Nonconservative traceless type gravity

Abstract

Extensions of the gravity theory in order to obtain traceless field equations have been widely considered in the literature. The leading example of such class of theories is the unimodular gravity, but there are other possibilities like the mimetic gravity and the Rastall gravity with a coupling parameter $\lambda =1/2$. The unimodular gravity proposal is a very interesting approach in other to address the cosmological constant problem. When coupled to matter such theories may imply that the energy-momentum tensor is not divergence free anymore. In this paper, a unimodular type theory will be developed by evading the conservation $T_{;\mu }^{\mu \nu }=0$. The cosmological consequences of the later, both at background as well as for scalar and tensor perturbations, are explored. Possible further extensions of this approach are discussed as well as its connection with the traditional unimodular gravity.

arXiv commentTitle changed. Matches version published in IJMPD

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• Rastall gravity extension of the standard $\Lambda$CDM model: theoretical features and observational constraints
• To conserve, or not to conserve: A review of nonconservative theories of gravity
• Diffusion in unimodular gravity: Analytical solutions, late-time acceleration, and cosmological constraints
• Nonconservative unimodular gravity: a viable cosmological scenario
• A clarification on prevailing misconceptions in unimodular gravity
• Inflation and the cosmological (not-so) constant in unimodular gravity
• Generalized nonconservative gravitational field equations from Herglotz action principle
• Effects of Rastall parameter on perturbation of dark sectors of the Universe
• Reconstruction of inflationary scenarios in non-conservative unimodular gravity
• Charged thin shells in unimodular gravity
• Spherical thin shells with charge in unimodular gravity