Unimodular gravity as an initial value problem

Abstract

Unimodular gravity is a compelling modified theory of gravity that offers a natural solution to the cosmological constant problem. However, for unimodular gravity to be considered a viable theory of gravity, one has to show that it has a well-posed initial value formulation. Working in vacuum, we apply Dirac's algorithm to find all the constraints of the theory. Then we prove that, for initial data compatible with these constraints, the evolution is well posed. Finally, we find sufficient conditions for a matter action to preserve the well-posedness of the initial value problem of unimodular gravity. As a corollary, we argue that the "unimodular" restriction on the spacetime volume element can be satisfied by a suitable choice of the lapse function.

8+1 pages. Accepted in PRD

References in corpus (23)

• Gravity, Lorentz Violation, and the Standard Model
• On the Numerical Integration of Einstein's Field Equations
• On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity
• Dark energy as the weight of violating energy conservation
• The quantization of unimodular gravity and the cosmological constant problem
• Dynamics of $k$-essence
• The Cauchy problem of scalar-tensor theories of gravity
• Well-posed formulation of Lovelock and Horndeski theories
• Strongly hyperbolic second order Einstein's evolution equations
• Hyperbolicity of the BSSN system of Einstein evolution equations
• Unimodular Gravity vs General Relativity: A status report
• Dark energy from quantum gravity discreteness
• Unimodular quantum gravity and the cosmological constant
• Well-posedness of the four-derivative scalar-tensor theory of gravity in singularity avoiding coordinates
• The path integral of unimodular gravity
• Gravity with more or less gauging
• Hamiltonian formulation of an effective modified gravity with nondynamical background fields
• Well-posed Cauchy formulation for Einstein-æther theory
• Unimodular Einstein--Cartan gravity: Dynamics and conservation laws
• Well-posedness of cubic Horndeski theories
• Symmetry algebra in gauge theories of gravity
• A clarification on prevailing misconceptions in unimodular gravity
• Energy nonconservation and relativistic trajectories: Unimodular gravity and beyond

Cited by in corpus (3)

• Charged thin shells in unimodular gravity
• Gravitational radiation from binary systems in Unimodular gravity
• Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor