Entropy Bounds, Holography and Generalized Second Law in Cosmology

A new covariant "causal entropy bound" on entropy within a generic space-like region of volume V, and energy E scales as √ {EV} , the geometric mean of Bekenstein's S/ER and holographic S/A bounds, R being the linear size and A the boundary area of the region. In the case of limited gravity, Bekenstein's bound is the strongest while naive holography is the weakest. In the case of strong gravity, causal entropy bound and Bousso's holographic bound are stronger than Bekenstein's, while naive holography is too tight, and hence typically wrong. A new generalized second law of thermodynamics in cosmology, based on the conjecture that causal boundaries and not only event horizons have geometric entropies proportional to their area, forbids certain cosmological singularities, and is compatible with entropy bounds. In string cosmology the second law provides new information about non-singular solutions.