Degravitation, Inflation and the Cosmological Constant as an Afterglow
  In this report, we adopt the phenomenological approach of taking the degravitation paradigm seriously as a consistent modification of gravity in the IR, and investigate its consequences for various cosmological situations. We motivate degravitation-- where Netwon's constant is promoted to a scale dependent filter function-- as arising from either a small (resonant) mass for the graviton, or as an effect in semi-classical gravity. After addressing how the Bianchi identities are to be satisfied in such a set up, we turn our attention towards the cosmological consequences of degravitation. By considering the example filter function corresponding to a resonantly massive graviton (with a filter scale larger than the present horizon scale), we show that slow roll inflation, hybrid inflation and old inflation remain quantitatively unchanged. We also find that the degravitation mechanism inherits a memory of past energy densities in the present epoch in such a way that is likely significant for present cosmological evolution. For example, if the universe underwent inflation in the past due to it having tunneled out of some false vacuum, we find that degravitation implies a remnant `afterglow' cosmological constant, whose scale immediately afterwards is parametrically suppressed by the filter scale ($L$) in Planck units $\Lambda \sim l^2_{pl}/L^2$. We discuss circumstances through which this scenario reasonably yields the presently observed value for $\Lambda \sim O(10^{-120})$. We also find that in a universe still currently trapped in some false vacuum state, resonance graviton models of degravitation only degravitate initially Planck or GUT scale energy densities down to the presently observed value over timescales comparable to the filter scale. 
Subodh P. Patil