For a minute suppose that Rome never falls. Rome is never divided, Rome never adopts Christianity, and Roman Empire never becomes ‘Holy Roman Empire’.
How different would today’s world be?
Now, this is a vast scenario. So much could go wrong and so much could go right.
But let’s follow my imagination for a moment. In this timeline, Rome is the ultimate power. Everything and everywhere else is Roman colonies. Rome has managed to conquer the world and retain its power for over two thousand years. The dominant religion in this timeline remains the worship of Roman gods and goddesses. Other religions exist but in many small numbers. Rome is surprisingly culturally tolerant.
Over the first few centuries of Roman power, Rome invades and conquers more and more lands. Rome steadfastly increases its eastern reaches. Roman empire keeps absorbing cultures as it extends its territory. And as a result, Renaissance occurs early. There are artistic innovations and this spans across the globe. Renaissance which was limited to only Europe in our timeline is now happening across the world – cultures mix and absorb each other at a scary rate.
When America is discovered around the same time it is in our timeline, Rome gets to expand even more. But not knowing about the size of America, Rome decides to make it a prison colony, to combat its increasing population. This works out for a while, and then the American tribes attack, Rome retaliates, and surprise America is so much bigger than we thought! Oh, wait, there two of them!
That solves Rome’s population problem.
Nearing the sixteenth century, Rome experiences a second Renaissance and this time the focus is more on science. AN equivalent of the industrial revolution except for the part where industrialization has been happening in Rome since the end of the twelfth century. Rome was incredibly advance even in our timeline, and some of the ideas which were on paper never made it to reality. This goes for both the Greeks and Rome.
I imagine a very steam-punk society even as far back as the start of this millennium. Flying crafts, engines, clockwork operated vehicles. You get the idea. The Second Renaissance leads to an incredible breakthrough and within fifty years humanity is flying off to the moon! Another two hundred years and so the ability to travel most of the solar system exists.
Also, I have no doubts about this – by the twenty-first century, Roman empire most defiantly would have colonized Andromeda Galaxy.