There are a few papers out there.
A good starting point os the (always relevant) Grossman and Stiglitz (1980) "On the Impossibility of Informationally Efficient Markets" which shows that markets cannot be perfectly efficient without analysts being rewarded for their efforts (and is mentioned by many of the following articles as explaining some of what is observed).
The paper mentioned by fesman in the comments is also excellent: Chabakauri and Rytchkov (2015) "Asset Pricing with Index Investing" shows index investing reduces market volatility but has an indeterminate effect on correlations.
Appel, Gormley, and Keim (2016) have a paper "Passive Investors, Not Passive Owners" which shows that index funds voting as a bloc leads to more oversight of firm management and changes which increase shareholder value.
He and Shi (2017) "Index portfolio and welfare analysis under heterogeneous beliefs" notes how in the presence of index investors, even investors with more accurate beliefs may benefit from switching to index investing.
Hirschleifer, Huang, and Teoh (2017) "Index Investing and Asset Pricing under Information Asymmetry and Ambiguity Aversion" shows that offering a risk-adjusted market portfolio may eliminate individual stock alphas.
Gregoire (2020) "The Rise of Passive Investing and Index-linked Comovement" shows that stocks in the S&P 500 tend to comove more with each other and less with other stocks. (This would seem to either disagree with or improve upon Chabakauri and Rytchkov's work.)
Russ Wermers has a forthcoming paper (2020?) "Active Investing and the Efficiency of Security Markets" which shows that active (and not passive, i.e. index) investing improves price efficiency.
Davidson Heath has a few which are in the working paper stage such as:
- "ETF Trading and the Bifurcation of Liquidity" (with Brogaard and Huang) which shows liquidity has been improved for index member stocks but not for other stocks;
- "On Index Investing" (with Coles and Ringgenberg) which shows index-linked investing reduces information production for individual index member stocks but that price efficiency is unchanged; and,
- "Do Index Funds Monitor?" (with Macciocchi, Michaely, and Riggenberg) which shows the rise of index investing leads to less corporate oversight if index member firms.
Since these disagree with (or add nuance to?) Appel, Gormley, and Keim (2016) and Wermers (2020?), I suspect they would make interesting counterpoints.
I could surely go on and list more (Steve Ross's APT paper, for example). however, that should be plenty to get you started.