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 } Hz – 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 can not 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 Hz – 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 .