Only altering the starting conditions or researching advent tech (Level one harmony can upgrade it by a third).

Only the Advent civ has research to accelerate research. Each civ has its own specialty, and the religious civ is a research civ, specializing in artifact research as well as speed-ups for other kinds of research. Rates are fixed otherwise for other civs.

To boost research rates, you have to mod a few files.
If you want researchrates to be quickened for all players and races, you can just go into "Gameplay.constants", and find:

researchSpeedData-Slow
researchRateGameSpeedScalar -2.0
researchSpeedData-Normal
researchRateGameSpeedScalar -1.0
researchSpeedData-Fast
researchRateGameSpeedScalar 0.0

and then just change the numbers to a higher positive number.

If you only want your own race to gain the benefits, then we have to cheat a bit.
Find your race and find a tech that only they have access to. You can find this by going into "PlayerPhase.entity", "PlayerPsi.entity", "PlayerTech.entity", "PlayerPirate.entity", and finding a suitable research subject.
In my example, I'll go with "PlayerPsi.entity", and I choose "RESEARCHSUBJECT_CULTURERATEPSI0.entity", as this is early on the Psi/Advent research tree. But any single item that only belongs to your chosen race will do.
I open "RESEARCHSUBJECT_CULTURERATEPSI0.entity", and go to the bottom, where it says:

researchFloatModifiers 2
researchModifier
modifierType "CultureSpreadRateAdjustment"
baseValue 0.000000
perLevelValue 0.050000
researchModifier
modifierType "CultureShieldMitigationAdjustment"
baseValue 0.000000
perLevelValue 0.010000
artifactPicture ""

change it to this:

researchFloatModifiers 3
researchModifier
modifierType "CultureSpreadRateAdjustment"
baseValue 0.000000
perLevelValue 0.050000
researchModifier
modifierType "CultureShieldMitigationAdjustment"
baseValue 0.000000
perLevelValue 0.010000
researchModifier
modifierType "ResearchBuildRateAdjustment"
baseValue 0.000000
perLevelValue 100.000000
artifactPicture ""

Notice that I change "researchFloatModifiers 2" to "researchFloatModifiers 3", and then I add:

researchModifier
modifierType "ResearchBuildRateAdjustment"
baseValue 0.000000
perLevelValue 100.000000

Changing the perLevelValue to a lower number will make the research slower. Just remember that it's a measurement of the percentile value of the original speed. So 100 will be instantaneous research, and 50 will be a doubling of original speed.

Just remember that you wont get the research boost until you've researched "RESEARCHSUBJECT_CULTURERATEPSI0.entity", which translates into "Zealous Worship".

I hope this helps you. Have fun.