The cosmological arrow of time
By 1927, the Belgian cosmologist Georges Lemaltre had applied Einstein’s GR to cosmology, proposing that the universe was expanding [Lemaltre, 1927]. Two years later, the American observer Edwin Hubble published data supporting this hypothesis [Hubble, 1929]. Since then, the ‘Big Bang’ model of the universe has been validated empirically on a number of fronts, notably the measurement in 1967 of the temperature of the cosmic background radiation field [Penzias & Wilson, 1967].
Assuming the expansion interpretation of the data is valid, this then defines the cosmological arrow of time: future states of the universe are going to be very different to those close to the Big Bang. A notable empirical fact is that all the empirically based arrows of time are consistent with the cosmological arrow of time, in that none of them has been found to switch direction relative to that arrow.
The radiative arrow of time
When we switch on a torch at night, the beam of light spreads out into the space around us. When this light encounters some nearby object, it may be reflected back to us, as in the case of a mirror, or stimulate that object to emit its own characteristic light, which we then observe. That is what a torch is for. The light that we emit is never observed to return to us completely: some or all of it is inevitably lost irreversibly as far as we are concerned. This asymmetry between what goes out and what comes back defines an arrow of time known as the radiative arrow of time.