Small-scale Effects of Thermal Inflation on Halo Abundance at High-zz, Galaxy Substructure Abundance and 21-cm Power Spectrum

We study the impact of thermal inflation on the formation of cosmological structures and present astrophysical observables which can be used to constrain and possibly probe the thermal inflation scenario. These are dark matter halo abundance at high redshifts, satellite galaxy abundance in the Milky Way, and fluctuation in the 21-cm radiation background before the epoch of reionization. The thermal inflation scenario leaves a characteristic signature on the matter power spectrum by boosting the amplitude at a specific wavenumber determined by the number of e-foldings during thermal inflation ($N_{\rm bc}$), and strongly suppressing the amplitude for modes at smaller scales. For a reasonable range of parameter space, one of the consequences is the suppression of minihalo formation at high redshifts and that of satellite galaxies in the Milky Way. While this effect is substantial, it is degenerate with other cosmological or astrophysical effects. The power spectrum of the 21-cm background probes this impact more directly, and its observation may be the best way to constrain the thermal inflation scenario due to the characteristic signature in the power spectrum. The Square Kilometre Array (SKA) in phase 1 (SKA1) has sensitivity large enough to achieve this goal for models with $N_{\rm bc}\gtrsim 26$ if a 10000-hr observation is performed. The final phase SKA, with anticipated sensitivity about an order of magnitude higher, seems more promising and will cover a wider parameter space.Comment: 28 pages, 8 figure

The Possibility of Inflation in Asymptotically Safe Gravity

We examine the inflationary modes in the cubic curvature theories in the context of asymptotically safe gravity. On the phase space of the Hubble parameter, there exists a critical point which corresponds to the slow-roll inflation in Einstein frame. Most of the e-foldings are attained around the critical point for each inflationary trajectories. If the coupling constants $g_i$ have the parametric relations generated as the power of the relative energy scale of inflation $H_0$ to the ultraviolet cutoff $\Lambda$, a successful inflation with more than 60 e-foldings occurs near the critical point.Comment: 14 pages, 4 figure

Critical Reviews of Causal Patch Measure over the Multiverse

In this talk, the causal patch measure based on black hole complementarity is critically reviewed. By noticing the similarities between the causal structure of an inflationary dS space and that of a black hole, we have considered the complementarity principle between the inside and the outside of the causal horizon as an attractive way to count the inflationary multiverse. Even though the causal patch measure relieves the Boltzmann brain problem and stresses physical reality based on observations, it could be challenged by the construction of counterexamples, both on regular black holes and charged black holes, to black hole complementarity.Comment: 6 pages, 2 figures; A proceeding for CosPA2008. Talk on the 29th of October, 2008, Pohang, Kore

CMB Spectral Distortion Constraints on Thermal Inflation

Thermal inflation is a second epoch of exponential expansion at typical energy scales $V^{1/4} \sim 10^{6 \sim 8} \mathrm{GeV}$. If the usual primordial inflation is followed by thermal inflation, the primordial power spectrum is only modestly redshifted on large scales, but strongly suppressed on scales smaller than the horizon size at the beginning of thermal inflation, $k > k_{\rm b} = a_{\rm b} H_{\rm b}$. We calculate the spectral distortion of the cosmic microwave background generated by the dissipation of acoustic waves in this context. For $k_{\rm b} \ll 10^3 \mathrm{Mpc}^{-1}$, thermal inflation results in a large suppression of the $\mu$-distortion amplitude, predicting that it falls well below the standard value of $\mu \simeq 2\times 10^{-8}$. Thus, future spectral distortion experiments, similar to PIXIE, can place new limits on the thermal inflation scenario, constraining $k_{\rm b} \gtrsim 10^3 \mathrm{Mpc}^{-1}$ if $\mu \simeq 2\times 10^{-8}$ were found.Comment: 18 pages, 7 figure

Minkowski Tensors in Two Dimensions - Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields

