Wednesday, March 27, 2013

decaying vorticity

can you show that in the course of linear structure formation during matter domination the vorticity $\omega=\mathrm{rot}\upsilon$ decays $\propto 1/a$ with the scale factor $a$? what's the relation during radiation domination? by how much has the vorticity decreased from the end of inflation (when vorticity modes could have been seeded) until today?

bonus question: what's the value of the integral
\begin{equation}
\int_0^\pi\mathrm{d}x\:\sin(x)^{x^x}
\end{equation}
CQW accepts numerical values and we'd be really interested in an analytical solution, because the numerical value is somewhat...suggestive.

1 comment:

  1. math bonus question: the value is $\simeq1.59057$, really close to $\pi/2$ with a relative deviation of $1.2\%$.

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