If the contingency fee agreement that was entered into does not specify about advanced costs, can the attorney still demand a deposit before he will decide if he will take the case to trial?

Without reading the contract, I could not say whether your attorney can make this demand.  Many considerations can affect the decision to proceed to trial and may be operating in your case.  If you want your case to go to trial but do not want to make a cost deposit, you can call other attorneys to see how they would handle the matter.  If you have a good case with significant damages, another attorney will be willing to take over the case.  If not, and you still want to pursue the case, you may have to contribute a deposit.