Graviton Mode Function in Inflationary Cosmology

We consider the production of gravitons in an inflationary cosmology by approximating each epoch of change in the equation of state as sudden, from which a simple analytic graviton mode function has been derived. We use this mode function to compute the graviton spectral energy density and the tensor-induced cosmic microwave background anisotropy. The results are then compared to the numerical calculations which incorporate a smooth radiation-matter phase transition. We find that the sudden approximation is a fairly good method. Besides, in determining the frequency range and amplitude of the mode function, we introduce a pre-inflationary radiation-dominated epoch and use a physically sensible regularization method.Comment: 26 pages, revtex, 4 figures (available upon request). We have added a new Section VIII with four new figures, in which Eq. (35) is used to calculate the graviton spectral energy density and the tensor-induced CMB anisotrop

Growth index with the exact analytic solution of sub-horizon scale linear perturbation for dark energy models with constant equation of state

Three decades ago Heath found the integral form of the exact analytic growing mode solution of the linear density perturbation $\delta$ on sub-horizon scales including the cosmological constant or the curvature term. Recently, we obtained the exact analytic form of this solution in our previous work \cite{SK}. Interestingly, we are able to extend this solution for general dark energy models with the constant equation of state $\omega_{de}$ in a flat universe. This analytic solution provides the accurate and efficient tools for probing the properties of dark energy models such as the behavior of the growth factor and the growth index. We investigate the growth index and its parameter at any epoch with this exact solution for different dark energy models and find that the growth index is quite model dependent in the redshift space, $0.25 \leq z \leq 1.5$, so observations of the structure growth around this epoch would be very interesting. Also one may be able to rule out some dark energy models by using the analysis from this exact solution. Thus, the analytic solution for the growth factor provides the very useful tools for future observations to constrain the exact values of observational quantities at any epoch related to the growth factor in the dark energy models.Comment: 8pages, 3figures, 1Table, minor revisions to match version accepted by PLB (add Fig1

Primordial Black Holes from Passive Density Fluctuations

In this paper, we show that if passive fluctuations are considered, primordial black holes (PBHs) can be easily produced in the framework of single-field, slow-roll inflation models. The formation of PBHs is due to the blue spectrum of passive fluctuations and an enhancement of the spectral range which exits horizon near the end of inflation. Therefore the PBHs are light with masses $\lesssim 10^{15}g$ depending on the number of e-folds when the scale of our observable universe leaves horizon. These PBHs are likely to have evaporated and cannot be a candidate for dark matter but they may still affect the early universe.Comment: 7 pages, 1 figure, to appear in Physics Letters