Flatness problem

In the case of the flatness problem, the parameter which appears fine-tuned is the density of matter and energy in the universe.

[4] According to Einstein's field equations of general relativity, the structure of spacetime is affected by the presence of matter and energy.

Since the time of the Planck era, shortly after the Big Bang, this term has decreased by a factor of around

The photons present at that stage have been propagating ever since, growing fainter and less energetic as they spread through the ever-expanding universe.

Comparing this distance to the redshift of the supernovae gives a measure of the rate at which the universe has been expanding at different points in history.

The cosmological parameters measured by Planck spacecraft mission reaffirmed previous results by WMAP.

Indeed, a very small departure of Ω from 1 in the early universe would have been magnified during billions of years of expansion to create a current density very far from critical.

) it would expand so quickly and become so sparse it would soon seem essentially empty, and gravity would not be strong enough by comparison to cause matter to collapse and form galaxies resulting in a big freeze.

In either case the universe would contain no complex structures such as galaxies, stars, planets and any form of life.

[13] This problem with the Big Bang model was first pointed out by Robert Dicke in 1969,[14] and it motivated a search for some reason the density should take such a specific value.

Some cosmologists agreed with Dicke that the flatness problem was a serious one, in need of a fundamental reason for the closeness of the density to criticality.

But there was also a school of thought which denied that there was a problem to solve, arguing instead that since the universe must have some density it may as well have one close to

[15] One solution to the problem is to invoke the anthropic principle, which states that humans should take into account the conditions necessary for them to exist when speculating about causes of the universe's properties.

These regions may be extremely far apart - perhaps so far that light has not had time to travel from one to another during the age of the universe (that is, they lie outside one another's cosmological horizons).

It requires only a single universe which is infinite - or merely large enough that many disconnected patches can form - and that the density varies in different regions (which is certainly the case on smaller scales, giving rise to galactic clusters and voids).

[18] For example, in 1979 Bernard Carr and Martin Rees argued that the principle "is entirely post hoc: it has not yet been used to predict any feature of the Universe.

Since many physicists and philosophers of science do not consider the principle to be compatible with the scientific method,[18] another explanation for the flatness problem was needed.

The standard solution to the flatness problem invokes cosmic inflation, a process whereby the universe expands exponentially quickly (i.e.

However, "In December, 1980 when Guth was developing his inflation model, he was not trying to solve either the flatness or horizon problems.

initially takes any arbitrary value, a period of inflation can force it down towards 0 and leave it extremely small - around

This success in solving the flatness problem is considered one of the major motivations for inflationary theory.

[27][28] In particular, in the absence of any firm evidence for what the field driving inflation should be, many different versions of the theory have been proposed.

[29] Many of these contain parameters or initial conditions which themselves require fine-tuning[29] in much the way that the early density does without inflation.

These have included non-standard interpretations of the effect of dark energy[30] and gravity,[31] particle production in an oscillating universe,[32] and use of a Bayesian statistical approach to argue that the problem is non-existent.

The latter argument, suggested for example by Evrard and Coles, maintains that the idea that Ω being close to 1 is 'unlikely' is based on assumptions about the likely distribution of the parameter which are not necessarily justified.

[34] In particular, in addition to the idea that Ω is not a suitable parameter in this context, other arguments against the flatness problem have been presented: if the universe collapses in the future, then the flatness problem "exists", but only for a relatively short time, so a typical observer would not expect to measure Ω appreciably different from 1;[35] in the case of a universe which expands forever with a positive cosmological constant, fine-tuning is needed not to achieve a (nearly) flat universe, but also to avoid it.

[37][38] This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable.

Including torsion gives the correct conservation law for the total (orbital plus intrinsic) angular momentum of matter in the presence of gravity.

Such an interaction averts the unphysical big bang singularity, replacing it with a bounce at a finite minimum scale factor, before which the Universe was contracting.

The rapid expansion immediately after the big bounce explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic.