Abstract
We present the locally supersymmetric formulation of unimodular gravity theory in D (1\le D \le 11) dimensions, namely supergravity theory with the metric tensor whose determinant is constrained to be unity. In such a formulation, the usual fine-tuning of cosmological constant is no longer needed, but its value is understood as an initial condition. Moreover, the zero-ness of the cosmological constant is concluded as the most probable configuration, based on the effective vacuum functional. We also show that the closure of supersymmetry gauge algebra is consistent with the unimodular condition on the metric.
Highlights
Ever since Einstein’s ‘blunder’ [1], how to understand the zero or extremely small cosmological constant without fine-tuning has been a long-standing problem both at the classical and quantum levels [2]
We present the lagrangian formulation of unimodular supergravity, in which the metric has a unit determinant as a field equation aided by lagrange multiplier fields
Our formulation of unimodular supergravity is more meaningful, when the value of cosmological constant is not determined by local supersymmetry itself, such as in 1 ≤ D ≤ 10
Summary
Ever since Einstein’s ‘blunder’ [1], how to understand the zero or extremely small cosmological constant without fine-tuning has been a long-standing problem both at the classical and quantum levels [2]. An interesting implication of this is that energy density ΩΛ associated with non-zero Λ is of the same order of magnitude as the matter density of the universe, giving rise to socalled second cosmological problem. In a certain formulation, the cosmological constant problem can be understood as an ‘initial condition’ instead of extremely small number adjusted by hand as an artificial ‘finetuning’. Such a theory is called ‘unimodular gravity’ theory, in which the determinant of the metric tensor is constrained to be unity, originally developed in [6][7]. We take the standpoint that a unimodular formulation for the cosmological constant is still important even in a supergravity theory
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