There is some recent evidence that they did, but when you put it in context, the question becomes both more complicated (and unanswerable) and interesting. As is true of most things in Archaeology, once you add context.
Here is the public summary of the work in question:
It has been suggested that Neandertals, as well as modern humans, may have painted caves. Hoffmann et al. used uranium-thorium dating of carbonate crusts to show that cave paintings from three different sites in Spain must be older than 64,000 years. These paintings are the oldest dated cave paintings in the world. Importantly, they predate the arrival of modern humans in Europe by at least 20,000 years, which suggests that they must be of Neandertal origin. The cave art comprises mainly red and black paintings and includes representations of various animals, linear signs, geometric shapes, hand stencils, and handprints. Thus, Neandertals possessed a much richer symbolic behavior than previously assumed.
This is from a paper by Hoffmann, Standish, Garcia-Diez, and a gazillion other authors (14 total) called “U-Th dating of carbonate crusts reveals Neandertal origin of Iberian cave art” in the current issue of Science.
The “art” in question is in three caves in Spain, La Pasiega (Cantabria), Maltravieso (Extremadura), and Doña Trinidad (or Ardales; Andalucía).
At La Pasiega, the rock art comprises mainly red and black paintings, including groups of animals, linear signs, claviform signs, dots, and possible anthropomorphs. Maltravieso was episodically used by hominin groups during the past 180 ka; it contains an important set of red hand stencils, which form part of a larger body of art that includes both geometric designs (e.g., dots and triangles) and painted and engraved figures. Ongoing excavations have shown that Ardales was occupied in the Middle and Upper Paleolithic. Its walls feature an impressive number (>1000) of paintings and engravings in a vast array of forms, including hand stencils and prints; numerous dots, discs, lines, and other geometric shapes; and figurative representations of animals, including horses, deer, and birds.
Uranium-Thorium dating was used to estimate the age of the pigment used to make the art in several cases. The short version is that the stuff painted on the walls is likely to be at least ca 65 thousand years old, which the authors note is 20 thousand years older than the earliest modern humans in Europe.
What is art?
I put “art” in “quotes” above in order to pique curiosity about this definition. And, I’m not going to say anything about it right now, other than these two things:
1) Of all the expressive output of humans today, we will happily argue over what is art, and what it means.
2) Humans or their close relatives engaging in expressive behavior tens of thousands of years ago do not escape that fascinating nexus of questions.
See Iain Davidson’s work for a much more detailed discussion of “art” (paintings and engravings) prior to the recent era. For example, this.
What is a human vs. a Neanderthal?
An argument has been made that the two groups are roughly equivalent. The argument has also been made that they are nothing like the same. I would make this argument: The range of variation in important traits across all Homo sapiens sapiens and the range of variation in important traits across all archaic Homo sapiens (to which Neanderthals belong) are each large, and there is some overlap in morphology. But, the behavioral variation does not track morphological variation in the human lineage very well at all until we get to very recent times (when agriculture seems to cause a reduction in brain size and an increase in various disease syndromes). Therefore, to me, it is possible to argue that the morphological non-overlap does not signify a behavioral non-overlap. Or, maybe it does.
Putting this a slightly different way, archaeologists and paleoanthropologists have almost always been more certain of what they are talking about with respect to Neanderthals and the Neanderthal-human difference than they’ve had a right to be. Nothing about this finding changes that.
Also, modern humans predate Neanderthals generally. Therefore, it is still possible that modern humans made this art, because they existed then. It is, however, probably difficult to make the argument that they lived in this part of Spain then. But not impossible.
How does typical Neanderthal or Human behavior emerge?
Elephants and apes can make art. Bonobos can communicate somewhat linguistically. It is possible to induce sorta-kinda- human behavior in other animals that are not that closely related to us, if they are predisposed and the proper context for this development is set up.
The following is therefor almost certainly true. Imagine a group of humans that live very far from the nearest Neanderthal, across a great desert you can’t cross, or a sea. Correspondingly, there is a Neanderthal group on the other side of that divide, with no contact with humans. Of course, both came from a common population of ancient times, but assume that these two hypothetical groups were separated from each other in the very earliest days of that phylogenetic (family tree) split.
