- #1
shinobi20
- 277
- 20
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##?
$$\ddot \phi + (3H+\Gamma)\dot \phi + V_\phi = 0 ,\quad H^2 = \frac{1}{3M_p^2} (\frac{1}{2} \dot \phi^2 + V)$$
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##?