### Abstract

We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the equations for the distortion tensor (torsion and non-metricity) become algebraic, which means that those variables are not dynamical. As a result, we can rewrite the basic equations in the form of Riemannian geometry. Although all classified models recover the Einstein gravity in the Palatini formalism (in which we assume there is no coupling between matter and the connections), but when matter field couples to the connections, the effective Einstein equations include an additional hyper energy-momentum tensor obtained from the distortion tensor. Assuming a simple extension of a minimally coupled scalar field in metric-affine gravity, we analyze an inflationary scenario. Even if we adopt a chaotic inflation potential, certain parameters could satisfy observational constraints. Furthermore, we find that a simple form of Galileon scalar field in metric-affine could cause G-inflation.

Original language | English |
---|---|

Article number | 104020 |

Journal | Physical Review D |

Volume | 99 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2019 May 15 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*99*(10), [104020]. https://doi.org/10.1103/PhysRevD.99.104020

**Metric-affine gravity and inflation.** / Shimada, Keigo; Aoki, Katsuki; Maeda, Keiichi.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 99, no. 10, 104020. https://doi.org/10.1103/PhysRevD.99.104020

}

TY - JOUR

T1 - Metric-affine gravity and inflation

AU - Shimada, Keigo

AU - Aoki, Katsuki

AU - Maeda, Keiichi

PY - 2019/5/15

Y1 - 2019/5/15

N2 - We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the equations for the distortion tensor (torsion and non-metricity) become algebraic, which means that those variables are not dynamical. As a result, we can rewrite the basic equations in the form of Riemannian geometry. Although all classified models recover the Einstein gravity in the Palatini formalism (in which we assume there is no coupling between matter and the connections), but when matter field couples to the connections, the effective Einstein equations include an additional hyper energy-momentum tensor obtained from the distortion tensor. Assuming a simple extension of a minimally coupled scalar field in metric-affine gravity, we analyze an inflationary scenario. Even if we adopt a chaotic inflation potential, certain parameters could satisfy observational constraints. Furthermore, we find that a simple form of Galileon scalar field in metric-affine could cause G-inflation.

AB - We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the equations for the distortion tensor (torsion and non-metricity) become algebraic, which means that those variables are not dynamical. As a result, we can rewrite the basic equations in the form of Riemannian geometry. Although all classified models recover the Einstein gravity in the Palatini formalism (in which we assume there is no coupling between matter and the connections), but when matter field couples to the connections, the effective Einstein equations include an additional hyper energy-momentum tensor obtained from the distortion tensor. Assuming a simple extension of a minimally coupled scalar field in metric-affine gravity, we analyze an inflationary scenario. Even if we adopt a chaotic inflation potential, certain parameters could satisfy observational constraints. Furthermore, we find that a simple form of Galileon scalar field in metric-affine could cause G-inflation.

UR - http://www.scopus.com/inward/record.url?scp=85066437241&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.99.104020

DO - 10.1103/PhysRevD.99.104020

M3 - Article

VL - 99

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 10

M1 - 104020

ER -