Does this actually give you the same intensity as sunlight? Or well, close enough to it that the light can diffuse into the rest of the room? In my experience my 4000lm projector doesn't have anywhere near the intensity to properly approach sunlight.
Outside direct sunlight can be 100,000 lux. With one fixture if you are standing in the sunbeam you are more likely to be at 2000 lux which is a long way off. You can add more fixtures to increase the light you are getting. However it turns out that one of the most important parts of natural light is “melanopic lux” which comes from light centered around 490nm (blue), if you get more or this spectrum it can have the same effect as having a lot more light from a low blue Light fixture. (I.e typical 2700k bulb) Some info about this; https://www.innerscene.com/products/circadian-sky/CircadianS... There is now a lot of research that looks into how much of this blue light you need and architects are starting to incorporate this into Building designs.