The landscape, the swampland and the era of precision cosmology

TL;DR

The paper scrutinizes the claim that de Sitter vacua cannot arise in string theory by reviewing advanced KKLT constructions and their dS supergravity realizations, then confronting swampland quintessence proposals with precision cosmology. It argues that established KKLT-based approaches evade classic no-go theorems and that current data strongly constrain exponential quintessence models, disfavouring scenarios with c ≥ √2. The authors conclude that the string landscape with dS vacua remains viable and that swampland-inspired accelerating-universe models are in tension with observations, highlighting conceptual issues such as quantum corrections, decompactification, and fifth-force constraints. Overall, the work emphasizes the need for carefully constructed, data-consistent string models of dark energy and argues against the no-dS no-go being a universal verdict on string theory cosmology.

Abstract

We review the advanced version of the KKLT construction and pure $d=4$ de Sitter supergravity, involving a nilpotent multiplet, with regard to various conjectures that de Sitter state cannot exist in string theory. We explain why we consider these conjectures problematic and not well motivated, and why the recently proposed alternative string theory models of dark energy, ignoring vacuum stabilization, are ruled out by cosmological observations at least at the $3σ$ level, i.e. with more than $99.7\%$ confidence.

Figures (10)

• Figure 1: There are many vacua before quantum corrections, and many vacua after quantum corrections. The ones on the right in the anthropically allowed range may originate from the ones on the left which were at all possible values of $\Lambda$. In this picture, quantum corrections may be large or small, but there will still be some vacua in the anthropic range, after all possible quantum corrections are made.
• Figure 2: Two-dimensional, marginalized constraints on $\lambda$ versus $\Omega_\text{M}$ (left panel) and $\lambda$ versus $\phi_0$ (right panel) for the quintessence model with the exponential potential $V(\phi) = V_0 e^{\lambda \phi}$. The contours show $68\%$, $95\%$ and $99.7\%$ confidence levels. Here, we have fixed the parameter $V_0$ to $0.7(3H_0^2)$ and varied the other parameters of the model, i.e. $\lambda$ and $\phi_0$, as well as $\Omega_\text{M}$. The one-dimensional, marginalized upper bounds on $\lambda$ are $\sim0.13$, $\sim0.54$ and $\sim0.87$, with $68\%$, $95\%$ and $99.7\%$ confidence, respectively.
• Figure 3: The same as in Fig. \ref{['fig:mainConstraints_V0p7']}, but when $\phi_0$ is fixed to $0$ and $V_0$ is varied. The marginalized, one-dimensional $68\%$, $95\%$ and $99.7\%$ upper bounds on $\lambda$ in this case are $\sim0.49$, $\sim0.80$ and $\sim1.02$, respectively. These results are in excellent agreement with our findings based on a frequentist, profile likelihood analysis, demonstrating that they are the least prior-dependent results we can obtain from an MCMC-based, Bayesian analysis, and provide the weakest possible bounds on $\lambda$.
• Figure 4: In the left panel we show how the two-field system of Section \ref{['O16']} with the scalar field potential (\ref{['Strcase2']}) evolves in time, starting with different initial conditions in the $\hat{\rho}-\hat{\tau}$ plane. In the right panel we present a longer time evolution, where the system evolves in the shallowest direction (depicted by a green line). For simplicity, the evolution is shown in the absence of matter and for $V_{\mathcal{R}} = 18 V_{\Lambda}$, in which case the shallowest direction is given by $\hat{\tau} = -{4 \hat{\rho}\over \sqrt 3}$; see eq. (\ref{['shall']}).
• Figure 5: Left panel: Reconstruction of the bound on the evolution of dark energy equation of state $w_\text{DE}$ provided by Agrawal et al. in Fig. 1 of Agrawal:2018own. The gray curves depict viable CPL-based $w_\text{DE}(z)$ corresponding to the $95\%$ contour in the $w_0-w_a$ plane given in Fig. 21 of Scolnic:2017caz. The upper envelope of these curves (thick, black curve) agrees with the exclusion curve provided in Fig. 1 of Agrawal:2018own. The blue curves show solely the curves which do not cross the phantom divide at any redshift $z<1$. Right panel: The thick, blue curve shows the $95\%$ exclusion bound on $w_\text{DE}$ obtained through the procedure of the left panel (corresponding to the upper envelope of blue curves). The orange curve shows the predicted exclusion bound inferred from the forecast analysis of Sprenger:2018tdb for the upcoming large-scale structure surveys Euclid and the SKA, in combination with the CMB constraints from Planck. The red curves show the exact, numerically calculated $w_\text{DE}(z)$ for three values of $\lambda=0.2, 0.6, 0.9$, while the dashed, black curves depict the corresponding CPL approximation according to eq. (\ref{['eq:CPL']}). For comparison, we have also shown (in green) the $95\%$ exclusion curve provided by Heisenberg et al. in Heisenberg:2018yae. See the text for a discussion of why this curve does not agree with the blue curve, although the analysis of Heisenberg:2018yae is a Fisher-matrix based approximation to the procedure illustrated in the left panel of this figure.