Gilbert Tostevin of the University of Minnesota has done interesting work that might indicate that when two groups of humansish creatures encounter each other, they may imitate observed products of technology without getting the same chain of physical operations that lead to that outcome. So when you see the physical evidence of making a certain kind of stone tool differ on two different sites where humans and Neanderthals overlapped or encountered each other, you may be seeing one group imitating the other group’s products, but inventing their own process to achieve that product. That is about as cool as paleolithic archaeology gets. I mention this because it is an example of the thought experiment I’m dragging you through.
Now, move the two up to now distant hypothetical groups of humans and neanderthals near each other so that, at the edges of each group, they can interact for a thousand years. Assume most of the interaction is friendly, but they never mate (just to make this simpler). There is zero chance in the world that they groups will not meld culturally (if at the same time they differentiate culturally as well). Neanderthaly things will be found among the nearby humans, and humany things will be found among the Neanderthals. They will, culturally, contaminate each other.
Over time, this contamination will spread across both groups, so in five or ten thousand years (if not much sooner) there may well remain major differences between them, but there will be things that are found pan-Homo, across both groups. Like, they will all adopt hand shaking as a greeting, or kissing as a way of showing affection, or a particular kind of sharp stick. Or the putting of expressions on walls using pigment.
The world in which modern humans lived 65,000 years ago (plus or minus a few thousand years, so we can get them, maybe, to Australia) is huge. It runs from the southern tip of Africa across the African continent in all directions, to somewhere in the Middle east, across southern Asia to southeast Asia, and into Australia. The only reason modern humans did not simply exist all the way across Europe is probably because there were already Neanderthals there. Considering that huge arid regions that exist now across Africa and Asia were probably wetter at that time (plus or minus) it is possible that the total land area across the Old World occupied by modern humans grew to a near-maximum point then, and has not increased in total amount since then, or nearly so, outside of the sparsely occupied tundra and taiga.
Then there were the Neanderthals, in a shrinking zone in Central and Western Europe. They had also been in the Middle East, and sort of in North Africa. (Our best evidence of Neanderthals in North Africa may be an atavistic Neanderthal behavior found among the humans there in ancient remains, interestingly). But the whole cool thing about Spain (where the art in question is found) is that Spain is where the Neanderthals made a sort of last stand, that is where the last ones lived before they ceased to be as a palaeontological entity.
When you look at textbook maps of humans vs Neanderthals, there are almost always two biases, or mistakes. One is to avoid filling in the vast regions where humans must have lived even if evidence is lacking in the form of bony remains (much of Africa, for example). The other is maximizing Neanderthal range to include all of it, at its maximum, in every map, as though it was never smaller than that maximum. Rarely do you see a map that tries to show the vastness of modern human distribution in relation to a realistic distribution on Neanderthals near the end of their existence.
So I did a quick sketch demonstrating the assumption that around the time of the paper in question plus or minus ten thousand years or so, modern humans had traversed Asia, at least the warm parts, are were either in Australia or nearly so, while at the same time, Neanderthals were shrinking from their former distribution which maxed out (east-west wise) at Spain through West Asia.
I call this a “reverse bias” map because it is intended to wind back the usual biases mentioned above using only a small bias in the opposite direction, or possibly no bias at all.
Given this, while it is quite possible that Neanderthals were making this early we’ll-call-it-art, it is probably just as likely that what they were doing was a modern human thing that had been picked up by them, and then traversed the remaining geographical range of their species.
One other thing
I am not entirely convinced that I personally understand the exact physical relationship between the samples taken and the art observed well enough to argue that there are no problems with it. Also, I’ve not evaluated the U-Th dates directly. The material needed to do that is in the supplementary material, and I’m having trouble with my Science subscription, and don’t have time to dig in to this right now. Others will, I’m sure, and eventually this will be refuted, accepted, argued about, confirmed or not or whatever. As per usual.