Last week, I did a brief post asking if anyone knew why the horizon problem was a problem since the universe had started as an infinitesimally small point. I received a lot of excellent replies, which I’m grateful for.
I had a couple of people ask me to post any answer I might eventually find. Unfortunately, I haven’t found an explicit authoritative answer, but after reading the responses, as well as diving into papers, that were technical way beyond my league, I have what I think is the answer.
To review, the horizon problem refers to the particle horizon, also known as the cosmological horizon. This is the largest distance over which matter or energy could have interacted since the start of the universe. This limit exists because the speed of light is the ultimate speed limit of anything within the universe. Nothing can travel faster than this speed, including particles, field interactions, or even gravity.
The universe is about 14 billion years old, which puts a limit to how far into the universe we can see. Due to the expansion of space, we can actually see further than 14 billion light years: out to about 46 billion actually, although due to the finite speed of light, the farther away we see, the further back in time we’re looking. So at the limits of our observation, we’re not seeing the universe as it is today, but as it was 14 billion years ago.
Around 380,000 years after the big bang, the universe’s density lowered to a point that light could travel, releasing a pent up store of photons, causing an enormous universe wide flash. The expansion of space since then has stretched that flash of light into the microwave bands. The cosmic microwave background is the furthest thing we can see in space and time.
So, the cosmological horizon then is currently 46 billions light years. However, we can look in the opposite direction and see just as far, another 46 billion light years. That makes the observable universe 92 billion light years in diameter. The observable universe is twice the diameter of the cosmological horizon.
The thing is, the cosmic microwave background has a consistent temperature in both directions, with only the most minute variation. It’s as though they were in or near thermal equilibrium, but they are outside of each other’s cosmological horizon.
Getting back to my original question, if the observable universe started as an infinitesimal point, wouldn’t it have had an opportunity to reach thermal equilibrium back then? The answer, I think, is that under the classic big bang timeline, the cosmological horizon was always smaller than what is now the observable universe.
Given the classic understanding of a smooth expansion, at no point in the history of the universe was the cosmological horizon ever larger than what eventually expanded into the observable universe. The horizon started less in size than the observable universe and was never able to catch up as they both expanded.
Even one planck time after the big bang, when the cosmological horizon would have been one planck length, what is now the observable universe must have been two or more planck lengths in diameter. The matter and energy across the observable universe never had a chance to reach thermal equilibrium.
This is one of the reasons that Alan Guth postulated cosmic inflation. For the horizon problem, the magic is the short period before inflation, when the expansion was slower than the traditionally understood rate. This allowed the cosmological horizon to be bigger than what is now the observable universe, allowing thermal equilibrium across it. This is followed by a period of exponential expansion where space rapidly expands by many orders of magnitude, spreading the thermal equilibrium to everything we can currently see (and probably far beyond).
It’s worth noting that although nothing within the universe can travel faster than light, this prohibition doesn’t pertain to space itself, which can expand faster than light, or to the relative speeds of distant objects carried along by that expansion. Indeed, given the acceleration of the expansion of space, there is a limit to how much of the universe we will ever be able to see. Everything beyond that point is moving away from us faster than the speed of light. We are forever causally disconnected from those regions of the universe.
Of course, the horizon problem isn’t the only thing that cosmic inflation solves. It also helps with the flatness problem, and other problems such as the observed absence of magnetic monopoles. For a more in depth discussion of this, I recommend Ethen Siegel’s excellent post on cosmic inflation.
I hope this post is clear to my fellow learners, and that it does justice to the insights of those who responded to last week’s query. Thanks again to everyone who participated in that discussion. I learned things, which is always awesome! At the same time, if there are any physics experts out there who see misconceptions here, I’d be grateful to hear from you.
- Cosmology: Back to the beginning (theguardian.com)
- Behind the Curtains of the Cosmos 1: Inflation and the Microwave Background (writescience.wordpress.com)
- Space-time ripples hint at physics beyond the big bang (newscientist.com)
- 5 Reasons to Care About New Big Bang Discovery (davidreneke.com)