Early dark energy (EDE) is an extension to the ΛCDM model, proposed
to reduce the tension between the measurements of the Hubble constant H0
from the cosmic microwave background (CMB) and from the local cosmic distance
ladder. However, this model increases the S8 tension between CMB and large
scale structure measurements. Analyses of galaxy clustering and lensing
correlation functions report a decreased preference for EDE and its effect on
the Hubble tension. Smooth dark energy models affect growth of structure
through the background expansion. In this work, we study the inclusion of a
general, smooth late-time dark energy modification in combination with EDE and
obtain constraints on EDE marginalized over the late-time expansion. We assess
the impact on the S8 and Hubble tensions. In order to generalize the late
expansion, we use a late dark energy fluid model with a piecewise constant
equation of state w(z) over 3, 5 and 10 redshift bins in the window z∈[0,3]. We show that, when analyzing ACT and Planck CMB data combined with
Pantheon supernovae, BAO from 6dF, SDSS and BOSS, Planck 2018 CMB lensing and
Dark Energy Survey cosmic shear and clustering data, the inclusion of a general
smooth dark energy modification at late times has no significant effect on
S8 and EDE parameter constraints. Using the aforementioned datasets, the EDE
fraction constraint with late-time expansion marginalization is fEDE=0.067−0.027+0.019 using 3 redshift bins, with similar results for 5
and 10 redshift bins. This work shows that in order to solve simultaneously the
Hubble and S8 tensions, one needs a mechanism for increasing the clustering
of matter at late times different from a simple change in the background
evolution of late dark energy. [Abridged]Comment: 22 pages, 9 figure