The primordial density perturbation in the curvaton scenario
The primordial density perturbation in the curvaton scenario
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Curvaton场景中的原始密度扰动
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通讯作者：
D. Wands
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作者：
D. Lyth;C. Ungarelli;D. Wands
现在很清楚，宇宙结构的起源是一个原始的密度扰动，当宇宙尺度开始进入视界时就已经存在了。观测结果与密度扰动是完全绝热的、高斯的和尺度无关的假设是一致的，但是数据仍然允许与这种状态有显著的偏离。特别地，不排除绝热密度扰动可能伴随着显著的等曲率密度扰动[1，2]。暴胀为微扰提供了一个自然的起源，因为它将每个无光标量场的真空涨落转化为经典的与标度无关的微扰。这些场扰动中的一个或多个可能引起原始密度扰动。通常假设暴胀涉及一个缓慢滚动的场，称为暴胀子，其值决定暴胀的结束。暴胀子场中的扰动不能引起等曲率扰动，但在某种程度上不可避免地引起绝热扰动。通常的假设[3]是暴胀子是唯一负责观察到的绝热密度扰动。在这个“暴胀子假设”下，通常的单场模型中排除了显著的非高斯性[4，5]。在多场模型中，存在一系列可能的暴胀子轨迹在场空间中弯曲，显著的非高斯性是可能的[6，7]，但显然只是以极端微调指定暴胀子轨迹的初始条件为代价。任何等曲率密度扰动都是由某个非暴胀子场的扰动引起的。在暴胀子假设下，这意味着等曲率密度扰动（如果存在）取决于与绝热密度扰动不同的物理参数。因此，可观测量级的等曲率扰动将需要对物理参数进行微调，或者在它们之间存在某种尚未预见的联系。另一种假设[8-11]是绝热密度扰动起源于不同于暴胀子的某个“曲率”场中的扰动。在这种情况下，绝热密度扰动仅在暴胀之后从对应于纯粹等曲率扰动的初始条件产生[12]。[1]本文的目的是探讨在这一假设下原始密度扰动的性质。在曲率场景中，显著的非高斯性可以容易地存在，因为曲率密度与曲率场的平方成比例。此外，曲率密度扰动可以导致曲率衰减后，在宇宙流体的各种成分的密度等曲率扰动。这些，我们称之为“残余”isocurvature组件，是完全相关的或完全反相关的绝热密度扰动，具有可计算的和一般显着的相对幅度。本文的结构如下。我们在第二节讨论绝热微扰及其可能的非高斯性。在第三节中，我们制定的描述等曲率扰动，在某种程度上，这将使我们能够分析CDM，重子和中微子扰动在一个统一的方式。在第四节中，我们计算了冷暗物质（CDM）和重子的剩余等曲率微扰。在第五节中，我们给出了描述原始中微子等曲率微扰的一般形式，首次考虑到轻子数的关键问题。然后我们用它来计算剩余的等曲率中微子微扰。我们的结论总结在第六节。
It is now clear that the origin of structure in the Universe is a primordial density perturbation, existing already when cosmological scales start to enter the horizon. Observation is consistent with the hypothesis that the density perturbation is perfectly adiabatic, Gaussian and scale–independent, but significant departures from this state of affairs is still allowed by the data. In particular it is not excluded that the adiabatic density perturbation may be accompanied by a significant isocurvature density perturbation [1,2]. Inflation provides a natural origin for the perturbation, since it converts the vacuum fluctuation of each light free scalar field into a classical scale–independent perturbation. One or more of these field perturbations may cause the primordial density perturbation. It is usually assumed that inflation involves a slowlyrolling field, dubbed the inflaton, whose value determines the end of inflation. The perturbation in the inflaton field cannot cause an isocurvature perturbation, but does inevitably cause at some level an adiabatic perturbation. The usual hypothesis [3] is that the inflaton is solely responsible for the observed adiabatic density perturbation. Under this ‘inflaton hypothesis’ significant nonGaussianity is excluded in the usual one–field models [4,5]. In multi–field models, where there is a family of possible inflaton trajectories curved in field space, significant non-Gaussianity is possible [6,7] but apparently only at the expense of extreme fine–tuning of the initial condition that specifies the inflaton trajectory. Any isocurvature density perturbation must be caused by the perturbation of some non–inflaton field. Under the inflaton hypothesis this means that the isocurvature density perturbation (if present) depends on different physical parameters from the adiabatic density perturbation. As a result, an isocurvature perturbation of observable magnitude would require fine-tuning of the physical parameters, or else some as-yet unforseen connection between them. An alternative hypothesis [8–11] is that the adiabatic density perturbation originates from the perturbation in some ‘curvaton’ field different from the inflaton. In this scenario the adiabatic density perturbation is generated only after inflation, from an initial condition which corresponds to a purely isocurvature perturbation [12]. 1 The object of the present paper is to explore the nature of the primordial density perturbation under this hypothesis. In the curvaton scenario, significant non-Gaussianity may easily be present because the curvaton density is proportional to the square of the curvaton field. Also, the curvaton density perturbation can lead, after curvaton decay, to isocurvature perturbations in the densities of the various components of the cosmic fluid. These, which we term ‘residual’ isocurvature components, are either fully correlated or fully anti-correlated with the adiabatic density perturbation, with a calculable and generally significant relative magnitude. The paper is organized as follows. We deal in Section II with the adiabatic perturbation and its possible nonGaussianity. In Section III we formulate the description of isocurvature perturbations, in a way which will allow us to analyse CDM, baryon and neutrino perturbations in a unified manner. In Section IV we calculate the residual isocurvature perturbations of cold dark matter (CDM) and baryons. In Section V we give a general formalism for describing the primordial neutrino isocurvature perturbation, taking into account for the first time the crucial issue of lepton number. Then we use it to calculate the residual isocurvature neutrino perturbation. Our conclusions are summarised in Section VI.