Rye starter might not double in size, and that's fine. In fact, mine usually go through a period of hyper-growth 2-3 days after they are initiated, but that is
not when they are ready: if I make bread then, it comes out overly sour/acidic. I learned to wait another 4-5 days until the starter stabilizes and stops growing like crazy, which gives me a better balance of bacteria and fungi.
Mind you, this is with a starter based on while rye flour. So, a side note: HN is predominantly US, and for some reason everybody in the US seems to think whole rye flour is only good for making pumpernickel. None of the bread-baking books I saw listed this simple recipe: 350g whole rye flour, 250g wheat flour, around 500ml water, 10g salt, 50g starter, let grow for 8h, bake at 210C for 1h10.
No kneading, no fuss, bread for busy people, and extremely tasty at that. But you do need good quality whole rye flour.