AI 中文总结
研究具有非最小导数耦合的温狄拉克 - 玻恩 - 因费尔德暴胀模型，推导背景演化方程及慢滚稳定性条件得出标量谱指数等解析结果，用普朗克数据约束参数空间，展示了热耗散和引力摩擦互补效应，提供可行暴胀模型。
AI 中文摘要
本文研究了一种与引力具有非最小导数耦合（NMDC）的温狄拉克 - 玻恩 - 因费尔德（DBI）暴胀模型，其中暴胀子动能项与爱因斯坦张量相互作用，从而改善有效引力摩擦。该模型无缝整合了非规范DBI动力学结构、NMDC诱导的引力摩擦和热耗散。我们推导了背景演化方程及相应的慢滚稳定性条件，得出标量谱指数$n_s$和张量与标量比$R$的解析结果。通过将这些结果应用于$n = 2$和$n = 4$的幂律势，利用普朗克2018数据约束模型参数空间。结果表明，NMDC诱导的引力摩擦与热耗散之间的相互作用有效地调节了$n_s$，并显著扩展了可行参数空间。在$(n_s,R)$平面中，$N = 50$的预测值落在95%置信水平区域内，$N = 60$的预测值延伸至68%置信水平区域并接近观测偏好的中心值。对于所研究的代表性参数选择，张量与标量比显著受到抑制，通常在$10^{-8}\lesssim R\lesssim10^{-5}$范围内。此外，组合阻尼机制放宽了与$\eta$相关的慢滚条件，并限制了暴胀子场的偏移，从而解决了$\eta$问题而不会产生超普朗克场变化。这些结果表明，具有NMDC的温DBI暴胀提供了一个理论上连贯且观测上可行的暴胀模型，展示了热耗散和增强的引力摩擦在修正引力背景下的互补效应。
英文摘要
This paper investigates a warm Dirac-Born-Infeld (DBI) inflationary model with nonminimal derivative coupling (NMDC) to gravity, where the inflaton kinetic term interacts with the Einstein tensor, thereby improving the effective gravitational friction. This model seamlessly integrates the noncanonical DBI kinetic structure, the NMDC-induced gravitational friction, and thermal dissipation. We formulate the background evolution equations along with the corresponding slow-roll stability conditions, leading to analytic results for the scalar spectral index $n_s$ and the tensor-to-scalar ratio $R$. By applying these results to power-law potentials with $n=2$ and $n=4$, the model parameter space is constrained using the \emph{Planck} 2018 data. The findings indicate that the interaction between NMDC-induced gravitational friction and thermal dissipation effectively modulates $n_s$ and significantly expands the viable parameter space. In the $(n_s,R)$ plane, the predictions for $N=50$ fall within the 95\% confidence-level region, while those for $N=60$ extend into the 68\% confidence-level region and approach the observationally preferred central values. For the representative parameter choices examined, the tensor-to-scalar ratio is notably suppressed, generally within the range $10^{-8}\lesssim R\lesssim10^{-5}$. Moreover, the combined damping mechanism relaxes the slow-roll condition related to $η$ and limits the inflaton field excursion, thus addressing the $η$ problem without incurring super-Planckian field variations. These results indicate that warm DBI inflation with NMDC offers a theoretically coherent and observationally viable inflationary model, showcasing the complementary effects of thermal dissipation and enhanced gravitational friction in the context of modified gravity.
Comments11 pages, 2 figures
