I notice when I capture a border city with another AI civ close by, the AI civ's borders typically push out a lot more. Oftentimes the border goes right to the city tile itself, and my borders only grow out in the opposite direction. I have tried using the great artist culture bomb, and it worked, but that method seems unreliable since I don't get a lot of great artists. So what do I do without a GA? It seems I lose population too when capturing a city, making the issue even tougher.