Ok so if I increase research time, the years / date will not slow down as well?
Each game speed has 7-8 entries of that type that are intended to be read sequentially. So you do X turns at Y years per turn, then the next Z turns at W years per turn, and so on down the line. The SUM of those entries' numbers of turns is what defines the Time victory condition, so it's not purely aesthetic, but for the most part the numbers in that table only affect the year number in the upper-right corner. If you slow down research rates, the turn:year conversion won't change unless you also adjust all of the values in that table.
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As to the original question: yes, as others have said, you can slow down research by tweaking those numbers.
And if you do, a whole lot of things will break. You see, the game's systems are heavily interconnected; changing one thing changes a lot of others. While we can tell you how to change tech costs in very short answers, telling you how to do it without breaking the game takes a LOT longer.
If you double the amount of turns it takes to unlock a tech, and don't also double the time needed to produce units or buildings, then
you'll end up building twice as many units or buildings. Sounds fine for a human player, who can adapt to the change, but an AI will quickly go bankrupt from overproducing units and making buildings it doesn't need because
it won't understand WHY it's going bankrupt and will continue to act the way it would in a normal game, following a hardcoded strategy that's no longer a good idea. The unit maintenance equation is semi-exponential, so out-of-control unit production can very quickly wipe out the AI's income.
Likewise, if you don't also slow down the city growth rate by a corresponding amount, then cities will be larger than they were intended to be at each stage of the game. Larger cities mean more production and research, but they also mean more unhappiness, and most of the ways of dealing with happiness are tech-limited. So you'll have cities with extreme unhappiness because in a normal game you'd unlock Colosseums before your cities reached size 6, while now they'll be size 8 or 9 and you STILL won't have unlocked the Colosseum yet. This sort of thing is much more harmful to the AI than to a human, because an AI doesn't know how to use things like Avoid Growth to prevent these issues.
Also, if you try to extend the techs in the early game you'll have real problems with the AI. For instance, if a human player has Cotton near his home city, he'll probably head for Calendar ASAP to get the Pasture needed to harvest that resource for the Happiness boost. The AI doesn't pick techs to research like that; everything for the AI is Flavor-based, which does not consider the actual situation of an empire. The more you slow down the early game, the bigger the advantage for the human.
There's a LOT more, but these should give you a rough idea of the problem. There's a reason that all of the existing game speeds simply multiply everything (research cost, unit cost, building cost, policy cost, etc.) by the same value. If you want to slow things down, then there are quite a few ways to do so, and several balance mods exist that do this in a well-balanced way. But it's not even close to being as simple as a one-line update.
