Reheating t does inflation really workI

2

ReheatingWe have seen that we can come

up with forms of Vlt whichsatisfy the SR conditions andtherefore give inflation and enoughe folding For a model toowork however it should alsoprovide on endr for inflationand it should leave us witha radiation dominated universe

filled with the particles we

know and Love The better

prosess is known as reheating

The equation of motion of the field isÅ t 3Hå this V'lol o

The SRA consisted in neglectingthe fist term When inflationends this assumption is no longervalid

Let us assume that Uiolooks like this µ

ø t

and look at the situation if we

negleet the friction term 311Åit was this term that male slow roll

possible so when the skrur rollconditions are broken it could bebecause this term has henne

negligibleThe equation for at vi then

To the lø o_0

Let s expand V around the minimumat 4 0 i

Vlt I lo TV cos ø t EV lojalt0 0

assumption knalminimm

V o f

3Så vid av listand

å få told o

which we recognize as an equation

for harmonic oscillations withfrequency w gires byr

at hiv 10

It can be shown that the fieldnow behaves like partides with

man må kw avlvekrities vi Ccc vi other wordslike non relativistic matter Sowe expert Solås a 3 ond af this

during this phase

tonar to truly end inflationwe must also create the

particles of the standard Modeland some other µ perhapsTo do this must be

coupled to matter andradiation and transfer some of itsenergy to them

4In other words d must devourinto partides al radiation atsome rate T and the

energy density will thereforedecrease as see S Wennberg Cosmology pay

altene eTilt tev

sør Søltuello 1where I have assumed that the oscillations

and decay start as soon as the

slow roll conditions Breakdown

The energy density of the particlescreated satisfies a continuityequationwith a some term

If t 34 spit Pp Tsaop fem products

If we answer that the dwarfproducts are relativistic så that

Pp Spells then again seeWeinberg

Sp Ltte Stoltenberga 4 Ut

Innatt eTA tundti

5We see that Sp Itera å 0

because the integral vanishes fort tendIn the extreme case when T tl Hadit can be shown Weinberg againthat Spot increased vervrapidly to Sølturjo and

then started to decrease as åSo vi this case all the energerof the scale field is dumpedeinto partides This is to beexpected since T Heltene

means that the fiction termfrom the expansion å negligible

When this assumption doesnot hell only part ofthe energy stored vi theinflaten field goes intocreating particles and radiationthe rest is test to thefruition term i e the expansion

So the idea of inflation Iseems to work It is possibleto find scalar field potentialsthat give rise to a period ofslow roll inflation white solvesthe horizon flutnernanlemonopoleproblems before the fieldgracefully decays and leavesbehind the particles we knowand Love However thereare some questions that couldbe raised at this point

Does inflation really workmmr

Here are some questions we have

ignored so far1 A tåknaical question In theSRA i å snål this Vlt O

becomes

Stå tho V'lolIn other words a second order

differential equation vi

approximated by oneof fistorderButton solve we needtwo initial conditions are on

and me on it To sikrewe justneed on initial

condition on 4For this to work thecondition on å must vi someway be redundant How can

that be

2 More fundamental and

more problematic I vitroduetinflation as an answer to

why the universe is doseto being spatially Hat andwhy the CMB is isotropicBut in all the ukulationsI have user the equationsderived for a homogeneous

and isotropic universe andI neglected the curvature termSo I haven't really provedanything han 1

8Answers

1 It is possible for initialconditions to be redundant

if the solutions of thedifferential equation hasan attractor That is

the equation is snek thatregardless of their initialevolution they end upon the same trendAnd fortunately this termsout to be the use for thecoupled system of and FI

see the weekly problems

2 Thiis is a serious questionWould we end up witha universe described bythe flat RW leie elementif we started out withsomething more general

gThe answer is that yesin many cases we wouldFor example if the universewas initially anisotropicthe rapid expansion duringinflation would drive itto isotropy You can

read more about so calledCosmic no hair theoremsvi chapter 8 of The Eater Univene

by E Koller and M S Turneravailable from the likarHowever inflation will not

always work You saw

an example of this inthe problem session where

you looked at a model

which collapsed beforeinflation could startSå inflation doesn'tanswer all questions butit is the best we havecome up with so far