Cosmic rays may have contributed to the start of life on Earth. Here, we investigate the evolution of the Galactic cosmic ray spectrum at Earth from ages $t = 0.6-6.0,$Gyr. We use a 1D cosmic ray transport model and a 1.5D stellar wind model to derive the evolving wind properties of a solar-type star. At $t=1,$Gyr, approximately when life is thought to have begun on Earth, we find that the intensity of $sim$GeV Galactic cosmic rays would have been $sim10$ times smaller than the present-day value. At lower kinetic energies, Galactic cosmic ray modulation would have been even more severe. More generally, we find that the differential intensity of low energy Galactic cosmic rays decreases at younger ages and is well described by a broken power-law in solar rotation rate. We provide an analytic formula of our Galactic cosmic ray spectra at Earths orbit for different ages. Our model is also applicable to other solar-type stars with exoplanets orbiting at different radii. Specifically, we use our Galactic cosmic ray spectrum at 20$,$au for $t=600,$Myr to estimate the penetration of cosmic rays in the atmosphere of HR$,$2562b, a directly imaged exoplanet orbiting a young solar-type star. We find that the majority of particles $<0.1$GeV are attenuated at pressures $gtrsim10^{-5},$bar and thus do not reach altitudes below $sim100,$km. Observationally constraining the Galactic cosmic ray spectrum in the atmosphere of a warm Jupiter would in turn help constrain the flux of cosmic rays reaching young Earth-like exoplanets.
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