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Title: Unimodular theory: A little pedagogical vision

Abstract

Under the generic designation of unimodular theory, two theoretical models of gravity are considered: the unimodular gravity and the TDiff theory. Our approach is primarily pedagogical. We aim to describe these models both from a geometric and a field-theoretical point of view. In addition, we explore connections with the cosmological-constant problem and outline some applications. We do not discuss the application of this theory to the quantization of gravity.

Authors:
Publication Date:
OSTI Identifier:
22403445
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 350; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COSMOLOGICAL CONSTANT; GRAVITATION; QUANTIZATION

Citation Formats

Fernández Cristóbal, Jose Ma, E-mail: jmariaffc@gmail.com. Unimodular theory: A little pedagogical vision. United States: N. p., 2014. Web. doi:10.1016/J.AOP.2014.07.046.
Fernández Cristóbal, Jose Ma, E-mail: jmariaffc@gmail.com. Unimodular theory: A little pedagogical vision. United States. doi:10.1016/J.AOP.2014.07.046.
Fernández Cristóbal, Jose Ma, E-mail: jmariaffc@gmail.com. Sat . "Unimodular theory: A little pedagogical vision". United States. doi:10.1016/J.AOP.2014.07.046.
@article{osti_22403445,
title = {Unimodular theory: A little pedagogical vision},
author = {Fernández Cristóbal, Jose Ma, E-mail: jmariaffc@gmail.com},
abstractNote = {Under the generic designation of unimodular theory, two theoretical models of gravity are considered: the unimodular gravity and the TDiff theory. Our approach is primarily pedagogical. We aim to describe these models both from a geometric and a field-theoretical point of view. In addition, we explore connections with the cosmological-constant problem and outline some applications. We do not discuss the application of this theory to the quantization of gravity.},
doi = {10.1016/J.AOP.2014.07.046},
journal = {Annals of Physics (New York)},
number = ,
volume = 350,
place = {United States},
year = {Sat Nov 15 00:00:00 EST 2014},
month = {Sat Nov 15 00:00:00 EST 2014}
}
  • The unimodular theory of gravity with a constrained determinant {ital g}{sub {mu}{nu}} is equivalent to general relativity with an arbitrary cosmological constant {Lambda}. Within this framework {Lambda} appears as an integration constant unrelated to any parameters in the Lagrangian. In a quantum theory the state vector of the universe is thus expected to be a superposition of states with different values of {Lambda}. Following Hawking's argument one concludes that the fully renormalized {Lambda}=0 completely dominates other contributions to the integral over {Lambda} in the vacuum functional. In this scenario of the unimodular theory of gravity the cosmological constant problem ismore » solved. Furthermore, this formulation naturally provides an external (cosmic) time for time ordering of measurements so that the quantum version of the unimodular theory can have a normal Schroedinger'' form of time development, giving a simpler interpretation to the equation of the universe.« less
  • Einstein's theory of gravity is reformulated so that the cosmological constant becomes an integration constant of the theory, rather than a coupling'' constant. However, in the Hamiltonian form of the theory, the Hamiltonian constraint is missing, while the usual momentum constraints are still present. Replacing the Hamiltonian constraint is a secondary constraint, which introduces the cosmological constant. The quantum version has a normal Schr{umlt o}dinger'' form of time development, and the wave function does not obey the usual Wheeler-DeWitt'' equation, making the interpretation of the theory much simpler. The small value of the cosmological constant in the Universe at presentmore » becomes a genuine question of initial conditions, rather than a question of why one of the coupling constants has a particular value. The key weakness'' of this formulation is that one must introduce a nondynamic background spacetime volume element.« less