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dark energy: theory Takeshi Chiba Nihon University College of Humanities and Sciences ?

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dark energy: theory

Takeshi ChibaNihon University

College of Humanities and Sciences

?

topics to be discussed

• prejudice about L• recent progress(?) on vacuum energy:

string landscape• observational evidence (for what?)• search for alternative• observational target: w and w’

why theorists dislike L(@vacuum energy)?

• it is unnaturally miniscule:

rL ~ 10-120 mpl4

theoretical prejudice: L should be zero!

• some still hope to find dynamical mechanism to tune L@ 0

string theory should determine the vacuum but…

• string landscape (2000-):string theory contains huge number (~10300~101000) of vacua with different vacuum energy/physical constants/coupling constants

string theory should determine the vacuum but…

• string landscape (2000-):string theory contains huge number (~10300~101000) of vacua with different vacuum energy/physical constants/coupling constants

• there are some vacua (10120 vs. 10300)which look like our universe (L@ 0)

observational evidence for a >0(not dark energy)

• modify RHS(matter) of the Einstein equation:dark energy

• modify LHS(curvature) :modified (non-Einstein) gravity

obs. : distant supernovae are not so blightdL(z)=(1+z)Ûda/aH(a)

logical possibilities

• Einstein gravity with dark energy:L>0 (cosmological constant)

or L=0 and scalar field(s) with V(f) (mini-inflation)

or both• or non-Einstein gravity without dark energy

(Occam’s razor)

• or both (non-Einstein with dark energy)

dark energy

models of scalar field dark energy(quintessence)

• quintessence:f-n

e-lf

cos(f/M)-1extendedmulti fields

k-essence:p(f,df/dt)

• inflation:oldnewchaoticpower-lawextended,hyperextendednaturalhybridassisted(multi)…

models of scalar field dark energy(quintessence)

• quintessence:f-n

e-lf

cos(f/M)-1extendedmulti fields

k-essence:p(f,df/dt)

• inflation:oldnewchaoticpower-lawextended,hyperextendednaturalhybridassisted(multi)…

searching for catch phrase

• x-matter(Chiba-Sugiyama-Nakamura)

• non-minimally coupled quintessence

(Chiba)• kinetically driven

quintessence(Chiba-Okabe-Yamaguchi)

• quintessence (Caldwell-Dave-Steinhardt)/dark energy (M.Turner)

• extended quintessence(Perrota-Baccigalupi-Mattarese)

• k-essence(Armendatiz-Picon -Mukhanov-Steinhardt)

parameterizing dark energy

• equation of state:w=p/r (w=-1: cosmological constant)w’=dw/Hdt=dw/dlna

(historical note: x-matter parameterization: p=w0r0+cs2(r -r0), Chiba-Sugiyama-Nakamura,MNRAS,289(1997)L5-L7,in prior to Caldwell-Dave-Steinhardt)

• current observational bounds:w=-1.08+0.20-0.18 (157 SNIa+WMAP, GOODS,2004)w=-1.023+-0.090(stat)+-0.054(sys)

(71 SNIa+SDSS(BAO), SNLS,2005)w’=-1.48+0.90-0.81 (GOODS,2004)

fate of the universe

• -1/3 > w ¥-1: forever expansion

• w ¥ -1/3: forever expansion orrecollapse(Big Crunch)

• w<-1: future Big Rip

Chiba,Takahashi, Sugiyama,Classical and Quantum Gravity,

vol. 22, 3745-3758 (2005)

Caldwell-Linder,PRL(05) Chiba, PRD(06) (March)

s(w’)<0.1~0.5 if |1+w|<0.1(window may be large for w<-1)

3w(1-w)(1+w)

3(1-w)(1+w)

3w(1-w)(1+w)/(1-2w)

strategy

1. determine w=-1 or not2. if w∫-1 then determine w’=0 or not

note: if w∫-1 , dark energy is necessarily inhomogeneous; the sound speed of dark energy cs is a new parameter (cs =1 for canonical scalar field dark energy)

Chiba-Sugiyama-Nakamura,MNRAS,289(1997)L5-L7

alternatives

Who ordered dark energy?• Einstein ordered

cosmological constant• but he never dreamed of

currently accelerating universe

• dark energy can be dilaton, but string theory does not have predictive power at very very low energy scale

• dark energy only produces problems

• GUT ordered (old/new) inflation

• success of inflationary cosmology ordered more successful models

• inflation solves horizon/flatness/monopole problems

• but, inflation cannot (should not) be the guiding principle of unified theory

alternatives: non-Einstein gravity

• non-Einstein gravity can be tested bylocal experiments

• solar system experiments(Cassini satellite,Lunar Laser Ranging(Apollo 11))

→ Einstein is 99.9999% right !!and dG/dt/G<4x10-13 yr-1

Rise and fall of 1/R gravity(Carroll et al.,2003)

• F(R) gravity is equivalent to Scalar-Tensor Gravity (Higgs,Whitt,Maeda,Wands,Chiba):

Scalar-tensor with vanishing Brans-Dicke parameter: ω=0

can be in conflict with solar system experiments(ω>20000, Cassini satellite) if Brans-Dicke scalar

is (almost) masslessThis is the case for 1/R gravity (Chiba):m ~ H0

• 1/R gravity modifies gravity not only at large scales but also at local scale

Einstein

1/Rscale

ずれ

Rise and Fall of 1/R Gravity

So much ado…• F(R,P,Q) gravity?(Carroll et al.,2004)

P=RabRab, Q=RabcdRabcd

→ higher derivative (4th order) theory→ (generically) Ghosts appear

(Stelle1977,Nunes-Solganik,Chiba)propagator:

cross coupling:

The situation is much worse!!

• God may be subtle, but he is not malicious.(神は老獪だが意地悪はない)

Summary• (string) theory appears not to determine

the vacuum uniquely• So, it is important to check the nature of

the vacuum experimentally• It is only possible by astronomical

observations!• w=-1 or not is the key• alternatives to dark energy are (currently)

in trouble and can be tested by other experiments