what is in the black box of dark energy: variable cosmological parameters or multiple (interacting)...
DESCRIPTION
Cosmic coincidences ● w presently close to -1 ● possible CC boundary crossing at small redshift ● the ratio of dark energy density and matter energy density presently of order 1 ● Variable cosmological parameters (phenomenology, RGE approaches, holographic DE, 4D effective description of the dynamics in higher dimensions) ● composite dark energy (multiple dark energy components) observational features proposed approaches S. Hannestad, E. Mortsell, JCAP 0409 (2004) 001 A. Upadhye, M. Ishak, P.J. Steinhardt, Phys. Rev. D 72 (2005) H.K. Jassal, J.S. Bagla, T. Padmanabhan, astro-ph/ G-B. Zhao, J-Q. Xia, B. Feng, X. Zhang, astro-ph/TRANSCRIPT
What is in the black box of dark energy: variable cosmological parameters or multiple (interacting) components?
Hrvoje ŠtefančićUniversitat de Barcelona
IRGAC 2006, BarcelonaJuly 14, 2006
Accelerating universe● accelerating universe – observationally
established● mechanism behind the acceleration?● dark energy● alternative mechanisms: modified gravity,
braneworlds, ...● dark energy – single component which encodes
all our ignorance – efficient effective description - “a black box”
Cosmic coincidences
● w presently close to -1
● possible CC boundary
crossing at small redshift
● the ratio of dark energy density and matter energy density presently of order 1
● Variable cosmological parameters (phenomenology, RGE approaches, holographic DE, 4D effective description of the dynamics in higher dimensions)
● composite dark energy (multiple dark energy components)
observational features
proposed approaches
S. Hannestad, E. Mortsell, JCAP 0409 (2004) 001 A. Upadhye, M. Ishak, P.J. Steinhardt, Phys. Rev. D 72 (2005) 063501 H.K. Jassal, J.S. Bagla, T. Padmanabhan, astro-ph/0601389 G-B. Zhao, J-Q. Xia, B. Feng, X. Zhang, astro-ph/0603621
Formalism – variable cosmological parameters
● modification of GR at the level of Einstein equation
● Generalized Bianchi identity
● GR as a limit (for nonvariable parameters)
Cosmology – variable cosmological term picture
● FRW metrics – generalized Bianchi identity gives
1)
2)
3)
4)
variable CC energy density matter density (possibly interacting)
Variable cosmological term picture● variability of parameters with redshift
● Hubble parameter
Cosmology – dark energy picture
● standard formalismdark energymatter (noninteracting)
Matching of pictures
● Effective dark energy behaviour – matching of pictures
● general results J. Solà, H. Š., Mod. Phys. Lett. A 21 (2006) 479
+ + Generalized Bianchi identity
Matching of pictures (2)
● redshift dependence of the efective dark energy EOS
existence of z* close to z=0
Effective dark energy EOS● slope of the effective dark energy
monotonously growing with redshiftphantom-likequintessence-like
monotonously falling with redshift quintessence-likephantom-like
Dark energy effective EOS● noninteracting (conserved – standard scaling)
An example – RG motivated model
● Hubble parameter as a RG scale
J. Solà, H. Š., Phys. Lett. B 624 (2005) 147
Redshift dependence of the effective EOS (1)
Redshift dependence of the effective EOS (2)
Explanation of w(z) “coincidence”● If it exists (to be hopefuly resolved by the
upcoming observational data), the CC boundary transition – should happen at small redshift– is allowed for a wide range of parameters (no special
values need to be chosen) ● The parameter of effective dark energy EOS is at
present close to w(0)=-1 (general result)● w(z) may exibit substantial variation with the
redshift
Composite dark energy● matter component (noninteracting)
● two (interacting) dark energy components: (variable) cosmological term + additional dynamical component
J. Grande, J. Solà, H. Š., gr-qc/0604057
interaction
dynamics
Evolution of analytical (closed form) solution – simple expressions for =const
stopping of the expansion: H(z)=0
r has a maximum! How high is it?
the redshift dependence of (z)?
Parameter constraints
● nucleosynthesis bound: ● existence of the expansion stopping ● height of the maximum of r :
Parametric dependence● dependence
Time evolution ● The peak of r(z) is less pronounced
Special cases and extensions
● The effect persists for . r is not bounded from below
● Variable cosmological term Lambda and variable Newton coupling G – similar results
J. Grande, J. Solà, H. Š., in preparation
Conclusions● effective dark energy picture for the cosmological models with
variable parameters
● general and simple analitic results - “RG like” relation between and
● counterintuitive behaviour of the effective dark energy density
● explanation of w(z) “coincidences”
● composite dark energy – solution of the r(z) coincidence problem – when the expansion of the universe stops, r(z) is bounded from
above– r(z) may stay close to r(0) for a nonnegligible volume of the
parametric space
Auxilliary slides
Observational evidence
● Dark energy EOS w(z) – various parametrizations used– variability with the redshift– w(z) close to -1 – indication of CC boundary crossing
S. Hannestad and E. Mortsell, JCAP 0409 (2004) 001
w(a)=w0 w1(aq + asq)/(aq w1+as
q w0)
Variable cosmological parameters – motivation (1)
● Phenomenological approaches – “relaxation” of CC – solution of the CC problem– Dirac – big number hypothesis – variable G– cosmology with a decaying vacuum -K. Freese, F.C.
Adams, J.A. Frieman, E. Mottola, Nucl. Phys. B 287 (1987) 797
– variable CC interacting with matter - J.M. Overduin, F.I. Cooperstock, Phys. Rev. D 58 (1998) 043506
– variable G and CC - A. Beesham, Nuovo Cim. B 96 (1986) 17
Variable cosmological parameters – motivation (2)
● RG cosmology– quantum field theory in curved space-time
● soft decoupling -importance of the most massive fields– scale dependent effective quantum gravity action
(Einstein-Hilbert truncation)● RG flow - IR fixed point hypothesis
I.L. Shapiro, J. Solà, Phys. Lett. B 475 (2000) 236 I.L. Shapiro, J. Solà, JHEP 0202 (2002) 006 A. Babić, B. Guberina, R. Horvat, H. Š., Phys. Rev. D 65 (2002) 085002 I.L. Shapiro, J. Solà, C España-Bonet, P. Ruiz-Lapuente, Phys. Lett. B 574 (2003) 149
A. Bonnano, M. Reuter, Phys. Rev. D 65 (2002) 043508A. Bonnano, M. Reuter, Phys. Lett. B 527 (2000) 9
Variable cosmological parameters – motivation (3)
● A.G. Cohen, D.B. Kaplan, A.E. Nelson, Phys. Rev. Lett. 82 (1999) 4971
● Effective field theory + entropy constraint = relation between UV( ) and IR (1/L) cutoffs
● excluding all states that lie within their Schwarzschield radius
● Holographic dark energy – M. Li, Phys. Lett. B 603 (2004) ● Variable cosmological term - R. Horvat, Phys. Rev. D 70
(2004) 087301
Variable cosmological parameters – motivation (4)
● Higher-dimensional models (e.g. GR in 4+N dimensions)
● Variability of e.g. G due to dynamics of extra (compactified) dimensions
Effective dark energy EOS
Redshift dependence of the effective EOS (3)