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An important future goal in exoplanetology is to detect and characterizepotentially habitable planets. Using nulling interferometry, LIFE will allow usto constrain the radius and effective temperature of (terrestrial) exoplanets,as well as provide unique information about their atmospheric structure andcomposition. We explore the potential of LIFE in characterizing emissionspectra of Earth at various stages of its evolution. We perform Bayesianretrievals on simulated spectra of 8 different scenarios, which correspond tocloud-free and cloudy spectra of four different epochs of the evolution of theEarth. Assuming a distance of 10 pc and a Sun-like host star, we simulateobservations obtained with LIFE using its simulator LIFEsim, considering allmajor astrophysical noise sources. With the nominal spectral resolution (R=50)and signal-to-noise ratio (assumed to be S/N=10 at 11.2 $\mu$m), we canidentify the main spectral features of all the analyzed scenarios (most notablyCO$_2$, H$_2$O, O$_3$, CH$_4$). This allows us to distinguish between inhabitedand lifeless scenarios. Results suggest that particularly O$_3$ and CH$_4$yield an improved abundance estimate by doubling the S/N from 10 to 20. Weconclude that the baseline requirements for R and S/N are sufficient for LIFEto detect O$_3$ and CH$_4$ in the atmosphere of an Earth-like planet with anabundance of O$_2$ of around 2% in volume mixing ratio. This information isrelevant in terms of the LIFE mission planning. We also conclude thatcloud-free retrievals of cloudy planets can be used to characterize theatmospheric composition of terrestrial habitable planets, but not the thermalstructure of the atmosphere. From the inter-model comparison performed, wededuce that differences in the opacity tables (caused by e.g. a different linewing treatment) may be an important source of systematic errors.

Large Interferometer For Exoplanets (LIFE): V. Diagnostic potential of a mid-infrared space-interferometer for studying Earth analogs