If we assume that they believed in a spiritual God and Goddess, a special world outside our own could be assumed to be a requirement, somewhere for them to reside.
Cave art suggests that they believed in a spirit world and that they could express glimpses of that world through painting. Images of grids and dots are found in some of the deepest and most inaccessible parts of cave complexes, in places where they might never be seen by others. Our ancestors clearly went to a great deal of effort making these images. They would first have to obtain and grind pigments, some of which must have been precious. Then they would need a carrier for the pigment, such as fat or water. Also implements to paint with. They would carry these and a light source deep into the cave, risking injury, and paint images metres above the cave floor. And these images were often very abstract, occurring as dots, lines, grids, zig-zags, catenary curves and filligrees. In recent years it has become possible to induce visions of similar patterns in the minds of modern people by variously stimulating the retina and visual cortex of the brain. These are called entoptic phenomena. They can also be achieved using hallucinogenic drugs. So our ancestors were seeking altered states of conciousness. They might have used hallucinogens or could have induced visions through sensory deprivation deep in the caves. Perhaps they sat and waited until visions came to them out of the mysterious darkness. These visions must have been strange to them as they did not match anything in the known world. Perhaps they came from another world?
So seated deep within the womb of Mother Earth they revceived visions, perhaps glimpses of another world, perhaps messages. Their senses must have been spinning, we have all been in dark barely lit places and seen strange shadows, heard strange noises, felt the hair stand up on the back of our necks, felt a presence. Many shamanistic cultures still seek visions like this, inducing trance through sensory deprivation, fasting, hallucinogens, chanting, drumming and meditation in dark or exposed places. Did our ancestors enter the cave with questions and come out with answers? Were they leaving messages or offerings from our world to the spirit world? Were they being initiated and leaving the cave reborn? We will never know for sure, but for them there was clearly another world that could be communicated with.
For many years it was thought that our ancestors might have been asking the spirit world for direct intercession, carrying out sympathetic magic to help them in hunting. It now seems that this is not the case. The remains of prey animals do not generally match animals in the cave paintings. For example, the inhabitants of the Lascaux caves mostly ate wild goat. Far easier to kill than bison, and safer too! So they were seeing very clear visions of animals in their mind and representing them on cave walls in two dimensions. Most of the animals depicted are in profile and although they have colour, there is no shading, no perspective and no composition. They are making a very clear image of the animal and its physical characteristics so that there is no mistaking it. So rather than asking to kill such animals, they might have been asking for their help or some of their power. And if this is the case they might have been trying to link with the animal spirit.
Today, shamans still attempt to link with animal spirits and many people claim to have animal spirit guides. Shamans and initiates in all sorts of cultures don costumes and masks and imitate animal spirits. Much later mesolithic finds from Star Carr hint at shamanistic rites - deer skulls with holes drilled could be head dresses or masks.
Animal spirits are not just about food, they bring messages, power, help and guidance. The movements of animals are also interpreted in divination. Even today, people see a single magpie as a portent for bad luck. In many cultures the gods can disguise themselves as animals (or even plants and objects).
So cave artists were certainly depicting visions of things imagined and real. Later beliefs in the spirit world suggest that it was believed that these came from somewhere else, outside of the artist. It is interesting to note that many modern artistic geniuses have described the feeling that they are just channeling their art from the outside and even describe a trance like state - they are a conduit. Given the beauty, accuracy and skill of the prehistoric cave painters we could attribute genius to them. Afterall, on entering the Altamira caves Picasso is quoted as saying: "after Altamira, all is decadence"......."we have learned nothing!"