An infinite-rank summand of knots with trivial Alexander polynomial

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