Inflation and de Sitter conjectures in 8-dimensional $R+γR^n$ Gravity

TL;DR

This work investigates inflation arising from an eight-dimensional $R+\gamma R^n$ gravity theory, transforming it into 4D scalar-tensor dynamics via Weyl transformation and compactification. It derives both a single-field inflaton potential and a two-field potential involving a radion, computes slow-roll observables, and assesses compatibility with Planck data and swampland de Sitter conjectures. The single-field model generally aligns with $n_s$ and $r$ but yields an $A_s$ somewhat larger than Planck, while the two-field model can fit $n_s$ and $r$ but requires careful moduli stabilization and produces a large running unless tuned. Regarding quantum gravity constraints, the single-field potential does not satisfy the original dS conjecture but can satisfy the further refined bound for suitable $(a,q)$, whereas the two-field potential can satisfy both the original and the further refined swampland conditions, suggesting landscape compatibility under certain parameter choices.

Abstract

In this work, we study two potentials, the single-field and the two-field, from the modified ($R+γR^n$) gravity in D=8 dimensions. From those potentials, we calculate four observable quantities in inflation, including scalar-to-tensor ratio, spectral index, running index and scalar amplitude. Then, we compare them to the experimental data to verify the righteousness of the models. Last but not least, de Sitter conjectures are brought up with these two potentials to investigate that it is possible or not the theory lay in the Landscape of quantum gravity.

Figures (7)

• Figure 1: Two-fields potential (\ref{['2fieldspotential']}) with a = 9.1027, $F^2 = 10^6$ and $\tilde{\Lambda}_8 = 0.01$.
• Figure 2: The dependence of a) $n_s$, b) r, c) $A_s$ and d) $\frac{dn_s}{d(lnk)}$ on $\lambda$
• Figure 3: The dependence of a) $n_s$, b) r, c) $A_s$ and d) $\frac{dn_s}{d(lnk)}$ on $\omega$ and $\delta$
• Figure 4: The dependence of a) $n_s$, b) r, c) $A_s$ and d) $\frac{dn_s}{d(lnk)}$ at optimal values of parameters $\omega =-6.9$ and $\delta = 0.9$ on e-folding numbers
• Figure 5: The variation of the boundary of a) $c_1$ and b) $c_2$ depends on $\lambda$