# Matlab Is MATLAB better for numerical simulation

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1. Jan 16, 2017

### shinobi20

From cosmology, the tensor to scalar ratio is $r=16\epsilon$ where $\epsilon=-\frac{\dot H}{H^2}$ is the Hubble slow roll parameter. From warm inflation,
$$\ddot \phi + (3H+\Gamma)\dot \phi + V_\phi = 0 ,\quad H^2 = \frac{1}{3M_p^2} (\frac{1}{2} \dot \phi^2 + V)$$
where $H$ is the Hubble parameter, $\Gamma$ is the dissipation term, $V$ is the potential ,and $V_\phi$ is the derivative of the potential.
Example: $V = \frac{1}{2}m^2\phi^2$ where we can set $m=1$

$$\ddot \phi + (3H+\Gamma)\dot \phi + \phi = 0 ,\quad H^2 = \frac{1}{6M_p^2} (\dot \phi^2 + \phi^2)$$

I want to run a simulation where in I want to run $\Gamma$ for different points and get different values for $r$, but they are related indirectly, so I need to solve $H$ in order to get $\epsilon$ therefore $r$. So, I need to find $H$ with respect to different $\Gamma$ so that I can find $r$. But the problem is, they are written in a complex differential equations. Is Mathlab capable of solving this kind of problem and is it capable of printing (not plotting) different points of $r$ for different $\Gamma$?

2. Jan 17, 2017