We apply the Minkowski Tensor statistics to two dimensional slices of the three dimensional density field. The Minkowski Tensors are a set of functions that are sensitive to directionally dependent signals in the data, and furthermore can be used to quantify the mean shape of density peaks. We begin by introducing our algorithm for constructing bounding perimeters around subsets of a two dimensional field, and reviewing the definition of Minkowski Tensors. Focusing on the translational invariant statistic $W^{1,1}_{2}$ - a $2 \times 2$ matrix - we calculate its eigenvalues for both the entire excursion set ($\Lambda_{1},\Lambda_{2}$) and for individual connected regions and holes within the set ($\lambda_{1},\lambda_{2}$). The ratio of eigenvalues $\Lambda_{2}/\Lambda_{1}$ informs us of the presence of global anisotropies in the data, and $\langle \lambda_{2}/\lambda_{1} \rangle$ is a measure of the mean shape of peaks and troughs in the density field. We study these quantities for a Gaussian field, then consider how they are modified by the effect of gravitational collapse using the latest Horizon Run 4 cosmological simulation. We find $\Lambda_{1,2}$ are essentially independent of gravitational collapse, as the process maintains statistical isotropy. However, the mean shape of peaks is modified significantly - overdensities become relatively more circular compared to underdensities of the same area. When applying the statistic to a redshift space distorted density field, we find a significant signal in the eigenvalues $\Lambda_{1,2}$, suggesting that they can be used to probe the large-scale velocity field.Comment: 17 pages, accepted for publication in AP

Anthropic Likelihood for the Cosmological Constant and the Primordial Density Perturbation Amplitude

Weinberg et al. calculated the anthropic likelihood of the cosmological constant using a model assuming that the number of observers is proportional to the total mass of gravitationally collapsed objects, with mass greater than a certain threshold, at t \rightarrow \infty. We argue that Weinberg's model is biased toward small \Lambda, and to try to avoid this bias we modify his model in a way that the number of observers is proportional to the number of collapsed objects, with mass and time equal to certain preferred mass and time scales. Compared to Weinberg's model, this model gives a lower anthropic likelihood of \Lambda_0 (T_+(\Lambda_0) ~ 5%). On the other hand, the anthropic likelihood of the primordial density perturbation amplitude from this model is high, while the likelihood from Weinberg's model is low. Furthermore, observers will be affected by the history of the collapsed object, and we introduce a method to calculate the anthropic likelihoods of \Lambda and Q from the mass history using the extended Press-Schechter formalism. The anthropic likelihoods for $\Lambda$ and Q from this method are similar to those from our single mass constraint model, but, unlike models using the single mass constraint which always have degeneracies between \Lambda and Q, the results from models using the mass history are robust even if we allow both \Lambda and Q to vary. In the case of Weinberg's flat prior distribution of \Lambda (pocket based multiverse measure), our mass history model gives T_+(\Lambda_0) ~ 10%, while the scale factor cutoff measure and the causal patch measure give T_+(\Lambda_0) \geq 30%.Comment: 28 pages, 10 figure

Modeling Cosmological Perturbations of Thermal Inflation

We consider a simple system consisting of matter, radiation and vacuum components to model the impact of thermal inflation on the evolution of primordial perturbations. The vacuum energy magnifies the modes entering the horizon before its domination, making them potentially observable, and the resulting transfer function reflects the phase changes and energy contents. To determine the transfer function, we follow the curvature perturbation from well outside the horizon during radiation domination to well outside the horizon during vacuum domination and evaluate it on a constant radiation density hypersurface, as is appropriate for the case of thermal inflation. The shape of the transfer function is determined by the ratio of vacuum energy to radiation at matter-radiation equality, which we denote by $\upsilon$, and has two characteristic scales, $k_{\rm a}$ and $k_{\rm b}$, corresponding to the horizon sizes at matter radiation equality and the beginning of the inflation, respectively. If $\upsilon \ll 1$, the universe experiences radiation, matter and vacuum domination eras and the transfer function is flat for $k \ll k_{\rm b}$, oscillates with amplitude $1/5$ for $k_{\rm b} \ll k \ll k_{\rm a}$ and oscillates with amplitude $1$ for $k \gg k_{\rm a}$. For $\upsilon \gg 1$, the matter domination era disappears, and the transfer function reduces to being flat for $k \ll k_{\rm b}$ and oscillating with amplitude $1$ for $k \gg k_{\rm b}$.Comment: 17 pages, 5 figures, submitted to JCA