## Abstract

The Palatini gravitational action is enlarged by an arbitrary function of the determinants of the Ricci tensor and the metric, . The resulting Ricci-determinant theory exhibits novel deviations from general relativity. We study a particular realization where the extension is characterized by the square-root of the Ricci determinant, , which corresponds to the famous Eddington action. We analyze the obtained equations for perfect fluid source and show that the affine connection can be solved in terms of the energy density and pressure of the fluid through an obtained disformal metric. As an application, we derive the hydrostatic equilibrium equations for relativistic stars and inspect the significant effects induced by the square-root of the Ricci tensor. We find that an upper bound on , at which deviations from the predictions of general relativity on neutron stars become prominent, corresponds to the hierarchy between the Planck and the vacuum mass scales. The Ricci-determinant gravity that we propose here is expected to have interesting implications in other cosmological domains.

Original language | English |
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Article number | 064049 |

Journal | Physical Review D |

Volume | 104 |

Issue number | 6 |

DOIs | |

Publication status | Published - 15 Sept 2021 |

### Bibliographical note

Publisher Copyright:© 2021 American Physical Society

### Funding

The work of H. A. and S. N. is supported by the United Arab Emirates University (UAEU) under UAEU Program for Advanced Research (UPAR) Grant No. 12S004. The work of C. K. is supported by İstanbul Teknik Üniversitesi Bilimsel Araşt𝚤rma Projeleri (İTÜ BAP) Grant No. TAB-2020-42312.

Funders | Funder number |
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UAEU Program for Advanced Research | 12S004 |

United Arab Emirates University | |

İstanbul Teknik Üniversitesi Bilimsel Araşt𝚤rma Projeleri | TAB-2020-42312 |