(Non)eternal brane inflation

The random walk type eternal inflation in brane inflationary scenarios is reviewed. Unlike inflation in field theory with standard kinetic term, the DBI nature of the action describing the brane motion introduces extra constraints on eternal inflation. Constraints also appear due to the finite size of extra dimensions. In the context of false vacuum eternal inflation, we note that the Coleman-De Luccia instanton for a D-brane receives corrections due to the DBI nature of the action. This can enhance vacuum decay for a fine-tuned region of parameter space. Finally, some recent work on the stochastic Langevin description of the D-brane motion is reviewed. This leads to a modification to the Hawking Moss probability distribution.