Trace-free Einstein gravity as a constrained bigravity theory

Montesinos, Merced; Gonzalez, Diego

doi:10.1103/physrevd.110.064057

Phys. Rev. D

2024

DOI: 10.1103/physrevd.110.064057

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Trace-free Einstein gravity as a constrained bigravity theory

Merced Montesinos,

Diego Gonzalez

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2024

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Cited by 2 publications

References 18 publications

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Trace-free Einstein gravity as two interacting constrained BF theories

Montesinos,

Gonzalez

2024

Class. Quantum Grav.

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A theory of gravity alternative to general relativity is trace-free Einstein gravity, which has the remarkable property that the cosmological constant emerges as an integration constant. In this paper, we report two fully diffeomorphism-invariant actions for trace-free Einstein gravity. They describe the theory as two $BF$ theories supplemented with some constraints. The first action comprises two copies of the constrained $BF$ theory for the Husain-Kucha\v{r} model plus an interaction term involving the fields that impose the constraints on the $B$ fields. The second action employs two copies of the chiral Plebanski action for general relativity plus an additional constraint. Both actions use complex variables, and naturally include one of the reality conditions imposed in the Plebanski formulation of general relativity. The new actions have the advantage of not involving any nondynamical fields or unimodular condition, and their only gravitational sector is trace-free Einstein gravity.

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Trace-free Einstein gravity as two interacting constrained BF theories

Montesinos,

Gonzalez

2024

Class. Quantum Grav.

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Cosmological constant as an integration constant

Feng,

Chen

2024

Eur. Phys. J. C

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The discrepancy between the observed value of the cosmological constant (CC) and its expected value from quantum field theoretical considerations motivates the search for a theory in which the CC is decoupled from the vacuum energy. In this article, we consider the viability of theories in which the Einstein equations are recovered (without additional constraints) and in which the CC is regarded as an integration constant. These theories include trace-free Einstein gravity, theories constructed from the Codazzi equation (which includes Cotton gravity and a gauge-gravity inspired theory), and conformal Killing gravity. We remark on a recent debate regarding Cotton gravity and find that while the Codazzi equation of that theory is indeed underdetermined, the solutions of the Codazzi equation trivialize to $$\lambda g_{ab}$$ λ g ab on generic backgrounds, and that in principle, one can close the system with the divergence-free condition and an appropriate choice of initial data. We also propose a full variational principle (full in the sense that variations in all variables are considered) for each of the aforementioned theories that can incorporate the matter sector; in this manner, we can obtain the trace-free Einstein equations without a unimodular constraint. The resulting actions require additional (auxiliary) fields and are therefore only expected to be effective, but they may provide a useful starting point in bottom up approaches to constructing more fundamental theories.

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Trace-free Einstein gravity as a constrained bigravity theory

Cited by 2 publications

References 18 publications

Trace-free Einstein gravity as two interacting constrained BF theories

Trace-free Einstein gravity as two interacting constrained BF theories

Cosmological constant as an integration constant

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