Cosmologia-5 - Istituto Nazionale di Fisica Nuclearebartolo/Course_Cosmology_Early_Universe... ·...
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Transcript of Cosmologia-5 - Istituto Nazionale di Fisica Nuclearebartolo/Course_Cosmology_Early_Universe... ·...
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LastscaOeringsurface:CMBphotonsdecoupleatrecombina8onepochz~1100(tr~380,000years)LightcouldhavetravelledL~ctr(horizon)Suchadistancewouldsubtendanangleofabout1degree.WeactuallyseeCMBphotonswithnearlythesameTatbiggerangularscales>7°(e.g.COBEsatellite)
>7°
2causallydisconnectedregionsatrecombina8on
THEHORIZONPROBLEM
AdaptedfromhOp://benasque.org/2011Astrophysics/talks_contr/172_Lewis.pdf
Here we give a viewpoint on the horizon problem whichconnects directly with observations of CMB photons
η
Χ
ηlastscaOering
A B
ηsingularity
PastlightconeofA PastlightconeofB
AandBnevercommunicatedwitheachother
StandardCosmology(FRW)
In this page we instead give a viewpoint on the horizon problem which derives from analyzing the causal structure of space-time within the standard Hot Big-Bang model. In the next page the inflationary solution is explained within this kind of analysis.
η
Χ
ηlastscaOering
A B
ηrehea8ng
PastlightconeofA PastlightconeofB
Infla8onaryCosmology
CommonpastofAandBηsingularity
INFLATION
soluzione
quantita`
T
Pl
Ahugeexpansion
Takearegionofsizeatthebeginningofinfla8on:Since,itgetsinflatedby!!!!
8 THE AUTHOR
(100) h =2⇤⇤
H
mPl
(101)⇤
H ⇥ V (⌅)1/4
(102) �⌅ =
(103) ⇥H = 1/Hinfl
(104) ⇥H ⇥ a(t)
number of e-foldingsN = ln(af/ai) =� tf
ti
Hdt � 60(105)
(105)
8 THE AUTHOR
(100) h =2⇤⇤
H
mPl
(101)⇤
H ⇥ V (⌅)1/4
(102) �⌅ =
(103) ⇥H = 1/Hinfl
(104) ⇥H ⇥ a(t)
number of e-foldingsN = ln(af/ai) =� tf
ti
Hdt � 60(105)
(105)
BRIEF ARTICLE 9
(114) ⇥⇧ =
(115) ⌅H = 1/Hinfl
(116) ⌅H ⇧ a(t)
(117) number of e-foldingsN = ln(af/ai) =⇤ tf
ti
Hdt ⇥ 60
(118)af
ai⌅ e60 ⌅ 1026
(119) gij = ⇥ij + hij , hii = ⌥ihij = 0
(120) L[⇧] = L2 + L3 + ...
(121)�T
T⌅ 1
3⇥ = �1
5⇤ ⇤ 10�5
(122) ⌅phys ⇧ a(t)
(123) ⌃⇥⌃k1⇥⌃⇥k2⌥
(124) X = �12gµ�⇧,µ ⇧,� , f(⇧) = ⌅/⇧4
(125) fDBINL = �(35/108)
�1c2s� 1
⇥, cs ⌅ 3/(�N)
(126) ns � 1 = �4/N
(127) ns � 1 = 0.9603± 0.0073
f equilNL = �42± 75 (68%CL)(128)
forthoNL = �26± 39 (68%CL)
BRIEF ARTICLE 9
(114) ⇥⇧ =
(115) ⌅H = 1/Hinfl
(116) ⌅H ⇧ a(t)
(117) number of e-foldingsN = ln(af/ai) =⇤ tf
ti
Hdt ⇥ 60
(118)af
ai⇥ e60 ⌅ 1026
(119) gij = ⇥ij + hij , hii = ⌥ihij = 0
(120) L[⇧] = L2 + L3 + ...
(121)�T
T⌅ 1
3⇥ = �1
5⇤ ⇤ 10�5
(122) ⌅phys ⇧ a(t)
(123) ⌃⇥⌃k1⇥⌃⇥k2⌥
(124) X = �12gµ�⇧,µ ⇧,� , f(⇧) = ⌅/⇧4
(125) fDBINL = �(35/108)
�1c2s� 1
⇥, cs ⌅ 3/(�N)
(126) ns � 1 = �4/N
(127) ns � 1 = 0.9603± 0.0073
f equilNL = �42± 75 (68%CL)(128)
forthoNL = �26± 39 (68%CL)
FromS.Dodelson``ModernCosmology’’,AcademicPress(2003)
