In a 4 quart pot, heat the olive oil over medium-high heat. Add the onions and stir until they sizzle. Reduce the heat to medium and stir frequently. after about 5 minutes, stir in the garlic and lemon zest and stir.
Add the tomatoes, carrots, salt, spaghetti and water. Increase the heat to high and bring to a boil.
Stir and turn for 12 minutes, using a metal spatula or tongs to keep the pasta from sticking together or to the bottom of the pan.
When the pasta is cooked and the liquids have thickened and are coating the pasta, stir in the arugula and turn until barely wilted.