On the Cosmological Implications of the String Swampland

TL;DR

This work investigates how two Swampland criteria—restricted field excursion $| abla\phi|/V$ bounds and a maximal field range $|\,\Delta\phi|<\Delta$ with $\Delta, c=\mathcal{O}(1)$—shape cosmology. By applying these criteria to inflation and to present/future dark energy, the authors show that inflation is generically in tension with the criteria, while certain quintessence models can satisfy both and remain compatible with current data. They derive model-independent constraints on $c$ and $\Delta$ from observations, including a bound $c\lesssim0.6$ and a lower limit on $(1+w)_0\gtrsim0.15\,c^2$, and they connect the allowed dynamics to a potential future phase transition within a few Hubble times. The results have implications for upcoming measurements of the tensor-to-scalar ratio $r$ and the dark-energy equation of state $w$, and motivate exploration of dark-matter couplings and equivalence-principle tests in the dark sector. Additionally, the paper discusses how the absence of de Sitter vacua reframes the cosmological constant problem and hints at a possible link between the dark-energy scale and high-energy physics scales such as the GUT scale.

Abstract

We study constraints imposed by two proposed string Swampland criteria on cosmology. These criteria involve an upper bound on the range traversed by scalar fields as well as a lower bound on $|\nabla_φ V|/V$ when $V >0$. We find that inflationary models are generically in tension with these two criteria. Applying these same criteria to dark energy in the present epoch, we find that specific quintessence models can satisfy these bounds and, at the same time, satisfy current observational constraints. Assuming the two Swampland criteria are valid, we argue that the universe will undergo a phase transition within a few Hubble times. These criteria sharpen the motivation for future measurements of the tensor-to-scalar ratio $r$ and the dark energy equation of state $w$, and for tests of the equivalence principle for dark matter.

Figures (1)

• Figure 1: (a) The black curve shows the current observational $2\sigma$ bound on $w(z)$ for $0<z<1$ based on SNeIa, CMB and BAO data Scolnic:2017caz. This is compared with the predicted $w(z)$ for exponential quintessence potentials with different values of constant $\lambda$ under the constraint that $\Omega_{\phi}(z=0)= 0.7$ and assuming initial conditions $x=y\approx 0$. From this we observe that the upper bound on $\lambda$ is $\sim 0.6$ (blue curve). (b) The blue curve shows the trajectory in the $(x,y)$ plane corresponding to constant $\lambda=0.6$, the upper bound allowed in Fig. 1(a), assuming initial conditions $(x,y)=(0,0)$. The current $(x,y)$ is where the blue curve meets the green; the dashed blue curve illustrates its future asymptotic behavior. Trajectories to the right of the blue curve have a larger $w(z)$ at $0<z<1$ and, hence, violate the observational constraints in Fig. 1(a). As explained in the text, trajectories to the left of the blue curve extrapolate back in time, hit the $y$-axis at some finite $y$ and then continue on to $(x,y)=(-1,0)$ or $\Omega_{\phi} \rightarrow 1$. These trajectories disrupt matter domination and, hence, large-scale structure formation. Hence, the bound for constant $\lambda$, $c<0.6$ in Fig. 1(a), is also the bound for general $\lambda(\phi)>c$.