preprints.org > physical sciences > theoretical physics > doi: 10.20944/preprints202309.0672.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 8 September 2023 / Approved: 11 September 2023 / Online: 11 September 2023 (10:14:05 CEST)

The compatibility between the de Sitter Swampland conjecture and Ho\v{r}ava-Lifshitz $F(\bar{R})$ theories with a flat FLRW metric is studied. We first study the standard $f(R)$ theories and show that the only way in which the dS conjecture can be made independent of $R$ is by considering a power law of the form $f(R)\sim R^{\gamma}$. The conjecture and the consistency of the theory puts restrictions on $\gamma$ to be greater but close to $1$. For the $F(\bar{R})$ theories described by its two parameters $\lambda$ and $\mu$ we use the equations of motion to construct the function starting with an ansatz for the scale factor in the Jordan frame of the power law form. By doing a conformal transformation on the three metric to the Einstein frame we can obtain an action of gravity plus a scalar filed by relating the parameters of the theory. The non-projectable and projectable cases are studied and the differences are outlined. The $F(\bar{R})$ function obtained consists of terms of the form $\bar{R}^{\gamma}$ with the possibility of having negative power terms. The dS conjecture leads to inequalities for the $\lambda$ parameter, in both versions it gets restricted to be greater but close to $1/3$. For the general case in which $\mu$ and $\lambda$ are considered as independent, the action contains an extra term but we propose that the conjecture is still applicable. Once again the non-projectable and projectable cases are studied. The $F$ function obtained has the same form as before, the consistency of the theory and the dS conjecture lead to a set of inequalities on both parameters that are studied numerically. In all cases $\lambda$ is restricted by $\mu$ around $1/3$ and we obtain $\lambda\to1/3$ if $\mu\to0$. Finally we consider the $f(R)$ limit $\mu,\lambda\to1$ and we obtain consistent results.

Gravitation; Horava-Lifshitz theory; Swampland conjectures

Physical Sciences, Theoretical Physics

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