  We show that there exists a $\mathbb{Z}^\infty$-summand in the subgroup of
the knot concordance group generated by knots with trivial Alexander
polynomial. To this end we use the invariant Upsilon $\Upsilon$ recently
introduced by Ozsv\'ath, Stipsicz and Szab\'o using knot Floer homology. We
partially compute $\Upsilon$ of $(n,1)$-cable of the Whitehead double of the
trefoil knot. For this computation of $\Upsilon$, we determine a sufficient
condition for two satellite knots to have identical $\Upsilon$ for any pattern
with nonzero winding number.
