Primordial Gravitational Waves and the Swampland

Abstract

The swampland conjectures seek to distinguish effective field theories which can be consistently embedded in a theory of quantum gravity from those which can not (and are hence referred to as being in the swampland). We consider two such conjectures, known as the Swampland Distance and de Sitter Conjectures, showing that taken together they place bounds on the amplitude of primordial gravitational waves generated during single field slow-roll inflation. The bounds depend on two parameters which for reasonable estimates restrict the tensor-to-scalar ratio to be within reach of future surveys.

Figures (2)

• Figure 1: Mass spectrum in string theory. Generically we find little space to fit the masses of KK modes, winding modes and other moduli masses parametrically above $m_{\ell}$. The NLM with mass $m_h$ will belong to this last class. The light field with mass $m_l\lesssim H$ is the inflaton.
• Figure 2: Comparison of swampland constraints (SDC + SdSC) and combined observational constraints from Planck and BICEP2/Keck Array:2015xqh. Taking $N_e = 60$ and $\mathcal{D} = 1/c = m_{h}/m_{\ell}$, the darker red region shows the bounds from a NLM mass hierarchy of $m_{h}/m_{\ell} =10$, which gives $0.08 \leq r \leq 0.22$. We see that this hierarchy is already under some tension even with current constraints. For a mass hierarchy of $m_{h}/m_{\ell} =100$, the swampland constraints are much broader $0.0008 \leq r \leq 22$ (the upper bound is not shown). Nevertheless, even for this large hierarchy, it will be possible to probe the lower bound with future observational surveys.