TY - JOUR

T1 - Metric-affine gravity and inflation

AU - Shimada, Keigo

AU - Aoki, Katsuki

AU - Maeda, Kei Ichi

N1 - Funding Information:
K. S. acknowledges Shoichiro Miyashita, Shinji Mukohyama, and Masahide Yamaguchi for eye-opening discussions and advice throughout this work. We would also thank Tommi Tenkanen for fruitful comments. Furthermore, K. S. will like to thank the Yukawa Institute for Theoretical Physics for their kind hospitality during his stay. The work of K. A. was supported in part by a Waseda University Grant for Special Research Projects (No. 2018S-128). This work was also supported in part by JSPS KAKENHI Grants No. JP16K05362 (K. M.) and No. JP17H06359 (K. M.).
Publisher Copyright:
© 2019 American Physical Society.

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.

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U2 - 10.1103/PhysRevD.99.104020

DO - 10.1103/PhysRevD.99.104020

M3 - Article

AN - SCOPUS:85066437241

VL - 99

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 10

M1 - 104020

ER -