2017/08/28 by Zhongkai Guo, Zhong-Kai Guo
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Geometry #Lambda #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Monomial #Order (exchange) #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Solar and Space Plasma Dynamics #Tensor (intrinsic definition) #Upper and lower bounds #astro-ph.CO
paper · pdf · doi:10.1103/physrevd.96.123521
published as Phys. Rev. D 96, 123521 (2017) · 7 pages, 3 figures
arxiv created 2017/08/28 · openalex publication_date 2017/12/18 · arxiv updated 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We compute the tensor and scalar spectral index nt, ns, the tensor-to-scalar ratio r, and the consistency relation nt/r in the general monomial multifield slow-roll inflation models with potentials V\ensuremath∼\ensuremath∑i\ensuremathλi|\ensuremathφi|^pi. The general models give a novel relation that nt, ns and nt/r are all proportional to the logarithm of the number of fields Nf when Nf is getting extremely large with the order of magnitude around O(1040). An upper bound Nf\ensuremath\lesssimN*e^ZN* is given by requiring the slow variation parameter small enough where N* is the e-folding number and Z is a function of distributions of \ensuremathλi and pi. Besides, nt/r differs from the single-field result \ensuremath-1/8 with substantial probability except for a few very special cases. Finally, we derive theoretical bounds r>2/N* (r\ensuremath\gtrsim0.03) and for nt, which can be tested by observation in the near future.