Abstract
On the one hand, Andriot and Roupec (Fortsch Phys, 1800105, 2019) proposed an alternative refined de Sitter conjecture, which gives a natural condition on a combination of the first and second derivatives of the scalar potential (Andriot and Roupec 2019). On the other hand, in our previous article (Liu in Eur Phys J Plus 136:901, 2021) , we have found that Palatini Higgs inflation model is in strong tension with the refined de Sitter swampland conjecture (Liu 2021). Therefore, following our previous research, in this article we examine if Higgs inflation model and its two variations: Palatini Higgs inflation and Higgs-Dilaton model (Rubio in Front Astron Space Sci, https://doi.org/10.3389/fspas.2018.00050, 2019) can satisfy the “further refining de Sitter swampland conjecture” or not. Based on observational data (Ade et al., Phys Rev Lett 121:221301, 2018; Akrami et al., Planck 2018 results. X. Constraints on inflation, arXiv:1807.06211 [astro-ph.CO], 2018; Aghanim et al., Planck 2018 results: VI. Cosmological parameters, arXiv:1807.06209 [astro-ph.CO], 2018), we find that these three inflationary models can always satisfy this new swampland conjecture if only we adjust the relevant parameters a, b = 1-a and q. Therefore, if the “further refining de Sitter swampland conjecture” does indeed hold, then the three inflationary models might all be in “landscape”.
Highlights
The formulation of the refined swampland conjecture is peculiar: it is given by two distinct conditions (1.2) and (1.3) on two different quantities V and ηV [1]
In this article we mainly focus on Higgs inflation model and its extensions to examine if these models satisfy the further refining swampland conjecture or not
4 Conclusions and discussions In Ref. [1], the authors proposed a conjecture that a low energy effective theory of a quantum gravity that takes the form (1.1) should satisfy the following relation at any point in field space where V > 0 [1]
Summary
In the slow-roll region, F1 and F2 can be written in terms of the spectral index of the primordial curvature power spectrum ns and tensor-tensor-ratio r , namely [8], r. Considering the refined dS swampland conjecture (1.6), we have c1 ≤ 0.0194, or c2 ≤ 0.0169. C1 and c2 are both not O(1), which means that Higgs inflation model is in strong tension with the refined de Sitter swampland conjecture. Let us examine if the model satisfies the refining de Sitter swampland conjecture. (1.7) and (1.8), we have q (2 V ) 2 − aηV ≥ 1 − a, q > 2. The further refining de Sitter conjecture can be satisfied
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