Can someone explain how the current fear of inflation will affect stock prices and index like S&P 500?

High inflation means the Fed would need to increase interest rates to rein in inflation.

Higher interest rates means the future cash flows of companies, especially for growth companies whose cash flow is still a question mark, will have to be discounted at a high clip, resulting in a fall in the net present value of current share price. Higher interest rates also mean higher capital costs for companies (esp for new biz) to raise funds to growth rapidly

When you are investing in S&P500, we generally hope to get returns in 2 forms, dividend and capital gains from stock prices.

Dividend is much more straightforward, if everything stays the same but inflation increases, the future value of the dividend gets eroded. (I know this is oversimplification, but i believe this is enough to get the big picture).

For capital gains it is much more blur, in the sense that S&P500 is a diversified index consists of hundreds of companies in different sectors. But in simple terms, (i) cost of raw materials goes up and (ii) when you want to borrow from banks, the banks will know that the value of interest they will receive will get eroded if they charge low interest rate as now, so they hike it and the company will pay more interest. All (i) and (ii) will impact company’s future profit and hence pressure on stock returns.