One of the issues at the core of my research is the speed of human evolution, particularly over the last 10,000 years. There are several potential arguments to suggest that the speed of human evolution is increasing, such as a larger population (creating a larger source of mutations) and the huge changes in environment that humans have experienced.
One of the obstacles to this argument is the largely monogamous nature of marriages, especially in more recent times and developed countries. If each man pairs with a single woman, and there are roughly equal numbers of each, inability to pair will no longer be a significant evolutionary factor. However, it is possible to argue that sexual selection can play a role even if there is pure monogamy (i.e. assuming no infidelity or serial monogamy).
Suppose that males and females can each be ranked in order of fitness - that is, their probability of surviving to adulthood. When it is time to match, the highest fitness male and female will pair off. The second highest ranked of each sex would like to pair with the highest ranked of the opposite sex, but given the highest ranked is already paired off, the two second highest ranked settle for each other. This continues down the rankings until the lowest ranked of each sex pair.
Now consider the offspring of these pairs. The offspring from the highest ranked pair will have the highest fitness. In fact, if you wanted to produce an offspring of the highest possible fitness, you would pair these two individuals. Similarly, if you aimed to produce the lowest possible fitness offspring, you would have done so by matching the lowest ranked pair.
The net result of this process is that the offspring in the population will have the largest possible range of fitness. Fitness matching concentrates harmful mutations in low fitness babies. With this large range of fitness, natural selection is faster, with the lowest fitness offspring least likely to survive and helpful genes concentrated in the high fitness offspring.
The result of this fitness spreading process is that sexual selection provides a platform for natural selection to have an increasing effect. Even in a perfectly monogamous society, sexual selection can still be a force.