBH constraints for the parti…
We investigate the probability of obtaining an observable curvature perturbation, using as an example the minimal curvaton-higgs (MCH) model. We determine 'probably observable' and 'probably excluded' regions of parameter space assuming generic initial conditions and applying a stochastic approach for the curvaton's evolution during inflation. Inflation is assumed to last longer than the N_{obs} = 55 observable e-folds, and the total number of e-folds of inflation determines the particular ranges of parameters that are probable. For the MCH model, these 'probably observable' regions always lie…
The evolution of the curvature perturbation is highly non-trivial for curvaton models with self-interactions and is very sensitive to the parameter values. The final perturbation depends also on the curvaton decay rate $Γ$. As a consequence, non-gaussianities can be greatly different from the purely quadratic case, even if the deviation is very small. Here we consider a class of polynomial curvaton potentials and discuss the dynamical behavior of the curvature perturbation. We point out that, for example, it is possible that the non-gaussianity parameter $\fnl\simeq 0$ while $\gnl$ is non-zero…
In this paper we analyse three models of the early universe, for which the respective mechanisms for generating the curvature perturbation are considered disparate. We find that in fact the mechanisms are very similar, and hence explain why they give rise to a large non-gaussianity. We show that the mechanism for generating the primordial curvature perturbation, and hence the observable non-gaussianity, is similar in both the Curvaton and Modulated Reheating models. In both cases the model can be written in terms of an energy transfer between the constituting fluids. We then show that this is …
We investigate the possibility of embedding the vector curvaton paradigm in D-brane models of inflation in Type IIB string theory in a simple toy model. The vector curvaton is identified with the U(1) gauge field that lives on the world volume of a D3-brane, which may be stationary or undergoing general motion in the internal space. The dilaton is considered as a spectator field which modulates the evolution of the vector field. In this set up, the vector curvaton is able to generate measurable statistical anisotropy in the spectrum and bispectrum of the curvature perturbation assuming that th…
We consider the constraints for a curvaton with mass m ~ 1 TeV and show that they are not consistent with a purely quadratic potential. Even if the curvaton self-interactions were very weak, they must be accounted for as they affect the dynamical evolution of the curvature perturbation. We show that the only TeV-mass curvaton interaction potential that yields the correct perturbation amplitude, decays before the dark matter freeze-out, and does not give rise to non-Gaussian perturbations that are in conflict with the present limits, is given by V_int= sigma^8/M^4. The decay width of the curvat…
