Qing-Guo Huang
A red tilted primordial power spectrum is preferred by WMAP five-year data and a large positive local-type non-Gaussianity $f_{NL}$ might be observed as well. In this short note we find that a red tilted and large non-Gaussian primordial power spectrum cannot be naturally obtained in curvaton model, because $f_{NL}$ is related to the initial condition of inflation.
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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…
The spectral index is studied at the point where scalar fields deviate from slow-roll during inflation. Considering the deviation that may cause a significant difference to the time derivative of the Hubble parameter and also to the terms in the evolution equation, we show how the deviation affects the spectral index of the curvature perturbations. Considering conventional inflation, curvatons and other inhomogeneous scenarios as mechanisms for generating the cosmological perturbation, we examine whether the spectral index induced by the deviation from the standard slow-roll can explain the sp…
We show that a sizable running spectral index suggested by the recent SPT data can be explained in the axionic curvaton model with a potential that consists of two sinusoidal contributions of different height and period. We find that the running spectral index is generically given by d ns/dlnk ~ (2pi/dN)(n_s - 1), where dN is the e-folds during one period of modulations. In the string axiverse, axions naturally acquire a mass from multiple contributions, and one of the axions may be responsible for the density perturbations with a sizable running spectral index via the curvaton mechanism. We n…
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.
In slow roll inflation, the running of the spectral tilt is generically proportional to the square of the deviation from scale invariance, $α_s \propto (n_s-1)^2$, and it is therefore currently undetectable. We present a mechanism able to generate a much larger running within slow roll. The mechanism is based on a curvaton field with a large mass term, and a time evolving normalization. This may happen for instance to the angular direction of a complex field in presence of an evolving radial direction. At the price of a single tuning between the mass term and the rate of change of the normaliz…
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…
We follow the evolution of the curvaton on superhorizon scales and check that the spectral tilt of the curvaton perturbations is unchanged as the curvaton becomes non-relativistic. Both inflation and pre-big bang cosmology can be treated since the curvaton mechanism within the two scenarios works the same way. We also discuss the amplitude of the density perturbations, which leads to some interesting constrains on the pre-big bang scenario. It is shown that within a SL(3,R) non-linear sigma model one of the three axions has the right coupling to the dilaton and moduli to yield a flat spectrum …
We argue that sneutrinos can be embedded in a multi-field inflation framework where two inflatons and a curvaton simultaneously contribute to primordial fluctuations, which is consistent with current constraints on the spectral index and the tensor-to-scalar ratio from Planck and BICEP/Keck 2018. We also show that the same framework can also explain the baryon asymmetry of the Universe via leptogenesis realized by the decay of the lightest sneutrino. We investigate the parameter range for the scenario to work such as that of sneutrino masses. In particular, we show that the tensor-to-scalar ra…
We investigate the scale-dependence of f_NL in the self-interacting curvaton model. We show that the scale-dependence, encoded in the spectral index n_{f_NL}, can be observable by future cosmic microwave background observations, such as CMBpol, in a significant part of the parameter space of the model. We point out that together with information about the trispectrum g_NL, the self-interacting curvaton model parameters could be completely fixed by observations. We also discuss the scale-dependence of g_NL and its implications for the curvaton model, arguing that it could provide a complementar…
We calculate the three-point correlation function of the comoving curvature perturbation generated during an inflationary epoch driven by false vacuum energy. We get a novel false vacuum shape bispectrum, which peaks in the equilateral limit. Using this result, we propose a scenario which we call "old curvaton". The shape of the resulting bispectrum lies between the local and the false vacuum shapes. In addition we have a large running of the spectral index.
