skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Geodesic measures of the landscape

Abstract

We study the landscape models of eternal inflation with an arbitrary number of different vacua states, both recyclable and terminal. We calculate the abundances of bubbles following different geodesics. We show that the results obtained from generic timelike geodesics have dependence on initial conditions. In contrast, the predictions extracted from 'eternal' geodesics, which never enter terminal vacua, do not suffer from this problem. We derive measure equations for ensembles of geodesics and discuss possible interpretations of initial conditions in eternal inflation.

Authors:
 [1]
  1. Arnold-Sommerfeld-Center for Theoretical Physics, Department fuer Physik, Ludwig-Maximilians-Universitaet Muenchen, Theresienstr. 37, D-80333, Munich (Germany)
Publication Date:
OSTI Identifier:
20935220
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.023524; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ABUNDANCE; BUBBLES; EQUATIONS; GEODESICS; INFLATIONARY UNIVERSE

Citation Formats

Vanchurin, Vitaly. Geodesic measures of the landscape. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.023524.
Vanchurin, Vitaly. Geodesic measures of the landscape. United States. doi:10.1103/PHYSREVD.75.023524.
Vanchurin, Vitaly. Mon . "Geodesic measures of the landscape". United States. doi:10.1103/PHYSREVD.75.023524.
@article{osti_20935220,
title = {Geodesic measures of the landscape},
author = {Vanchurin, Vitaly},
abstractNote = {We study the landscape models of eternal inflation with an arbitrary number of different vacua states, both recyclable and terminal. We calculate the abundances of bubbles following different geodesics. We show that the results obtained from generic timelike geodesics have dependence on initial conditions. In contrast, the predictions extracted from 'eternal' geodesics, which never enter terminal vacua, do not suffer from this problem. We derive measure equations for ensembles of geodesics and discuss possible interpretations of initial conditions in eternal inflation.},
doi = {10.1103/PHYSREVD.75.023524},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
  • An analytic model is developed for understanding the abrupt onset of geodesic acoustic mode (GAM) in the presence of chirping energetic-particle-driven GAM (EGAM). This abrupt excitation phenomenon has been observed on LHD plasma. Threshold conditions for the onset of abrupt growth of GAM are derived, and the period doubling phenomenon is explained. The phase relation between the mother mode (EGAM) and the daughter mode (GAM) is also discussed. This result contributes to the understanding of “trigger problems” of laboratory and nature plasmas.
  • Motivated by the famous Waddington’s epigenetic landscape metaphor in developmental biology, biophysicists and applied mathematicians made different proposals to construct the landscape for multi-stable complex systems. We aim to summarize and elucidate the relationships among these theories from a mathematical point of view. We systematically investigate and compare three different but closely related realizations in the recent literature: the Wang’s potential landscape theory from steady state distribution of stochastic differential equations (SDEs), the Freidlin-Wentzell quasi-potential from the large deviation theory, and the construction through SDE decomposition and A-type integral. We revisit that the quasi-potential is the zero noise limit ofmore » the potential landscape, and the potential function in the third proposal coincides with the quasi-potential. We compare the difference between local and global quasi-potential through the viewpoint of exchange of limit order for time and noise amplitude. We argue that local quasi-potentials are responsible for getting transition rates between neighboring stable states, while the global quasi-potential mainly characterizes the residence time of the states as the system reaches stationarity. The difference between these two is prominent when the transitivity property is broken. The most probable transition path by minimizing the Onsager-Machlup or Freidlin-Wentzell action functional is also discussed. As a consequence of the established connections among different proposals, we arrive at the novel result which guarantees the existence of SDE decomposition while denies its uniqueness in general cases. It is, therefore, clarified that the A-type integral is more appropriate to be applied to the decomposed SDEs rather than its primitive form as believed by previous researchers. Our results contribute to a deeper understanding of landscape theories for biological systems.« less