Connecting Primordial Gravitational Waves and Dark Energy

Cosmic acceleration manifested in the early universe as inflation, generating primordial gravitational waves detectable in the cosmic microwave background (CMB) radiation. Cosmic acceleration is occurring again at present as dark energy, detectable in cosmic distance and structure surveys. We explore the intriguing idea of connecting the two occurrences through quintessential inflation by an $\alpha$-attractor potential without a cosmological constant. For this model we demonstrate robustness of the connection $1+w_0\approx 4/(3N^2r)$ between the present day dark energy equation of state parameter $w_0$ and the primordial tensor to scalar ratio $r$ for a wide range of initial conditions. Analytics and numerical solutions produce current thawing behavior, resulting in a tight relation $w_a\approx-1.53(1+w_0)\approx -0.2\,(4\times 10^{-3}/r)$. Upcoming CMB and galaxy redshift surveys can test this consistency condition. Within this model, lack of detection of a dark energy deviation from $\Lambda$ predicts a higher $r$, and lack of detection of $r$ predicts greater dark energy dynamics.