Detecting primordial features with LISA
  Oscillations in the frequency profile of the stochastic gravitational wave
background are a characteristic prediction of small-scale features during
inflation. In this paper we present a first investigation of the detection
prospects of such oscillations with the upcoming space-based gravitational wave
observatory LISA. As a proof of principle, we show for a selection of feature
signals that the oscillations can be reconstructed with LISA, employing a
method based on principal component analysis. We then perform a Fisher forecast
for the parameters describing the oscillatory signal. For a sharp feature we
distinguish between the contributions to the stochastic gravitational wave
background induced during inflation and in the post-inflationary period, which
peak at different frequencies. We find that for the latter case the amplitude
of the oscillation is expected to be measurable with $< 10\%$ accuracy if the
corresponding peak satisfies $h^2 \Omega_\textrm{GW} \gtrsim
10^{-12}$-$10^{-11}$, while for inflationary-era gravitational waves a
detection of the oscillations requires a higher peak amplitude of $h^2
\Omega_\textrm{GW}$, as the oscillations only appear on the UV tail of the
spectrum. For a resonant feature the detection prospects with LISA are
maximised if the frequency of the oscillation falls into the range
$\omega_\textrm{log} = 4$ to $10$. Our results confirm that oscillations in the
frequency profile of the stochastic gravitational wave background are a
worthwhile target for future detection efforts and offer a key for
experimentally testing inflation at small scales.
