T he Cosmological Constant, Inflation, and Dark Energy * John D. Barrow

The Cosmological Constant,The Cosmological Constant, Inflation,Inflation,

andandDark EnergyDark Energy

**John D. BarrowJohn D. Barrow

T = 2.7255 T = 2.7255 0.0006 K 0.0006 K

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

Neff = 3.046 is standard 3 light neutrino standard model

New Physics?New Physics?

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

InflationInflation

Early-time inflation at t Early-time inflation at t 10 10-35-35 s s

Acceleration requires Acceleration requires + 3p/c + 3p/c22 <0 <0

1992 2003 2013

Planck Mission Microwave Sky MapPlanck Mission Microwave Sky Map

The Spectrum of Temperature FluctuationsThe Spectrum of Temperature Fluctuations

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 =-

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

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

Our Universe can have a beginningOur Universe can have a beginningButBut

The Multiverse need have no beginningThe Multiverse need have no beginning

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

Infinities in PhysicsInfinities in Physics

Are they always saying Are they always saying

“must try harder”“must try harder”

??

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

Late-time AccelerationLate-time Acceleration

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

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 ?

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?