the hypothesis of inflation

8/14/2019 The Hypothesis of Inflation

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The hypothesis of

inflationThe problem of the horizonWe have seen that the cosmological microwave radiation isexceedingly homogeneous, in 1 part for 100,000. Why ?Of course, nothing forbids this uniformity of the cosmos, but tosay that it is about a coincidence, it is maybe to pass next toan essential point. In order to get a better understanding, wemust begin by defining the notion of causality.

Physics is always based upon the notion of causality : a causealways precedes the effect. What's more, according to thetheory of relativity, the information cannot move faster thanlight. Hence, you cannot detect an effect before a time at bestequal to the necessary time for light to travel from the cause.From this point, we can define the "sphere of causality" of anevent : it is the set of places which, at a definite moment, canperceive the event.Naturally, this sphere is growing with time at the speed of light.

When the fossil radiation was emitted, the universe was onemillion years old : so, the sphere of causality of the particleswhich emitted this radiation was one million light years wide.
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COBE, in the center, is lookingat the fossil radiation whichhas travelled for 14 billions

light years.Each emitting particle has asphere of causality which isonly 1 million light yearswide.

So, how can they all be at thesame temperature ?

The individual spheres of causality don't overlap. In theseconditions, we must deduce that atoms outside of theirindividual sphere of causality were at the same temperature.What is at least curious.

This effect is known as the problem of the horizon, where thehorizon is the furthest observable distance.

Another way to consider theproblem :

All the matter which is fillsthe observable universetoday occupied, during thePlanck's time, a greatervolume than the horizon atthis moment.

And yet, the temperature ofthe universe is homogeneous(on a large scale).

Note : scales are notrespected.
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To explain this fact, the American physicist Alan Guthsuggested the hypothesis of inflation.

The cosmological inflation

We saw that the separation of the forces during the early timesof the universe was comparable to a -change of phase, in thesame way as the water which becomes ice.But, even when the temperature is lower than 0C, water canexist for short times. This phenomenon is called superfusion.

When the temperature of the watercomes down, this one can remain liquidbelow 0C.But there will come a time where it willfreeze, and at this moment, thetemperature of the whole water will riseto reach the 0C of the transition of

phase.

The same phenomenon appears at the time of thedifferentiation of the forces. The forces can remain unified evenwhen the temperature has gone lower than the temperature ofseparation.At this moment, the energy of the scalar field associated to theunification of the forces becomes greater than the temperatureof the universe. This field becomes equivalent to a repulsiveforce, which will make the universe to inflate in a hugeproportion : at the time of the breaking of great symmetry,

around 10

28

K, the radius of the universe increases 10

50

times.
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As the change ofphase takesplace, after thesuperfusion, thescalar fieldsuddenlydisappear,because itrepresents theunification of theforces.

Its energy istransformed into

an expansion ofthe universe.

This change of phase must have happened three times duringthe Big Bang :

a first time during the breaking of great unification,around 1028 K,

a second time, when the electromagnetic and weak forcesseparate, around 1015 K,

and a last time around 1012

K, when quarks are becomingconfined, and hadrons begin to appear. The effects of thislast transition can be seen as negligible.

The effects of the inflation

What are the effects of this sudden increase of size of the

universe?

First of all, this inflation allows us to solve the problem of thehorizon that we have previously seen : indeed, all the distancesare exceedingly increased in a very short time. The spheres ofcausality of the various points which are emitting the fossil
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radiation can have previously overlapped, and hence explainthe homogeneity of this radiation.

All thematter of

theobservableuniverse ishold insidea volumewhich issmallerthan thecausal

horizon atthePlanck'stime :The whole

points oftheuniversearecausally

dependent, and canhave thesamecharacteristics.

The speed of the increase of size of the universe was fargreater than the speed of light : this does not violate thetheory of relativity, because no information was moved during

the inflation, only a geometrical property.

The second effect of the inflation is the flatness of theuniverse. Indeed, this inflation increases all the distances in theuniverse, including its radius of curvature, which tends towardsinfinity.In a classical scenario, the universe must begin flat in order to


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remain so. With the inflation, whatever is the curvature of theuniverse at the beginning, it ends flat.

The third effect of the inflation is the dilution of the elements ofthe universe. By increasing its size, the density of various

"exotic" objects, like primordial black holes or magneticmonopoles, decreases. These elements are foreseen by thetheory, but they have never been discovered.
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the hypothesis of inflation

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