## The inflation debate in Scientific American of April 2011

This document contains comments about the article The inflation debate by Paul Steinhardt In Scientific American of April 2011.
To read the article select: http://wwwphy.princeton.edu/~steinh/0411036.pdf In this copy the 8 pages are numbered from 36 to 43. In the original Scientific American magazine they are numbered from 18 to 25. I will use the copy numbering.
• The text in italics is copied from the article
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The term refers to a brief burst of hyperaccelerated expansion that, he argued (Alan H. Guth) may have occured during the first instants after the Big Bang.
This is very easy to proclaim, but very difficult to prove.
In many cases the proof goes like this:
1 second after the Big Bang the universe was flat.
Theory X predicts that the universe is flat 1 second after the Big Bang
That means Theory X is correct.
Read for theory X: Inflation theory. The details are not supplied i.e. what causes inflation and what stops inflation.
To this day the development and testing of the inflationary theory of the universe is one of the most active and successful areas of scientific investigation..
IMO this sentence is in conflict with the full message of the article: i.e. IMO we are not sure.
For instance it had to be extremely uniform, with only extremely tiny variations in distrubution of matter and energy.
The concept of matter is a typical concept of the present state of the Universe.
The universe during the first second after the Big Bang was much simpler (much less different particles) as we observe today. This immediate makes the universe also more uniform.
Also the universe had to be geometrically flat, meaning that the curves and warps in the fabric of space did not bend the paths of light rays and moving moving objects.
In the present universe the path of the lightrays is bended by mass i.e. by galaxies and black holes. Geometrical flat is a typical mathematical concept.
He (Alan Guth) argued that even if the universe had started off in total disarray - with a highly nonuniform distribution of energy and gnarled (knobby, twisted) shape - a spectacular growth spurth would have spread out energy until it was evenly dispersed and straigtened out any curves and wraps in space.
IMO when you envision inflation as some sort explosion (rapid change) than the chances are high that the result is highly nonuniform.
When this period of inflation ended, the universe would have continued to expand at the pace of the original Big Bang theory but now with just the right conditions for stars and galaxies to evolve to the state where we see them today.
In my opinion this looks like science through a glass bowl. First you have a theory which leads to a certain prediction. However this prediction is not in in agreement with observations. (There are no stars or to many) Next you modify your theory (You include inflation) Next your predictions are in concordance with observations (There are the right number of stars).
Conclusion: Your new theory with inflation is correct.
As someone who has contributed both to the inflationary theory [see "The inflationary Universe" by Alan H.Guth and Paul J.Steinhardt Scientific American May 1984] and to competing theories I feel torn and I sense that many of my colleagues are not sure what to make of the case, either.
For a review see: The Inflationary Universe in Scientific American May 1984

### The case for inflation

Inflation relies on a special ingredient known as inflationary energy which combined with gravity can drive the universe to expand by an astonishing amount over a brief instant.
Correct. But what are the details?
Its most unusual property of all is that its gravity must repel rather than attract. The repulsion is what causes space to swell so rapidly.
Correct. But what are the details?
The described complex mechanisme is a case against inflation.
Inflation smoothes the universe just as streching a rubber sheet smoothes its wrinkles, but it does not do so perfectly. Small irregularities remain because of quantum effects.
Streching a rubber band makes it very thin and brittle untill it breaks. Such a comparison for the whole of the universe is too simple.
The laws of quantum physics dictate that a field such as the inflation not have exactly the same strength everywhere in space but that it undergo random fluctuations.
Fields in general can not be used to explain something. A magnetic field can not be used to explain magnetism. A gravitational field can not be used to explain why matter attracts each other.
These spatial variations are the seeds that will eventually grow into stars and galaxies.
To assume that inflation is required in a way, such that space incorporates the exact fluctions to cause stars to devellop, is a pure guess.

