A simple solution to the flatness and horizon problems The flatness problem and the horizon problem are major problems in physics. These problems can be solved by assuming that the universe expanded sufficiently fast during a period just after the big bang, a scenario proposed by the inflation theory. This theory depends on an ad hoc and undiscovered form of energy to drive the expansion, thereby creating a new problem as to the nature of this energy. The leading cosmological model utilizes both general relativity and the inflation theory. See also about the horizon problem in New Scientist’s 13 things that do not make sense. Now I will show that general relativity already offers a simple solution to the flatness and horizon problems, in which case the inflation theory is superfluous and the cosmological model can be streamlined. In GR, observers on different planets can age at various rates due to gravitational time dilation. For example, twins who separate to live on different planets can be of widely different ages when they next meet. Hereafter let all distances be proper lengths, which are invariant quantities (all observers agree on them). Let observer X, on one planet, age at a rate that is a small fraction of the rate at which observer Y, on another planet, ages. Let the planets recede from each other at a rate of nearly one light year per year on Y’s clock. Then in X’s frame the other planet must recede at a rate of nearly one light year per small fraction of one year, which is to say it recedes at a rate of much more than one light year per year, because, while Y ages one year, X ages a small fraction of that. The rate at which X ages can be an arbitrarily small fraction of the rate at which Y ages. Then in a planetary observer’s frame, another planet can recede by an arbitrarily large number of light years per year. In other words, the universe can expand arbitrarily fast. This solves the flatness and horizon problems, using no new assumptions like those of the inflation theory. Note that nothing need exceed the speed of light as directly measured. Nor does space itself need to expand, as it does in the expansion proposed by the inflation theory. When the universe can expand arbitrarily fast without space itself needing to expand, the observable universe can be arbitrarily large at any given moment.
Hi zanket, I'm not sure how this addresses the flatness problem. Regarding the horizon problem, can you show mathematically using the Einstein field equations that regions of space at the edge of the observable universe on opposite sides of Earth were once causally connected?
The flatness problem is explained if the universe expanded sufficiently fast during some period in its history. The link I gave above says “Inflation's rapid expansion caused space to become flatter”. The proof I gave above shows that it is deducible from GR that the universe can expand arbitrarily fast. Using the field equations to do that would be overkill. In the inflation theory’s solution to the horizon problem, a small chunk of matter and energy in thermal equilibrium is expanded to the size of the observable universe, so that “regions of space at the edge of the observable universe on opposite sides of Earth” now have the same temperature. In my solution, only the expansion mechanism differs. I already give an incontrovertible proof that it is deducible from GR that the universe can expand arbitrarily fast. The only equation needed is that for gravitational time dilation.
I don't understand what you're saying that's any different to Guth's inflation. Ah, hang on... I don't understand your distinction between the universe expanding and space expanding.
In Guth’s inflation theory, what exactly drove the expansion is unknown. As the New Scientist article I gave above says, “The trouble is that no one knows what could have made that happen. So, in effect, inflation solves one mystery only to invoke another.” In my explanation, gravitational time dilation drove the expansion. Gravitational time dilation is already experimentally confirmed. There’s no new mystery with my explanation. Cosmic expansion is nothing more than all of the distant galaxies receding from one another. It could be caused by space expanding, or something else. When space itself expands, a sufficiently long straight thread floating in deep space is stretched and eventually breaks. In the leading cosmological model, expanding space explains cosmic expansion. Of course objects still have freedom of movement relative to the expanding space, a so-called peculiar movement. See also Cosmic expansion is not to blame for expanding waistlines. It is possible that cosmic expansion is due solely to peculiar movement. In that case a straight thread floating in deep space would not stretch regardless of its length.
So you are suggesting that matter is moving through space which is already present, opposed to space expanding along with the matter?
Almost. I'm saying that space does not need to expand in order for the universe to expand arbitrarily fast, when the mechanism driving that expansion is gravitational time dilation. In that case matter can simply move "through space which is already present", and SR is not violated. In the mechanism described by inflation theory, space expands, as it must so that SR is not violated.
It would be tricky explaining exactly how gravitational time dilation driving the expansion would also cause it to accelerate.
I'm suggesting that gravitational time dilation drives the "arbitrarily fast" aspect of the expansion, not the expansion itself. The expansion itself can just be objects receding from one another due to simple (so-called peculiar) movement. What causes the universe to accelerate in its expansion is another big mystery of physics. Inflation theory doesn't address it. (I solve it here in section 7. I show that SR is violated even locally if high-redshift objects do not accelerate away from us, and that is the observation that leads us to believe the universe is accelerating in its expansion.)
