Euclidean quantum gravity and stochastic inflation

In this paper, we compare dispersions of a scalar field in Euclidean quantum gravity with stochastic inflation. We use Einstein gravity and a minimally coupled scalar field with a quadratic potential. We restrict our attention to small mass and small field cases. In the Euclidean approach, we introduce the ground state wave function which is approximated by instantons. We used a numerical technique to find instantons that satisfy classicality. In the stochastic approach, we introduce the probability distribution of Hubble patches that can be approximated by locally homogeneous universes down to a smoothing scale. We assume that the ground state wave function should correspond to the stationary state of the probability distribution of the stochastic Universe. By comparing the dispersion of both approaches, we conclude three main results. (1) For a statistical distribution with a certain value, we can find a corresponding instanton in the Euclidean side, and it should be a complex-valued instanton. (2) The size of the Universe of the Euclidean approach corresponds to the smoothing scale of the stochastic side; the Universe is homogeneous up to the Euclidean instanton. (3) In addition, as the mass increases up to a critical value, both approaches break at the same time. Hence, generation of classical inhomogeneity in the stochastic approach and the instability of classicality in the Euclidean approach are related.open2

Mass inflation in f(R) gravity: A conjecture on the resolution of the mass inflation singularity

We study gravitational collapse of a charged black hole in f(R) gravity using double-null formalism. We require cosmological stability to f(R) models; we used the Starobinsky model and the R + (1/2)cR^2 model. Charged black holes in f(R) gravity can have a new type of singularity due to higher curvature corrections, the so-called f(R)-induced singularity, although it is highly model-dependent. As the advanced time increases, the internal structure will approach the Cauchy horizon, which may not be an inner apparent horizon. There is mass inflation as one approaches the Cauchy horizon and hence the Cauchy horizon may be a curvature singularity with nonzero area. However, the Ricci scalar is finite for an out-going null observer. This can be integrated as follows: Cosmologically stable higher curvature corrections of the Ricci scalar made it bounded even in the presence of mass inflation. Finally, we conjecture that if there is a general action including general higher curvature corrections with cosmological stability, then the corrections can make all curvature components finite even in the presence of mass inflation. This might help us to resolve the problem of inner horizon instability of regular black hole models.Comment: 31 pages, 15 figure

Dynamics of false vacuum bubbles: beyond the thin shell approximation

We numerically study the dynamics of false vacuum bubbles which are inside an almost flat background; we assumed spherical symmetry and the size of the bubble is smaller than the size of the background horizon. According to the thin shell approximation and the null energy condition, if the bubble is outside of a Schwarzschild black hole, unless we assume Farhi-Guth-Guven tunneling, expanding and inflating solutions are impossible. In this paper, we extend our method to beyond the thin shell approximation: we include the dynamics of fields and assume that the transition layer between a true vacuum and a false vacuum has non-zero thickness. If a shell has sufficiently low energy, as expected from the thin shell approximation, it collapses (Type 1). However, if the shell has sufficiently large energy, it tends to expand. Here, via the field dynamics, field values of inside of the shell slowly roll down to the true vacuum and hence the shell does not inflate (Type 2). If we add sufficient exotic matters to regularize the curvature near the shell, inflation may be possible without assuming Farhi-Guth-Guven tunneling. In this case, a wormhole is dynamically generated around the shell (Type 3). By tuning our simulation parameters, we could find transitions between Type 1 and Type 2, as well as between Type 2 and Type 3. Between Type 2 and Type 3, we could find another class of solutions (Type 4). Finally, we discuss the generation of a bubble universe and the violation of unitarity. We conclude that the existence of a certain combination of exotic matter fields violates unitarity.Comment: 40 pages, 41 figure

The causal structure of dynamical charged black holes

We study the causal structure of dynamical charged black holes, with a sufficient number of massless fields, using numerical simulations. Neglecting Hawking radiation, the inner horizon is a null Cauchy horizon and a curvature singularity due to mass inflation. When we include Hawking radiation, the inner horizon becomes space-like and is separated from the Cauchy horizon, which is parallel to the out-going null direction. Since a charged black hole must eventually transit to a neutral black hole, we studied the neutralization of the black hole and observed that the inner horizon evolves into a space-like singularity, generating a Cauchy horizon which is parallel to the in-going null direction. Since the mass function is finite around the inner horizon, the inner horizon is regular and penetrable in a general relativistic sense. However, since the curvature functions become trans-Planckian, we cannot saymore about the region beyond the inner horizon, and it is natural to say that there is a 'physical' space-like singularity. However, if we assume an exponentially large number of massless scalar fields, our results can be extended beyond the inner horizon. In this case, strong cosmic censorship and black hole complementarity can be violated.Comment: 23 pages, 23 figure

No-boundary measure and preference for large e-foldings in multi-field inflation

The no-boundary wave function of quantum gravity usually assigns only very small probability to long periods of inflation. This was a reason to doubt about the no-boundary wave function to explain the observational universe. We study the no-boundary proposal in the context of multi-field inflation to see whether the number of fields changes the situation. For a simple model, we find that indeed the no-boundary wave function can give higher probability for sufficient inflation, but the number of fields involved has to be very high.Comment: 16 pages, 2 figure

A Lactate-Induced Response to Hypoxia

SUMMARY Organisms must be able to respond to low oxygen in a number of homeostatic and pathological contexts. Regulation of hypoxic responses via the hypoxiainducible factor (HIF) is well established, but evidence indicates that other, HIF-independent mechanisms are also involved. Here, we report a hypoxic response that depends on the accumulation of lactate, a metabolite whose production increases in hypoxic conditions. We find that the NDRG3 protein is degraded in a PHD2/VHL-dependent manner in normoxia but is protected from destruction by binding to lactate that accumulates under hypoxia. The stabilized NDRG3 protein binds c-Raf to mediate hypoxia-induced activation of Raf-ERK pathway, promoting angiogenesis and cell growth. Inhibiting cellular lactate production abolishes the NDRG3-mediated hypoxia responses. Our study, therefore, elucidates the molecular basis for lactate-induced hypoxia signaling, which can be exploited for the development of therapies targeting hypoxia-induced diseases