Why would the Earth or indeed the Universe cease to exist if humans ceased to exist? The Universe and the Earth happily existed for billions of years without us. In fact, humans have existed for only a tiny percentage of the age of the Earth.
Imagine if all humans suddenly died next week of some illness. Would the Earth and the Universe still exist. Of course they would.
Descartes had more than one axiom and his goal was not to doubt everything, it was to go give philosophy a new fresh start, clearing the field from old philosphy. From this new ground, certain knowledge was to be built through deduction.
Objective - existing independently of minds, ok, but the word "truth" is connected to language and thinking wich is connected to minds. "Truth" aims to build a bridge between the mind and the outside world. The notion "objective truth" suggests that the mind can through language produce descriptions of the world that are absolute. I would argue, like many others here, that this is never the case. A perfect description of the world/the universe would be an, in tiniest detail, exact copy of the world/the universe. The mind tries to recreate inner images of what the world is, these images are then encoded with the obtuse tool that is language. The distance between words, letters, sentences and an exact copy of the world/the universe is the distance between subjective language-creating and objective truth. The distance should be quite long in other words.
The notion "objective truth" implies universality and eternity. Something that happens on regular basics is that researchers rewrite their theories to better suit the world. The basic assumption is that the world is static, and that the new theories are coming closer and closer to describe this world once and for all. I think that the universe is in constant movement, and that the theories are local and temporary. One could maybe try to describe how universe is changing, but I think that this is in vain, since we are talking about an enormous chaos. And in this case chaos realtive to what the brain is trying to make of it. The patterns described in theories tells more about the human brains need to make order around itself. There is no order in universe, only the temporary ones that it makes sense for the human brain to describe. Apart from those maps, we are living in a positive "chaos" that in itself doesnt call for mapping. All efforts are locale, temporary and pragramaticly dependent on humans/reserachers temporary needs.