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Nöether Symmetry in Inflation with Gauss-Bonnet Coupling
New Phys.: Sae Mulli 2019; 69: 113~118
Published online January 31, 2019;
© 2019 New Physics: Sae Mulli.

Seoktae KOH*

Department of Science Education, Jeju National University, Jeju 63243, Korea
Correspondence to:
Received September 11, 2018; Revised October 29, 2018; Accepted November 22, 2018.
cc This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The simplest ways for an accelerating expansion in the early universe are to introudce a scalar field with its potential in Einstein gravity. When we try to consider the quantum effect of gravity, introducing the Gauss-Bonnet term seems to be quite natural. Modified gravity, like the Gauss-Bonnet term, is widely considered in order to explain the late-time acceleration as well as the early-time acceleration. In this work we consider inflation driven by a single canonical scalar field in Einstein gravity with a Gauss-Bonnet term. For the non-trivial effect on the background dynamics due to the Gauss-Bonnet term, we need a nonminmal coupling function to the Gauss-Bonnet term. No first principle exists for the choice of the scalar field potential or the Gauss-Bonnet coupling function. In this work, we impose Nöether symmetry on the inflationary model and then determine the scalar field potential and the coupling function. In addtion, we investigate the constant-roll inflation with the Gauss-Bonned term to determine whether these obtained scalar field potential and coupling function can satisfy the constant-roll conditions.
PACS numbers: 98.80.Cq, 04.62.+v, 04.50.Kd, 11.30.-j
Keywords: Gauss-Bonnet, Nöether symmetry, Slow-roll inflation, Constant-roll inflation

June 2019, 69 (6)
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