I am wondering if more and more mining centers will switch to the use of alternative energy, will it allow to reduce the cost of bitcoin? After all, while mining is very expensive
It all depends on the economics of it. There aren't a lot of scenarios where you could effectively pay into alternative energy and have it net you a decent return. For example, if a miner has no river or lakes near them, they can't do hydro. If their location also lacks significant wind activity, they now can't use wind power either. If they're far from the equator it might also be difficult for them to supply their energy needs during winter months, as the sun won't shine as much as necessary to keep all of their miners operational, in the case of solar panels. If anything, alternative energy might increase the cost of Bitcoin because of the setup costs.
That, and now you have to think about how you'd store excess energy, if at all. Batteries that could store the amount of electricity required to run miners for a night would cost, at least, tens if not hundreds of thousands of dollars.
There are some ways that they could notionally reduce the expenses, such as selling the energy they produce back to the grid, but the same issues I mentioned above still apply. Renewable resources are not an end-all-be-all when it comes to reducing energy expenditures.