Depends a bit upon what you mean by information. If by information you mean the full configuration of the wavefunction of the universe, then as long as the laws of physics are unitary the two points in time necessarily contain the exact same amount of information. This means that if you had the full state at the early time, you could calculate the late time knowing the laws of physics. If you had the full state at the late time, you could calculate the early time. It comes down to whether or not the laws of physics are unitary.