### The case against inflation

The first signs that a theory is failing are usually small discrepancies between observations and predictions. That is not the situation here: the data are in exquisite accord with the inflationary predictions set down in the early 1980's
The Friedmann's equations (which are part of the standard Big Bang theory) define a frame work to describe the evolution of the Universe. Inherent of these equations are a set of paramaters like the age of the universe, the Hubble constant, Omaga(Lambda) and Omega(m). These parameters are not a prediction of the theory but calculated based on observations.
The inflation theory which is an extension of the Standard Big Bang theory incorporates the same problems. The biggest problem is clearly to indentify which is which. In a certain sense the inflation theory makes the picture more difficult.
Instead the case against inflation challenges the logical foundations of the theory.
It should be better to challenge the physical foundations of the theory.
The difference between good and bad hinges on the precise shape of the energy curve, which is controlled by a numerical parameter that could in principle take on any value whatsoever.
The energy curve is one of the most problamatic issues of the inflation theory.
Physical problems are: How did it start, How did it end, How did it take so "long".
However a much larger problem. To assume that inflation started everywhere at the same moment is most probably a misconception. Most probably there where small fluctuations. The issue is that most probably inflation, the stretching of space, enlarged these fluctuations making in general the entire universe less homogeneous.

#### Unlikely to Be Good

But unless the inflation energy curve had a very specific shape (obtained by finely tuning one or more parameters, abbreviated Lamda here) the outcome would be "bad" - a huge volume with too high a density and the wrong distribution of galaxies.
Unfortunately the article does not give the details how the galaxy distribution is calculated and how this calculation dependents about inflation.
I expect nobody knows.
Given the range of possible Lambda values bad inflation seems more likely.
Given all the uncertainties involved all what is written around inflation could be wrong.

### Reflection

The box contains three examples which show the evolution of the universe based on three values of Lambda. The First example shows "Good" Inflation. The examples 2 and 3 show "bad" inflation. This means that as a result of inflation, using the wrong value of Lambda the predicted evolution of the universe is not accordingly to observations. That maybe true
The issue is how do you know that the range of predicted universes is correct as a function of Lambda?
IMO nobody knows. And what I think it is impossible to know.

### The perils of eternal inflation

ANATHER APPROACH reaching a similar conclusion extrapolates the history of the universe from its current conditions backward in time usingthe established physical laws.
What are the current conditions ?
This question is impossible to answer for the entire Universe.
Immediate next:
The extrapolation is not unique: given the average flat and smooth conditions today many different sequences of events could have come before.
In 2008 by Gibbins and Turok showed that an overwhelming number of extrapolations have insignificant amounts of inflation.
These simulations prove "nothing". How do you know that the calcultions, the simulations, the model used are correct?
For more detail read this: http://arxiv.org/abs/hep-th/0609095 The Measure Problem in Cosmology by G.W. Gibbons, Neil Turok 2 February 2008.
 In this article there are two interesting remarks at page 4: One obvious application of such a measure on the multiverse is in determining the probability of inflation, i.e., how likely is it that the universe started out in an inflationary state, within different models of the laws of fundamental physics. The issue is how do you do that and how do you know what you do is correct. One thing that is required is a clear mathematical description of what is inflation. Immediate next: This question is potentially an Achilles’ heel for inflation: if inflation is itself highly improbable, then it cannot be claimed to solve the classic cosmological fine tuning puzzles, of large-scale homogeneity, isotropy and flatness. Again the same remark: How do you know that the calculation to calculate the probability of inflation is correct? Suppose that the probability is high does that mean that the inflation theory is correct ?
Next we go back to the original article by Paul Steinhardt
The change in view began with the realization that inflation is eternal: once begun it never ends [See The Self-Reproducing Inflationary Universe in Scientific American of November 1994]
For a review of this article select: The Self-Reproducing Inflationary Universe November 1994 by Andrei Linde.

### Problem #2: Starting Conditions

#### It Had to be just So

Inflation was supposed to occur no matter what the initial conditions of the universe were.
The evolution of the universe is a physical process. Inflation is also a physical process. I think you can compare it with the explosion of an atomic bomb. For an atomic bomb to explode (excess neutrons) you need special initial condition to happen, For Inflation this is the same.
Further analysis suggests otherwise. Of all the ways the universe could have begun, only a tiny fraction would lead to the uniform flat state observed today.
Specific which observations has Paul in mind?
As for almost all what is written: How do you know that the calculations are correct.