In the near future we will have ground- and space-based telescopes that are designed to observe and characterize Earth-like planets. While attention is focused on exoplanets orbiting main sequence stars, more than 150 exoplanets have already been detected orbiting red giants, opening the intriguing question of what rocky worlds orbiting in the habitable zone of red giants would be like and how to characterize them. We model reflection and emission spectra of Earth-like planets orbiting in the habitable zone of red giant hosts with surface temperatures between 5200 and 3900 K at the Earth-equivalent distance, as well as model planet spectra throughout the evolution of their hosts. We present a high-resolution spectral database of Earth-like planets orbiting in the red giant habitable zone from the visible to infrared, to assess the feasibility of characterizing atmospheric features including biosignatures for such planets with upcoming ground- and space-based telescopes such as the Extremely Large Telescopes and the James Webb Space Telescope.
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