Affleck-Dine baryogenesis just after inflation

We propose a new scenario of Affleck-Dine baryogenesis where a flat direction in the MSSM generates B-L asymmetry just after the end of inflation. The resulting amount of baryon asymmetry is independent of low-energy supersymmetric models but is dependent on inflation models. We consider the hybrid and chaotic inflation models and find that reheating temperature is required to be higher than that in the conventional scenario of Affleck-Dine baryogenesis. In particular, non-thermal gravitino-overproduction problem is naturally avoided in the hybrid inflation model. Our results imply that Affleck-Dine baryogenesis can be realized in a broader range of supersymmetry and inflation models than expected in the literature.Comment: 35 pages, 7 figure

Anthropic Bound on Dark Radiation and its Implications for Reheating

We derive an anthropic bound on the extra neutrino species, $\Delta N_{\rm eff}$, based on the observation that a positive $\Delta N_{\rm eff}$ suppresses the growth of matter fluctuations due to the prolonged radiation dominated era, which reduces the fraction of matter that collapses into galaxies, hence, the number of observers. We vary $\Delta N_{\rm eff}$ and the positive cosmological constant while fixing the other cosmological parameters. We then show that the probability of finding ourselves in a universe satisfying the current bound is of order a few percents for a flat prior distribution. If $\Delta N_{\rm eff}$ is found to be close to the current upper bound or the value suggested by the $H_0$ tension, the anthropic explanation is not very unlikely. On the other hand, if the upper bound on $\Delta N_{\rm eff}$ is significantly improved by future observations, such simple anthropic consideration does not explain the small value of $\Delta N_{\rm eff}$. We also study simple models where dark radiation consists of relativistic particles produced by heavy scalar decays, and show that the prior probability distribution sensitively depends on the number of the particle species.Comment: 14 pages, 4 figures; V2: Added references; V3: Published version, Added the anthropic bound on the number of neutrino flavor

Hessian eigenvalue distribution in a random Gaussian landscape

The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential minima. In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues. The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of $1/N$ expansion, where $N$ is the dimensionality of the landscape. This approximation, however, is insufficient for the small eigenvalue end of the spectrum, where sub-leading terms play a significant role. We extend the saddle point method to account for the sub-leading contributions. We also develop a new approach, where the eigenvalue distribution is found as an equilibrium distribution at the endpoint of a stochastic process (Dyson Brownian motion). The results of the two approaches are consistent in cases where both methods are applicable. We discuss the implications of our results for vacuum stability and slow-roll inflation in the landscape.Comment: 33 pages, 10 figure

Primordial Black Holes from Polynomial Potentials in Single Field Inflation

Within canonical single field inflation models, we provide a method to reverse engineer and reconstruct the inflaton potential from a given power spectrum. This is not only a useful tool to find a potential from observational constraints, but also gives insight into how to generate a large amplitude spike in density perturbations, especially those that may lead to primordial black holes (PBHs). In accord with other works, we find that the usual slow-roll conditions need to be violated in order to generate a significant spike in the spectrum. We find that a way to achieve a very large amplitude spike in single field models is for the classical roll of the inflaton to over-shoot a local minimum during inflation. We provide an example of a quintic polynomial potential that implements this idea and leads to the observed spectral index, observed amplitude of fluctuations on large scales, significant PBH formation on small scales, and is compatible with other observational constraints. We quantify how much fine-tuning is required to achieve this in a family of random polynomial potentials, which may be useful to estimate the probability of PBH formation in the string landscape.Comment: 13 pages in double column format, 5 figures. V2: Added references and small clarification

Vacuum Decay in Real Time and Imaginary Time Formalisms

We analyze vacuum tunneling in quantum field theory in a general formalism by using the Wigner representation. In the standard instanton formalism, one usually approximates the initial false vacuum state by an eigenstate of the field operator, imposes Dirichlet boundary conditions on the initial field value, and evolves in imaginary time. This approach does not have an obvious physical interpretation. However, an alternative approach does have a physical interpretation: in quantum field theory, tunneling can happen via classical dynamics, seeded by initial quantum fluctuations in both the field and its momentum conjugate, which was recently implemented in Ref. [1]. We show that the Wigner representation is a useful framework to calculate and understand the relationship between these two approaches. We find there are two, related, saddle point approximations for the path integral of the tunneling process: one corresponds to the instanton solution in imaginary time and the other one corresponds to classical dynamics from initial quantum fluctuations in real time. The classical approximation for the dynamics of the latter process is justified only in a system with many degrees of freedom, as can appear in field theory due to high occupancy of nucleated bubbles, while it is not justified in single particle quantum mechanics, as we explain. We mention possible applications of the real time formalism, including tunneling when the instanton vanishes, or when the imaginary time contour deformation is not possible, which may occur in cosmological settings.Comment: 10 pages in double column format, 2 figures. V2: Further clarifications. Updated to resemble version published in PR