The false vacuum decay in a brane world model is studied in this work. We investigate the vacuum decay via the Coleman-de Luccia instanton, derive explicit approximative expressions for the Coleman-de Luccia instanton which is close to a Hawking-Moss instanton and compare the results with those already obtained within Einstein’s theory of relativity.

The Coleman integral is a p-adic line integral that encapsulates various quantities of number theoretic interest. Building on the work of Harrison [8], we extend the Coleman integration algorithms in [2] to even degree models of hyperelliptic curves. We illustrate our methods with numerical examples computed in Sage.

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