High energy physics and the very early universe with LISA

Gravitational wave experiments will play a key role in the investigation of the frontiers of cosmology and the structure of fundamental fields at high energies by either setting stringent upper limits on or by detecting the primordial gravitational wave background produced in the early Universe. Here we discuss the impact of space-borne laser interferometric detectors operating in the low-frequency window $\sim {10}^{-6}–1$ Hz; the aim of our analysis is to investigate whether a primordial background characterized by a fractional energy density $h_{100}^2\Omega \sim {10}^{-16}-{10}^{-15},$ which is consistent with the prediction of “slow-roll” inflationary models, might be detectable by the Laser Interferometer Space Antenna (LISA) or follow-up missions. In searching for stochastic backgrounds, the presently planned LISA mission suffers from the lack of two detectors with uncorrelated noise. We analyze the sensitivity improvements that could be achieved by cross-correlating the data streams from a pair of detectors of the LISA class; we show that this configuration is extremely compelling, leading to the detection of a stochastic background as weak as $h_{100}^2\Omega \simeq 5\times {10}^{-14}.$ However, such instrumental sensitivity cannot be fully exploited to measure the primordial component of the background, due to the overwhelming power of the signal produced by large populations of short-period solar-mass binary systems of compact objects. We estimate that the primordial background can be observed only if its fractional energy density $h_{100}^2\Omega$ is greater than $\approx 5\times {10}^{-13}.$ The key conclusion of our analysis is that the stochastic radiation from unresolved binary systems sets a fundamental limit on the sensitivity that can be achieved in searching for the primordial background in frequencies between $\sim {10}^{-6}$ Hz and 0.1 Hz, regardless of the instrumental noise level and the integration time. Indeed, the mHz frequency band, where LISA achieves optimal sensitivity, is not suitable to probe slow-roll inflationary models. We briefly discuss possible follow-up missions aimed at the frequency region $\sim 0.1–1$ Hz, which is likely to be free from stochastic backgrounds of astrophysical origin: no fundamental limits seem to prevent us from reaching $h_{100}^2\Omega \sim {10}^{-16},$ although the technological challenges are considerable and deserve careful study.