Is inflation a successful theory in explaining the issues not answered by the standard Big Bang theory?

The Big Bang model of our early universe has been widely accepted in the scientific community since the discovery of cosmic background radiation in 1965.[ However, certain aspects of our universe, whilst not in direct conflict with the big bang model, are not explained by it; the horizon problem and the flatness problem. Inflation was first proposed by Alun Guth in 1980 as an explanation to the non-existence of magnetic monopoles.  Inflation is the idea that in the very early universe there was a period of rapid expansion. Inflation has been used explain the “problems” stated above. However inflation is not without issues and is by no means undisputed in the scientific community.

The most significant problem with the Big Bang theory is the horizon problem (also referred to as the isotropy problem). A key factor in this problem is the finitude of the universe, if not in size then in age. Since the universe has a finite age then light can only have travelled a finite distance therefore we can only see things close enough for light from them to have reached us. We call this our observable universe and it has a radius of about 45 billion lightyears. A key property of the cosmic background radiation is its isotropic nature yet not even light could have had time to travel from one side of our observable universe to the other so no information can have been exchanged from one side to the other. Yet the cosmic background radiation is uniform which postulates at the beginning of the universe there must have been near perfect uniformity, the standard big bang model provides no explanation for this phenomenon.[

The other problem often cited with the horizon problem is the flatness problem.  “Flatness” refers to the geometry of space-time as laid out by Einstein’s Field Equations. For the universe to be flat the density of our universe has to be equal to that of the critical density from the Friedmann Equations (Friedmann’s solution to Einstein’s field equations).  Our Universe has been found to be remarkably flat since the BOOMERANG experiment was conducted in 2000[, that is the density parameter (the density of our universe over the critical density) very close to 1. At a conservative estimate we know the density parameter, W, is 0.1 < W < 10 but we know that the density parameter is a function of time, that is it increases with time. Thus the universe is not stably flat, unless W=1, thus any deviation in the density of the initial universe to that of the critical density would greatly increase with time resulting in the ever increasing curvature of space-time. Yet what we have found is our universe has a density very close to that of the critical density meaning that at  seconds after the big bang the difference between the critical density and the density of the universe has to be less than . Yet there is no reason, which can be found in the standard big bang model, to suggest why the universe should have this density over any other.  4

In the 1980s Alan Guth, among others, proposed inflation as a solution to these problems. Inflation is the rapid expansion of the very early universe, it is a period known as accelerated expansion where the distances between objects increased exponentially. The Planck time marks the point in the universe before which our normal laws of physics are not adequate at describing how matter, space and time behave. Inflation took place shortly after the Planck time at about 10−36 seconds after the Big Bang and sometime between 10−33 and 10−32 seconds. Conservative models of inflation have space expanding by a factor of 1028 which is the same as the expansion in the 13.8 billion years since inflation. What is key in this rapid expansion is that whilst the universe expanded it maintained the same density – the amount of mass in the universe is therefore also increased by significant orders of magnitude, the new mass is produced by the conversion of energy from the energy space vacuum, the cosmological constant, into mass. How does this solve the problems with the big bang model? Firstly, consider the horizon problem: Two points in our observable universe that cannot have been able to exchange information yet appear to be in thermal equilibrium. Inflation provides a mechanism for a section of the universe of radius more than small enough to thermalise to expand to a size greater than the observable universe. Therefore all sides of our observable universe are at the same temperature because they were, before inflation, in a state of thermal equilibrium.

Inflation’s solution to the flatness problem is more complex as the problem is by its nature more complex.  The Friedmann equation shows that the difference between the critical density and the density of the universe is directly proportional to not only time but also to the inverse square of the cosmic scale factor. The condition of inflation is that the second derivative of the cosmic scale factor, that is the rate at which the rate of increase is increasing, has to be positive and it is precisely this that forces the density of the universe towards the critical density. The cosmic scale factor increases with time during expansion therefore the difference between the critical density and the density of universe decreases with time (during inflation). Moreover the cosmic scale factor in Friedmann’s equation is squared so coupled with the exponential (or near exponential) nature of the expansion during inflation the density of the universe was forced so dynamically towards the critical density that even now the difference between them is not enough for them to rapidly diverge as would otherwise be expected.

It is all very well to assert that there was a period of rapid expansion in the early universe with properties which conveniently solve all of the problems with the previous model but without justification for this it is little more than a fudge factor. It is this criticism that has been levelled at the inflationary model. Guth’s explanation, postulating a false vacuum and quantum tunnelling was dismissed because the model didn’t reheat properly so it was replaced by slow-roll inflation. In this model a scalar field, an Inflaton, is in a high energy state before inflation. It undergoes a phase transition caused by random quantum fluctuations, releasing its potential energy as it reaches its lowest energy state. The potential energy released creates a repulsive force causing inflation. Alternatively, it can be described as scalar field rolling down a potential energy hill. This model provides not only a reason for both the beginning and end of inflation but also accounts for the asymmetry that was the building blocks of the structure in the universe (the random quantum fluctuations in the inflation). Furthermore it has been hypothesised that the Higgs Boson acted as the inflaton however the key point with the theory of inflation in general is that it is hypothesised and has little proof. The Inflationary model relies upon a cosmological constant, dark energy in order to produce a sort of negative gravity (in Einstein’s field equations “negative gravity” can be produced by negative pressure). However we know very little about dark energy other than this property and a reasonable prediction for the cosmological constant. There has been wide spread criticism in the scientific community of inflation. As pointed out by Roger Penrose inflation was necessary in part to explain how the universe could meet such specific initial conditions however inflation itself requires arguably more stringent initial conditions.[

Given the flaws and lack of proof for inflation it is perhaps unsurprising that there are alternatives to the theory. String theory is likely to rely on a quantum gravity theory and is believed to be incompatible with inflation. Also, whilst String theory offers an explanation to some aspects of the early universe (in the big bang model) it cannot provide an explanation for either the horizon problem or the flatness problem. Cyclic models of the universe offer an explanation to the horizon problem and the magnetic monopole problem. These models do not have the flatness problem simply because of their nature however there is no evidence to suggest a slowing down of inflation. Moreover, they are considered to be supplementary to inflation, with an inflationary period before the big bang stage although how the universe navigates between the big crunch and big bang stage of its supposed cycle is a source of significant criticism. There are variable speed of light theories that would solve the horizon problem however these are not mainstream ideas in physics and they do not offer a solution to any of the other issues raised with the big bang.[

In conclusion, the inflationary model does provide an explanation to the problems not explained by the big bang. Despite this there is very little concrete science behind inflation and the solution would appear to be a fudge factor adopted for convenience rather than actually addressing the problem. It is unsurprising that inflation is so widely accepted when one considers the alternatives, or lack of. Inflation may be adopted in the cosmological history of the universe simply because of a lack of alternatives. Moreover, with the adoption of inflation the big bang model of the universe has a number of significant similarities with the model that it replaced – the steady state model. So it could be that inflation is simply in need of a breakthrough in science to improve upon it or add more concrete theory to it; perhaps a review of relativity and more specifically that cosmological constant upon which its predecessor (steady state) depended.

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