In this talk I will review the cosmological science case for the Laser Interferometer Space Antenna (LISA), a space mission designed to detect gravitational waves (GWs) at lower frequencies with respect to the ones probed by current Earth-based GW interferometers. LISA will detect different populations of GW sources, some of which at large cosmological distances. Some of these sources will be used as cosmological distance indicators, which will allow us to probe the expansion of the universe at all redshift between roughly 0.01 to 10, without relying on the standard electromagnetic (EM) cosmic distance ladder. Tight constraints on cosmological parameters, together with new insights on the nature of dark energy and on possible deviations from LCDM and general relativity, are expected outcomes of the mission. Furthermore LISA may observe a stochastic background of GWs originated in the early universe through different high-energy processes such as first-order phase transitions, cosmic strings, and non-standard models of inflation. The detection of such a stochastic background of GWs would provide a direct way to test early-universe physics in a completely independent and complementary fashion with respect to common EM observations.
