T he Cosmological Constant, Inflation, and Dark Energy * John D. Barrow
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Transcript of T he Cosmological Constant, Inflation, and Dark Energy * John D. Barrow
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The Cosmological Constant,The Cosmological Constant, Inflation,Inflation,
andandDark EnergyDark Energy
**John D. BarrowJohn D. Barrow
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T = 2.7255 T = 2.7255 0.0006 K 0.0006 K
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Y(He-4)= 4Y(He-4)= 4He/H = 0.2534 He/H = 0.2534 0.0083 0.0083
D/H = 2.87 D/H = 2.87 0.22 0.22 10 10-5-5
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Neff = 3.046 is standard 3 light neutrino standard model
New Physics?New Physics?
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Habitable UniversesHabitable UniversesNeedNeed
Close to critical expansionClose to critical expansionIsotropic expansionIsotropic expansion
Graininess level of aboutGraininess level of about 1 part in 10 1 part in 1055
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InflationInflation
Early-time inflation at t Early-time inflation at t 10 10-35-35 s s
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Acceleration requires Acceleration requires + 3p/c + 3p/c22 <0 <0
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1992 2003 2013
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Planck Mission Microwave Sky MapPlanck Mission Microwave Sky Map
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The Spectrum of Temperature FluctuationsThe Spectrum of Temperature Fluctuations
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Scalar Fields and LambdaScalar Fields and Lambda
Pressure: Pressure: p = ½(dp = ½(d/dt)/dt)22 – V( – V() = KE - PE) = KE - PE
Energy density: Energy density: = ½(d = ½(d/dt)/dt)22 + V( + V() = KE + PE) = KE + PE
--cc22 ≤ p ≤ + ≤ p ≤ +cc22
dd22a/dta/dt22 = - 4 = - 4G(G( + 3p/c + 3p/c22)a/3 > 0 )a/3 > 0
+ 3p/c+ 3p/c22 < 0 < 0 Necessary for inflationNecessary for inflation
But kills the singularity theoremsBut kills the singularity theorems
V
dd/dt=0/dt=0 p =-p =-
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Pressure: Pressure: p = ½(dp = ½(d/dt)/dt)22 – V( – V() = KE - PE) = KE - PE
Energy density: Energy density: = ½(d = ½(d/dt)/dt)22 + V( + V() = KE + PE) = KE + PE
Eg with non-constant VEg with non-constant V
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ns = -3(V’/V)2 + 2(V’’/V) O(1/N) O(1/50)
dns /dln(k) = 2[4(V’/V)2 (V’’/V) – 3(V’/V)4 –V’V’’’/V2] O(1/N2,1/N3)
Gravitational Potential perts 1/(size)ns kns
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Our Universe can have a beginningOur Universe can have a beginningButBut
The Multiverse need have no beginningThe Multiverse need have no beginning
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Was there a beginning?
Eternal cycles Eternal changeBeginning
of timeBeginning
in time
no end In thefuture
will end In thefuture
Creation out of nothing
Creationout of
something
order chaos
order is transient
order ispermanent
no yes
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Infinities in PhysicsInfinities in Physics
Are they always saying Are they always saying
“must try harder”“must try harder”
??
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We don’t have any trustworthy theory of what happened at t < 10We don’t have any trustworthy theory of what happened at t < 10-43-43ss
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Late-time AccelerationLate-time Acceleration
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Why isn’tWhy isn’t 1010+66+66 cm cm-2-2
We observeWe observeobsobs 10 10-55-55 cm cm-2-2
????????No galaxies if > 10 > 10-54-54 cm cm-2-2
A Big Mystery
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1 = 1 = MM + + kk + + wherewhere
MM = = 88GG/3H/3H22
k k == – k/a – k/a22HH22
= = /3H/3H22
HH22 =8 =8GG/3 – k/a/3 – k/a22 + + /3/3
The Return of The Return of Lambda ?Lambda ?
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W p/ = wo + wa(1 – a) assumed for an evolving dark energy
Simple cosmological constant model iswo = -1 and wa = 0
Or is dark energy a time-changing version of lambda?Or is dark energy a time-changing version of lambda?
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