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…
In this paper, we consider large non-Gaussianity generated after D-term inflation in the case that the adiabatic curvature perturbation produced is dominated by a right-handed (RH) sneutrino curvaton. The cosmic string problem can also be evaded with around 10% contribution to the CMB power spectrum and the spectral index $n_s \simeq 1$. The non-Gaussianity produced can be as large as $10<f_{NL}<100$ for the right-handed sneutrino mass being around $m_Φ=10 {GeV}$ with the Yukawa coupling $λ_ν\sim 10^{-10}$. In this case, the lightest neutrino mass is $10^{-10}{eV}$ which favors RH sneutrino le…
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 …
The primordial curvature perturbation ζmay be generated by some curvaton field σ, which is negligible during inflation and has more or less negligible interactions until it decays. In the current scenario, the curvaton starts to oscillate while its energy density ρ_σis negligible. We explore the opposite scenario, in which ρ_σdrives a few e-folds of inflation before the oscillation begins. In this scenario for generating ζit is exceptionally easy to solve the ηproblem; one just has to make the curvaton a string axion, with anomaly-mediated susy breaking which may soon be tested at the LHC. The…
We study the scale dependence of the non-linearity parameters f_NL and g_NL in curvaton models with self-interactions. We show that the spectral indices n_fNL=d ln|f_NL|/(d ln k) and n_gNL=d ln |g_NL|/(d ln k) can take values much greater than the slow--roll parameters and the spectral index of the power spectrum. This means that the scale--dependence of the bi and trispectrum could be easily observable in this scenario with Planck, which would lead to tight additional constraints on the model. Inspite of the highly non-trivial behaviour of f_NL and g_NL in the curvaton models with self-intera…
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…
It is possible that the primordial non-Gaussianity is dominated by the higher order terms, such as that set by $g_{NL}$, not $f_{NL}$. In this paper we derive the spectral index and running of $g_{NL}$ from a single isocurvature scalar field. The scale dependences of non-Gaussianity parameters are detectable if the mass of isocurvature field is not too small compared to the Hubble parameter during inflation. In addition, we also apply our results to investigate the curvaton model with near quadratic potential in detail.
Prior to recombination, Silk damping causes the dissipation of energy from acoustic waves into the monopole of the Cosmic Microwave Background (CMB), resulting in spectral distortions. These can be used to probe the primordial scalar power spectrum on smaller scales than it is possible with CMB anisotropies. An enhancement of power on these scales is nevertheless required for the resulting distortions to be detectable by future experiments like PIXIE. In this paper, we examine all 49 single-field inflation models listed by Martin et al. in the Encyclopaedia Inflationaris [1] and find that only…
We revisit spectator field models including curvaton and modulated reheating scenarios, specifically focusing on their viability in the new Planck era, based on the derived expression for the spectral index in general spectator field models. Importantly, the recent Planck observations give strong preference to a red-tilted power spectrum, while the spectator field models tend to predict a scale-invariant one. This implies that, during inflation, either (i) the Hubble parameter varies significantly as in chaotic inflation, or (ii) a scalar potential for the spectator field has a relatively larg…
We investigate the possibility that the primordial perturbation has two sources: the inflaton and a spectator field, which is not dynamically important during inflation but which after inflation can contribute to the curvature perturbation. The recent Planck results on the power spectrum and non-Gaussianity allow us to put constraints on such mixed models. In the generic case, where no specific model for the inflaton or the spectator is assumed, one finds that in the mixed scenario it is possible to have a large trispectrum with tau_NL >> (f_NL)^2. The constraints on inflation models in the pl…
The three-year WMAP(WMAP3), combined with other cosmological observations from galaxy clustering and Type Ia Supernova (SNIa), prefers a non-vanishing running of the primordial spectral index independent of the low CMB multipoles. Motivated by this feature we study cosmological constraint on the neutrino mass, which severely depends on what prior we adopt for the spectral shape of primordial fluctuations, taking possible running into account. As a result we find a more stringent constraint on the sum of the three neutrino masses, m_ν< 0.76eV (2 σ), compared with m_ν< 0.90eV (2 σ) for the case …
Evaluating the mode function at horizon crossing, we obtained an incorrect expression for the spectral index for a rapidly decaying mode. See the recent paper astro-ph/0701432 for details.
New universal property of cosmological gravitational wave anisotropies
本文指出了宇宙学引力波各向异性的一个新普适性质：在绝热初始条件下，其角功率谱对大爆炸核合成前宇宙流体的状态方程不敏感，偏离此性质则暗示存在非绝热源，并基于curvaton场景验证了该结论。
Density perturbations generated from inflation almost always have a spectral index n_s which runs (varies with the wavelength). We explore a running spectral index scenario in which the scalar spectral index runs from blue (n_s >1) on large length scales to red (n_s<1) on short length scales. Specifically, we look for a correlation between the length scale at which n_s-1=0 and the length scale at which tensor to scalar ratio T/S reaches a minimum for single field slow roll inflationary models. By computing the distribution of length scale ratios, we conclude that there indeed is a new approxim…
We construct an inflationary model that is consistent with both large non-Gaussianity and a running spectral index. The scenario of modulated inflation suggests that modulated perturbation can induce the curvature perturbation with a large non-Gaussianity, even if the inflaton perturbation is negligible. Using this idea, we consider a multi-field extension of the modulated inflation scenario and examine the specific situation where different moduli are responsible for the perturbation at different scales. We suppose that the additional moduli (shooting-star moduli) is responsible for the curva…
The scalar spectral index n is an important parameter describing the nature of primordial density perturbations. Recent data, including that from the WMAP satellite, shows some evidence that the index runs (changes as a function of the scale k at which it is measured) from n>1 (blue) on long scales to n<1 (red) on short scales. We investigate the extent to which inflationary models can accomodate such significant running of n. We present several methods for constructing large classes of potentials which yield a running spectral index. We show that within the slow-roll approximation, the fact t…
We study a class of models in which the inflaton is minimally coupled to gravity with a term $f(R)\vp^2$. We focus in particular on the case when $f\sim R^2$, the expansion of the scale factor is driven by the usual potential energy, while the rolling of the inflaton is driven by the nonminial coupling. We show that the power spectrum is in general blue, and the problem of getting a running spectral index is eased. However, the inflaton potential must have a large second derivative in order to get a large running.
