We present the LWL formula which represents the long wavelengh limit of thesolutions of evolution equations of cosmological perturbations in terms of theexactly homogeneous solutions in the most general case where multiple scalarfields and multiple perfect fluids coexist. We find the conserved quantitywhich has origin in the adiabatic decaying mode, and by regarding this quantityas the source term we determine the correction term which corrects thediscrepancy between the exactly homogeneous perturbations and the $k \to 0$limit of the evolutions of cosmological perturbations. This LWL formula isuseful for investigating the evolutions of cosmological perturbations in theearly stage of our universe such as reheating after inflation and the curvatondecay in the curvaton scenario. When we extract the long wavelength limits ofevolutions of cosmological perturbations from the exactly homogeneosperturbations by the LWL formula, it is more convenient to describe thecorresponding exactly homogeneous system with not the cosmological time but thescale factor as the evolution parameter. By applying the LWL formula to thereheating model and the curvaton model with multiple scalar fields and multipleradiation fluids, we obtain the S formula representing the final amplitude ofthe Bardeen parameter in terms of the initial adiabatic and isocurvatureperturbations Keywords:cosmological perturbations,long wavelength limit,reheating,curvaton PACS number(s):98.80.Cq
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机译:我们提出了LWL公式,该公式代表了在多个标量场和多种完美流体共存的最一般情况下,在完全均匀的解的意义上,宇宙扰动演化方程解的长波长极限。我们找到了源于绝热衰减模式的守恒量,并以该量为源项,我们确定了校正项,该校正项将正好均匀的扰动和宇宙扰动演化的$ k \至0 $极限之间的偏差校正。这个LWL公式可用于研究宇宙早期的宇宙扰动的演变,例如通货膨胀后的再加热和曲线情景中的曲线衰减。当我们通过LWL公式从精确的同质微扰中提取宇宙微扰演化的长波长极限时,更方便地描述对应的精确的均匀系统,而不用宇宙学的时间,而用比例因子作为演化参数。通过将LWL公式应用于具有多个标量场和多种辐射流体的加热模型和曲线模型,我们得到了代表初始绝热和等曲率扰动的Bardeen参数最终振幅的S公式。关键词:宇宙学扰动,长波长极限,再加热,curvaton PACS编号:98.80.Cq
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