It is not possible to change the game pace once the game has already begun.
This article details the mathematics behind these mechanics and details how they're effected in the various game speeds.
This thread from the Steam forums details the effects the game speed has in less mathematical terms and also includes information on how map sizes effects gameplay as well.
In addition, the game speed also affects the number of turns in each gameaffects the number of turns in each game.
Game speed effects a fairly substantial number of the mechanics in the game, including but not limited to;
- The amount of production required to complete units/structures
- The amount of science required to learn new technologies
- The amount of culture required to purchase new policies
- Gold from defeated barbarian tribes
- The cost of research agreements
For example; (copied from the Steam link)
Game speed: QUICK
- Game Length (Turns) = 330,
- Production Cost (Hammers) = 26,
- Policy Cost (Culture) = 15
Game speed: STANDARD
- Game Length (Turns) = 500,
- Production Cost (Hammers) = 40,
- Policy Cost (Culture) = 25
Game speed: EPIC
- Game Length (Turns) = 750,
- Production Cost (Hammers) = 60,
- Policy Cost (Culture) = 35
Game speed: MARATHON
- Game Length (Turns) = 1500,
- Production Cost (Hammers) = 120,
- Policy Cost (Culture) = 75
Product cost = Cost (In Hammers) to produce a WARRIOR.
Policy cost = Cost (In Culture) to produce the 1st policy.