Post on 20-Jan-2016
Towards inflation and Towards inflation and dark energy cosmologies dark energy cosmologies
in string generated in string generated gravity modelsgravity modelsIshwaree NeupaneIshwaree NeupaneUniversity of CanterburyUniversity of Canterbury
March 1, 2006
40th Rencontres de Moriond, La Tuile 18-25 March 2006
OutlookOutlook The 20The 20thth Century Physics Century Physics
General Relativity vs Quantum MechanicsGeneral Relativity vs Quantum Mechanics The Physics of 80’s and 90’s The Physics of 80’s and 90’s
String Theory: A Theoretical Balancing ActString Theory: A Theoretical Balancing Act Ingredients: Extra Dimensions, Ingredients: Extra Dimensions,
SupersymmetrySupersymmetry String/M Theory: One Mo’ Time!String/M Theory: One Mo’ Time!
Beyond perturbative approach: Branes, Beyond perturbative approach: Branes, Fluxes, CyclesFluxes, Cycles
Inflation, Dark Energy and OpportunitiesInflation, Dark Energy and Opportunities
Big result in cosmology? still there in 2006?
High-z SNeIa are High-z SNeIa are fainterfainter
than expected in an than expected in an Einstein-deSitter Einstein-deSitter
modelmodel
The case for The case for 1)1)Hubble Hubble
diagramdiagram2)2)subtractionsubtraction
7.03.01
,3.0,1
Mtotal
Thanks to WMAP and Other Thanks to WMAP and Other Experiments for the Experiments for the coordinated support coordinated support
Already >50 dark energy Already >50 dark energy proposals in the market! proposals in the market!
Cosmological Concordance Cosmological Concordance ModelModel
Early InflationEarly Inflation de Sitter spacede Sitter space During 10^{-30} During 10^{-30}
secsec
Current AccelerationCurrent Acceleration Near de Sitter spaceNear de Sitter space During few billion During few billion
yearsyears
The ultimate laws of Nature might The ultimate laws of Nature might contain a fundamental and simple, contain a fundamental and simple, concise relation concise relation
between past and future between past and future
between close-by and far-awaybetween close-by and far-away
String Compactification?String Compactification?
How to get de Sitter or near de Sitter 4d space?How to get de Sitter or near de Sitter 4d space?
Duality WebDuality Web
gg /1 Cosmologically RichCosmologically Rich
Anti-de Sitter Holography, Brane WorldAnti-de Sitter Holography, Brane World
RR /1
A Remarkable Discovery in Physics (1995/1996)A Remarkable Discovery in Physics (1995/1996)
Cosmic Acceleration from Cosmic Acceleration from String Effective Action?String Effective Action?
Heterotic string theory, after its discovery back Heterotic string theory, after its discovery back in 1985/86, appeared to be the string theorist’s in 1985/86, appeared to be the string theorist’s dream as something like the real worddream as something like the real word
GVR
gxdS )()()(2
)(2
)(2
222
4
wherewhere abcd
abcdab
ab RRRRRG 42
is the Gauss-Bonnet integrandis the Gauss-Bonnet integrand
IPN (with Carter) IPN (with Carter) hep-th/0510109hep-th/0510109 (PRD/Rapid) , (PRD/Rapid) ,
hep-th/0512262 hep-th/0512262 (JCAP), (JCAP), hep-th/0602097hep-th/0602097
dilatondilaton
modulusmodulus
0)cosh(3
2)2ln()(
.....)( 0 e
In a known example of string In a known example of string compactificationcompactification
Unfortunately, we do not have a precise Unfortunately, we do not have a precise knowledge about the field knowledge about the field
potential . Any such potential might potential . Any such potential might take into account the non-perturbative take into account the non-perturbative
effects, as arising from the effects of effects, as arising from the effects of branes/fluxes present in the extra branes/fluxes present in the extra
dimensions.dimensions.
)(V
Frozen dilaton, no modulus Frozen dilaton, no modulus couplingcoupling
This simplifies the theory a lot This simplifies the theory a lot
2
24 )(
2)(
2
V
RgxdS
DefineDefine
22222 /),/(,)/(2
HHHVYHX
EOMsEOMs XY ,3
Different choice of implies different Different choice of implies different and hence different potentials! Is it and hence different potentials! Is it
then all worthy? then all worthy?
So Simple!So Simple!
Y
13
2
w
EOSEOS
Infinite number of Infinite number of possibilities?possibilities?
220 2
1)( mVV
n
V
04)(
0
4 cos)( cV
Quadratic/Quadratic/Chaotic Chaotic
Inverse power-Inverse power-law law
AxionAxion
eVV 0)(ExponetExponet
ialial
The issue is not merely to The issue is not merely to achieveachieve
1wFor the model to work a scalar For the model to work a scalar
field should field should relax its potential energy after relax its potential energy after
inflation down inflation down to a sufficiently low value, to a sufficiently low value,
presumably very close to the presumably very close to the observed value of the dark energyobserved value of the dark energy
Including stringy Including stringy correctioncorrection
eN
ttuHfU
22 )(8
GfVR
gxdS )()(2
)(2
22
4
)(24)(
24 223
2
HHHGaaa
AnsatzAnsatz
where ‘t’ can be where ‘t’ can be earlyearly or or latelate
))(ln( taN
Inflationary predictions with Inflationary predictions with can be significantly different from those can be significantly different from those
with with
constf )(constf )(
The solution isThe solution is
)(tanh 10 NN
2087294
1 ,
44 2
0
wherwhere e
)(cosh 10
0 NNHH eeNdN
ee
N
N
PHMV
X
1
10
t
220
20
uu
,
,)(2
ee
u
VV
)tanh(1(3)tanh(3
)cosh()(
00
22
00
Late-time Acceleration is Late-time Acceleration is possiblepossible
The solution is modelled such thatThe solution is modelled such that i
f
a
aNz ln)1ln(
Generation of Generation of PerturbationsPerturbations
51092.1~ HFixed value ofFixed value of e.g.e.g.
U=0U=0
01.0~ ,10~ 70 PMH
In a standard scenario In a standard scenario r <0.43r <0.43but with stringy correctionsbut with stringy corrections
0 ~ r < 0.40 ~ r < 0.4
Spectral IndexSpectral Index
1sn
89.0sn
95.0sn
Cmbgg OmOlCmbgg OmOlCMB
+
LSS
Nature of the dark energy
Tegmark et al 2004
Recent claim that w<-1
preferred with evolution from
w=0.
Alam et al.
?1w
pp
1w
Null dominant energy condition: Null dominant energy condition: energy doesn’t propagate outside the energy doesn’t propagate outside the
light conelight cone
A model withA model with
)(2
12
VL
negative kinetic energy fieldnegative kinetic energy field
Instabilities cured by higher Instabilities cured by higher derivative terms? string theory? …derivative terms? string theory? …
1w1w
Phantom Phantom Non-phantom Non-phantom Cosmology?Cosmology?
In the absence of (or trivial) scalar GB In the absence of (or trivial) scalar GB coupling, a transition between non-coupling, a transition between non-phantom and phantomphantom and phantom
cosmology is unlikely, but this cosmology is unlikely, but this is possible, e.g., with Gauss-Bonnet is possible, e.g., with Gauss-Bonnet
coupling coupling
)(
2.
0
eH
))(ln( ta
OutlookOutlook
Next 5-10 years dark sector of cosmology research will remain exciting to understand the theory of inflation and dark energy universe.
Thanks for your Thanks for your time….time….