We quantify the slow-roll corrections to primordial density perturbations arising from inflation driven by a four-dimensional scalar field with a monomial potential in a five-dimensional non-compact bulk spacetime. Although the difference between the classical brane-world solutions and standard four-dimensional solutions is large at early times, the change to the amplitude at late times of perturbations generated from quantum fluctuations is first-order in slow-roll parameters, leading to second-order slow-roll corrections to the spectral index. This confirms that the leading-order effects are…
We not only reconstruct the slow-roll parameters for fit to the running spectral index from WMAP three-year data in the usual slow-roll inflation model and noncommutative inflation model, but also investigate the evolution of these slow-roll parameters. Requiring slow-roll inflation lasts more than 20 e-folds after CMB scales leave the horizon suggests that the potential at the last stage of inflation takes the form $V(ϕ)=V_0(1+{η_c\over 2}{(ϕ-ϕ_c)^2\over M_p^2})$, where $η_c$ is a constant. A natural mechanism to end inflation at $ϕ=ϕ_c$ is hybrid type inflation.
One of the firm predictions of inflationary cosmology is the consistency relation between scalar and tensor spectra. It has been argued that such a relation -if experimentally confirmed- would offer strong support for the idea of inflation. We examine the possibility that trans-Planckian physics violates the consistency relation in the framework of inflation with a cut-off proposed in astro-ph/0009209. We find that despite the ambiguity that exists in choosing the action, Planck scale physics modifies the consistency relation considerably. It also leads to the running of the spectral index. Fo…
We compute the running of the scalar spectral index in general multi-field slow-roll inflation. By incorporating explicit momentum dependence at the moment of horizon crossing, we can find the running straightforwardly. At the same time, we can distinguish the contributions from the quasi de Sitter background and the super-horizon evolution of the field fluctuations.
In this paper we operate under the assumption that no tensors from inflation will be measured in the future by the dedicated experiments and argue that, while for single-field slow-roll models of inflation the running of the spectral index will be hard to be detected, in multi-field models the running can be large due to its strong correlation with non-Gaussianity. A detection of the running might therefore be related to the presence of more than one active scalar degree of freedom during inflation.
If a sizeable tensor-to-scalar ratio ~0.1 turns out to be detected and a negative running of the scalar spectral index ~0.01 is significantly required by the data, the vast majority of single field models of inflation will be ruled out. We show that a flat tree-level effective potential, lifted by radiative corrections and by the imprints of a high energy scale (in the form of non-renormalizable operators) can explain those features and produce enough inflation in the slow-roll regime.
We conjecture that the inflation models with trans-Planckian excursions in the field space should be in the swampland. We check this conjecture in a few examples and investigate the constraints on the spectral index for the slow-roll inflation model in string landscape where the variation of inflaton during the period of inflation is less than the Planck scale $M_p$. A red primordial power spectrum with a lower bound on the spectral index is preferred. Both the tensor-scalar ratio and the running can be ignored.
A model independent analysis shows that the running of the spectral index of the three year WMAP results can be nicely realized in noncommutative inflation. We also re-examine some concrete noncommutative inflation models. We find that a large tensor-scalar ratio is required, corresponding to a low number of e-folds before the end of inflation in some simple models.
We argue that a large negative running spectral index, if confirmed, might suggest that there are abundant structures in the inflaton potential, which result in a fairly large (both positive and negative) running of the spectral index at all scales. It is shown that the center value of the running spectral index suggested by the recent CMB data can be easily explained by an inflaton potential with superimposed periodic oscillations. In contrast to cases with constant running, the perturbation spectrum is enhanced at small scales, due to the repeated modulations. We mention that such features a…
At the beginning of inflation there could be extra dynamical scalar fields that will soon disappear (become static) before the end of inflation. In the light of multi-field inflation, those extra degrees of freedom may alter the time-dependence of the original spectrum of the curvature perturbation. It is possible to remove such fields introducing extra number of e-foldings prior to $N_e\sim 60$, however such extra e-foldings may make the trans-Planckian problem worse due to the Lyth bound. We show that such extra scalar fields can change the running of the spectral index to give correction of…
It is sometimes stated that $n_s = 0.98$ in hybrid inflation; sometimes that it predicts $n_s >1$. A number of authors have consider aspects of Planck scale corrections and argued that they affect these predictions. Here we consider these systematically, describing the situations which can yield $n_s =0.96$, and the extent to which this result requires additional tuning.
