  Ultralight axions and other bosons are dark matter candidates present in many
high energy physics theories beyond the Standard Model. In particular, the
string axiverse postulates the existence of up to $\mathcal{O}(100)$ light
scalar bosons constituting the dark sector. Considering a mixture of axions and
cold dark matter, we obtain upper bounds for the axion relic density $\Omega_a
h^2 < 0.004$ for axions of mass $10^{-31}\;\mathrm{eV}\leq m_a \leq
10^{-26}\;\mathrm{eV}$ at 95% confidence. We also improve existing constraints
by a factor of over 4.5 and 2.1 for axion masses of $10^{-25}$ eV and
$10^{-32}$ eV, respectively. We use the Fourier-space galaxy clustering
statistics from the Baryon Oscillation Spectroscopic Survey (BOSS) and
demonstrate how galaxy surveys break important degeneracies in the axion
parameter space compared to the cosmic microwave background (CMB). We test the
validity of the effective field theory of large-scale structure approach to
mixed ultralight axion dark matter by making our own mock galaxy catalogs and
find an anisotropic ultralight axion signature in the galaxy quadrupole. We
also observe an enhancement of the linear galaxy bias from 1.8 to 2.4 when
allowing for 5% of the dark matter to be composed of a $10^{-28}$ eV axion in
our simulations. Finally, we develop an augmented interpolation scheme allowing
a fast computation of the axion contribution to the linear matter power
spectrum leading to a 70% reduction of the computational cost for the full
Monte Carlo Markov chains analysis.
