The reheating constraints to natural inflation in Horndeski gravity

• Published in: The European physical journal. C, Particles and fields Vol. 82; no. 3; pp. 1 - 11
• Main Authors: Chien, Chen-Hsu, Koh, Seoktae, Tumurtushaa, Gansukh
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Astronomy; Astrophysics and Cosmology; Constraint modelling; Elementary Particles; Equations of state; Gravitation theory; Gravity; Hadrons; Heating; Heavy Ions; Inflation (Finance); Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Parameter sensitivity; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Scalars; String Theory; Symmetry; Tensors
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-022-10236-w

For the subclass of Horndeski theory of gravity, we investigate the effects of reheating on the predictions of natural inflation. In the presence of derivative self-interaction of a scalar field and its kinetic coupling to the Einstein tensor, the gravitational friction to inflaton dynamics is enhanced during inflation. As a result, the tensor-to-scalar ratio r is suppressed. We place the observational constraints on a natural inflation model and show that the model is now consistent with the observational data for some plausible range of the model parameter Δ , mainly due to the suppressed tensor-to-scalar ratio. To be consistent with the data at the 1 σ ( 68 % confidence) level, a slightly longer natural inflation with N k ≳ 60 e -folds, longer than usually assumed, is preferred. Since the duration of inflation, for any specific inflaton potential, is linked to reheating parameters, including the duration N re , temperature T re , and equation-of-state ω re parameter during reheating, we imposed the effects of reheating to the inflationary predictions to put further constraints. The results show that reheating consideration impacts the duration of inflation N k . If reheating occurs instantaneously for which N re = 0 and ω re = 1 / 3 , the duration of natural inflation is about N k ≃ 57 e -folds, where the exact value is less sensitive to the model parameter Δ compatible with the CMB data. The duration of natural inflation is longer (or shorter) than N k ≃ 57 e -folds for the equation of state larger (or smaller) than 1/3 hence N re ≠ 0 . The maximum temperature at the end of reheating is T re max ≃ 3 × 10 15 GeV, which corresponds to the instantaneous reheating. The low reheating temperature, as low as a few MeV, is also possible when ω re is closer to 1/3.