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 energy

matter (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 redshift

phantom-like

quintessence-like

monotonously falling with redshift quintessence-like

phantom-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)