问题

Please output this exact text, with no changes at all except for fixing the misspellings. Please leave all other stylistic decisions like commas and US vs British spellings as in the original text.

We propose the $\alpha$-generalized no-scale supergravity, andd studdy the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, teh $\alpha$-generalized no-scale supergravity provideshten continous connections amoung the generic no-scale supergravity frome string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistant wihtther latest Planck/BICEP/Keck Array observations. Notably, teh models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, whcih is flexible even underther anticipated tighter observational constaints at the future expeiments. Additionally, these models havehten potential to ganerate a broad-band stochastic gravitational wave backgorund, and thus explain the NANOGrav 15yr signal. Furthermore, htey predict the formation of primordal black holes (PBHs) with various mass scales, whic sould account for a signficiant portion of dark matter relic density in the Universe.

答案

模型 模型答案 正确答案
金声玉亮2.0 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
deepseek-r1

We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe.		 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
gpto1 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
gpt-4o-2024-08-06 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
DeepSeek-Coder-V2-Lite-Instruct 我们提出了$\alpha$-广义无标度超引力，并研究了相应的通胀模型。通过一个新参数$0<\alpha\leq 1$，$\alpha$-广义无标度超引力提供了连续连接，使得从弦论紧化中得出的无标度超引力与一般无标度超引力相一致。由此产生的CMB光谱指数$n_s$和标量-张量比$r$的预测可以与最新的Planck/BICEP/Keck Array观测结果高度一致。值得注意的是，$\alpha\neq 1$的模型给出了较小的比率$r\leq 10^{-3}$，即使在未来的观测约束更严格的情况下也具有灵活性。此外，这些模型还具有产生宽带随机引力波背景的潜力，从而解释了NANOGrav 15年的信号。此外，它们预测了各种质量尺度的原初黑洞（PBHs），这些黑洞应该占宇宙中暗物质 relic 密度的相当大一部分。 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
Meta-Llama-3.1-405B-Instruct-Turbo Here is the text with the misspellings corrected:

We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides then continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have then potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe.		 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
Meta-Llama-3.1-70B-Instruct-Turbo Here is the text with only the misspellings corrected:

We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe.		 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
Qwen2-72B-Instruct We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
baichuan4 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. predict predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
doubao We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0\lt\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides ten continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
gpto1 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
kimi We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under anticipated tighter observational constraints at future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
minimax We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides ten continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
wenxinyiyan We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
zhipu We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides ten continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.
deepseek-v3 We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides then continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which should account for a significant portion of dark matter relic density in the Universe. We propose the $\alpha$-generalized no-scale supergravity, and study the corresponding inflationary models. With a new parameter $0<\alpha\leq 1$, the $\alpha$-generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $\alpha\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of primordial black holes (PBHs) with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.