I was unable to generate accurate golden ratio spirals with the spiral tool. Instead I found a way to quickly generate them through parametric curves.
Create a square by pressing CTRL while using the rectangle/square tool.
With the square selected, navigate in the menu to Extensions -> Render -> Parametric Curves ...
Enter these values
Start t-value: 0
End t-value: 4.1
Checked -> Multiply t-range by 2*pi
X-value of rectangle's left: -1000
X-value of rectangle's right: 1000
Y-value of rectangle's bottom: -1000
Y-value of rectangle's top: 1000
I usually have Remove rectangle checked, and Draw Axes unchecked.
Credit to ragstian from this Inkscape Forum post: http://www.inkscapeforum.com/viewtopic.php?f=28&t=13427&start=25