Simultaneously solving the H0 and a8 tensions with late dark energy

In a model independent approach, we derive generic conditions that any late time modification of the ACDM expansion history must satisfy in order to consistently solve both the H0 and the a8 tensions. Our results are fully analytical and the method is merely based on the assumption that the late-time deviations from ACDM remain small. For the concrete case of a dark energy fluid with deviations encoded in the expansion history and the gravitational coupling constant, we present necessary conditions on its equation of state. Solving both the H0 and a8 tensions requires that w(z) must cross the phantom divide if Geff = G. On the other hand, for Geff = G + 8G(z) and w(z) < -1, it < alpha(z)8H(z) H(z) 8G(z) is required that G < 0 at some redshift z.(c) 2022 Published by Elsevier B.V.