In an economy with a working financial system there is no such thing as abundant or scarce capital, because financial capital is not used up when an investment is made, but merely transferred to the accounts of vendors and employees who then store it in funds which in turn seek new investments elsewhere.
The issue is how a speculative cash-flow is priced relative to the risk free cash-flow - what is the discount demanded of a speculative venture?
This discount, which is not the risk discount, but rather a measure of how risk is estimated, goes through secular swings:
As investments are seen to pay off, investors update their priors and view similar investments as less risky relative to the previous pricing. In a bust, people are convinced many of the same investments wont pay off and become more skeptical of ventures.
So I don't see this as a function of low rates so much as higher levels of confidence and optimism. That's all this is -- confidence and optimism, not scarcity or abundance of capital.
If this analysis is true, then the current climate will flip back once there is a high profile series of busts, rather than once rates are raised. But as raising rates tends to slow down the economy, rising rates may be the trigger that creates the busts, but it's not the only possible trigger.
Therefore, although I believe we are in a secular period of low rates, I don't believe we are in secular period of easy venture funding or "abundant capital". Note that one example would be Japan, where venture funding is historically hard to obtain as investors are much more conservative even though they have had a period of low rates for quite a while. This is because a risk free rate change from 1% to 2% isn't going to make a whole lot of difference to the discount demanded for a bet that has maybe a 50% chance to pay off. Updates of your assessment of risk are going to dominate the pricing of the venture's cashflow.