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Open page. Accelerating Universe and Scalar-Tensor Theories. L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina. Main Points. Dark Energy Equation of State w(z)=p/ρ may be crossing the w=-1 line. Minimally Coupled Quintessence is
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Open page Accelerating Universe and Scalar-Tensor Theories L. Perivolaropouloshttp://leandros.physics.uoi.gr Department of Physics University of Ioannina
Main Points Dark Energy Equation of State w(z)=p/ρ may be crossing the w=-1 line Minimally Coupled Quintessence is inconsistent with such crossing Scalar Tensor Quintessence is consistent with w=-1 crossing Extended Gravity Theories (DGP, Scalar Tensor etc) predict unique signatures in the perturbations growth rate
The Dark Energy Puzzle Friedmann Equation Flat General Relativity DirectlyObservable Dark Energy(Inferred) DirectlyObservable Not Consistent Q: Is GR the correct theory on the Largest Scales? What is the Correct Theory? No Yes What are the properties of the dark energy? What microphysical theory can reproduce these properties?
Hubble Diagram Accelerating Universe: (rate of expansion) was smaller in the past. Thus H-1(t) was larger in the past. Standard Candles SNeIa Luminus Objects of a given redshift appear to be further away (dimmer) in an Accelerating Universe
Observed Hubble Diagram z~0.5: Acceleration starts 157 SnIa
Negative Pressure Acceleration from Dynamics of scale factor a(t): Friedman eqn General Relativity Homogeneity-Isotropy Equation of State: Necessary condition for acceleration: Dark Energy Antigravity
Evolution Dark Energy Energy Conservation: Friedman Equation Best Fit ? (from large scale structure observations)
Best Fits for w(z) Gold dataset Riess -et. al. (2004) SNLS dataset Astier -et. al. (2005) Other data: CMB, BAO, LSS, Clusters S. Nesseris, L.P.astro-ph/0511040Phys.Rev.D72:123519,2005 Gold dataset Riess -et. al. (2004) SNLS dataset Astier -et. al. (2005) Other data: CMB, BAO, LSS, Clusters Other data: CMB, BAO, LSS, Clusters S. Nesseris, L.P.in prep.
Basic Question What theory produces crossing of the w=-1?
Minimally Coupled Scalar: No w=-1 crossing Homogeneous Minimally Coupled Scalar: +: Quintessence -: Phantom Equation of State: To cross the w=-1 line the kinetic energy term must change sign (impossible for single phantom or quintessence field) Generalization for k-essence:
Non-minimal Coupling: Scalar Tensor Theories Non-minimal Coupling Rescale Φ Theory Defined by Minimal Coupling
Cosmological Evolution in Scalar-Tensor Theories Vary ST action in flat FRW background assuming perfect fluid: +
JCAP 0511:010,2005 Crossing w=-1 line Reconstruction from Best Fit to Gold Dataset L.P. astro-ph/0504582, JCAP 0510:001,2005, S. Nesseris, L.P. astro-ph/0602053, Phys.Rev.D73:103511,2006 F(Φ) U(Φ) Minimum: Generic feature Φ Φ
Other Signature: Growth Factor Growth Factor: Growth Factor Evolution (Linear-Fourier Space): General Relativity: Koyama and Maartens (2006) DGP: Esposito-Farese and Polarski (2001)Uzan (2006) Scalar Tensor: Modified Poisson: Sealfon et. al. (2004)
Compare with Data (2dF) Flat Matter Only ΛCDM (SnIa best fit, Ωm=0.26) S. Nesseris, L.P.in prep. Scalar Tensor (α=-0.5, Ωm=0.26) DGP SnIa best fit+Flat Constraint Verde et. al. MNRAS 2002Hawkins et. al. MNRAS 2003 Future Prospect: Decrease Error Bars
SUMMARY • The Expansion of the Universe is currently accelerating. • This acceleration can be modeled either by a Dark Energy or by Extended Gravity Theories. • All recent data indicate that w(z) is close to -1. Thus w(z) may be crossing the w=-1 line. • Minimally Coupled Scalar predicts no crossing of w=-1 line • Scalar Tensor Theories are consistent with crossing of w=-1 • Extended Gravity Theories (DGP, Scalar Tensor etc) predict unique signatures in the growth rate of cosmological perturbations
Reconstruction Equations Convert t to z, solve for U and Φ': where positive energy of gravitons Constraints: Is there a theory satisfying the constraints and crossing the w=-1 line? Q:
Special Case: F(z)=1 (Minimal Coupling) Use in reconstruction equations to get: Constraint: The constraint is equivalent to w(z) > -1:
Special Case: F(z)=1 (Minimal Coupling) Use in reconstruction equations to get: Simplest Reconstruction Example: Cosmological Constant
Results G(z)~1/F(z) decreases at recent times thus boosting accelerating expansion Minimum: Generic feature