Planck favours a negative running of the spectral index, with the likelihood being dominated by low multipoles $l \lesssim 50$ and no preference for running at higher $l$. A negative spectral index is also necessary for the 2-$σ$ Planck upper bound on the tensor-to-scalar ratio $r$ to be consistent with values significantly larger than 0.1. Planck has also observed a hemispherical asymmetry of the CMB power spectrum, again mostly at low multipoles. Here we consider whether the physics responsible for the hemispherical asymmetry could also account for the negative running of the spectral index …
ACT Data and Positive Running of the Spectral Index for Scalar Theory and Modified Gravity
本文研究了在暴胀理论中谱指数运行为正的可能性，通过分析ACT数据和其他物理证据，探讨了在最小耦合标量场引力和修正引力中如何获得正运行的谱指数，并指出Einstein-Gauss-Bonnet理论在兼容GW170817事件的情况下，可以轻松实现正运行的谱指数。
The BICEP2 experiment confirms the existence of primordial gravitational wave with the tensor-to-scalar ratio $r=0$ ruled out at $7σ$ level. The consistency of this large value of $r$ with the {\em Planck} data requires a large negative running $n'_s$ of the scalar spectral index. Herein we propose two types of the single field inflation models with simple potentials to study the possibility of the consistency of the models with the BICEP2 and {\em Planck} observations. One type of model suggested herein is realized in the supergravity model building. These models fail to provide the needed $n…
We demonstrate that local, scale-dependent non-Gaussianity can generate cosmic variance uncertainty in the observed spectral index of primordial curvature perturbations. In a universe much larger than our current Hubble volume, locally unobservable long wavelength modes can induce a scale-dependence in the power spectrum of typical subvolumes, so that the observed spectral index varies at a cosmologically significant level (|Δns | ~ O(0.04)). Similarly, we show that the observed bispectrum can have an induced scale dependence that varies about the global shape. If tensor modes are coupled to l…
We calculate the running of the scalar index in the ekpyrotic and matter bounce cosmological scenarios, and find that it is typically negative for ekpyrotic models, while it is typically positive for realizations of the matter bounce where multiple fields are present. This can be compared to inflation, where the observationally preferred models typically predict a negative running. The magnitude of the running is expected to be between $10^{-4}$ and up to $10^{-2},$ leading in some cases to interesting expectations for near-future observations.
We revisit large field inflation models with modulations in light of the recent discovery of the primordial B-mode polarization by the BICEP2 experiment, which, when combined with the Planck + WP + highL data, gives a strong hint for additional suppression of the CMB temperature fluctuations at small scales. Such a suppression can be explained by a running spectral index. In fact, it was pointed out by two of the present authors (TK and FT) that the existence of both tensor mode perturbations and a sizable running of the spectral index is a natural outcome of large inflation models with modula…
We present a simple and efficient method to compute the superhorizon evolution of the spectral index in multi-field inflationary models, using transport equation techniques. We illustrate the evolution of n_s with time for various interesting potentials.
We present a new inflation model, known as noncommutative decrumpling inflation, in which space has noncommutative geometry with time variability of the number of spatial dimensions. Within the framework of noncommutative decrumpling inflation, we compute both the spectral index and its running. Our results show that the effects of both time variability of the number of spatial dimensions and noncommutative geometry on the spectral index and its running. Two classes of examples have been studied and comparisons made with the standard slow-roll formulae. We conclude that the effects of noncommu…
We investigate the index of the Neuberger's Dirac operator in abelian gauge theories on finite lattices by numerically analyzing the spectrum of the hermitian Wilson-Dirac operator for a continuous family of gauge fields connecting different topological sectors. By clarifying the characteristic structure of the spectrum leading to the index theorem we show that the index coincides to the topological charge for a wide class of gauge field configurations. We also argue that the index can be found exactly for some special but nontrivial configurations in two dimensions by directly analyzing the s…
Quantum harmonic oscillator, index theorem and spectral asymmetry
研究量子谐振子的谱不对称性，揭示其配分函数与索引定理的联系，展现内能作为非SUSY的索引定理表现。
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