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S . Nesseris Department of Physics University of Ioannina

Constraints on Dark Energy Models from the Legacy and Gold SnIa Datasets. S . Nesseris Department of Physics University of Ioannina. Main points of talk. Accelerating Expansion of the Universe and the SN Ia

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S . Nesseris Department of Physics University of Ioannina

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  1. Constraints on Dark Energy Models from the Legacy and Gold SnIa Datasets S. Nesseris Department of Physics University of Ioannina

  2. Main points of talk • Accelerating Expansion of the Universe and the SN Ia • Comparative Analysis of the 2 most robust SNIa datasets (Gold and SNLS) • Crossing of the PDL (w = -1): where the 2 sets differ and some implications of the crossing • Extended Gravity Theories: a test of Min. Coupled and Scalar- Tensor theories

  3. Some basics One of the best observational tools of cosmological interest at the the moment are the SNIa for various reasons: • Supernovae are stars that explode and the mechanism for this is very well understood. • They are “standard” candles, meaning that they all have the same luminosity. artistic image

  4. Obs Dist. Ind. Some basics The luminocity L is the energy radiated by a SN. The amount of light that reaches an observer is the apparent luminosity l: A measure of how bright a SN appears from Earth is the apparent magnitude m: and is directly related to the lum. distance through: where the absolute magnitude

  5. The expansion history The lum. distance in an expanding universe is determined by it's geometry and the latter by it's content through the Friedmann equation: Could include various components: matter, radiation, DE Every light signal is redshifted due to the expansion and this redshift z is related to the scale factor α by: ...and the distance between the observer and the emitter (the luminosity distance) is a complicated function of H(z):

  6. The expansion history Consider the DE as a fluid with pressure p and density ρ. Then it's equation of state is: It follows from the conservation equation: Then the Friedmann equation is: when w = -1 : (the familiar cosmological constant)

  7. COMPARATIVE ANALYSIS In the analysis, 3 datasets were used: • Full Gold set: 157 SNIa 0 < z < 1.75 (Riess et. al. 2004) • Trun. Gold set: 140 SNIa 0 < z < 1 (Riess et. al. 2004) • SNLS set: 115 SNIa 0 < z < 1 (Astier et. al. 2005) and the data are given in terms of the distance modulus μ defined as: To compare a theory to observations minimize: Best fit parameters of the model

  8. COMPARATIVE ANALYSIS The models 1. ΛCDM (non flat) 2. Par. A:Linear expansion of w(z) 3. Par. B: Interpolating ansatz of w(z) 4. Par. C: Quadratic expansion of H(z)

  9. The results ΛCDM (non flat case) S. N., L. Perivolaropoulos., Phys.Rev.D72:123519,2005astro-ph/0511040 Flat ΛCDM is more favored by the SNLS than by the Gold dataset as: Flat SCDM (Ωm=1) rulled out at more than 10σ

  10. The results Parameterizations A and B For the SNLS, the flat ΛCDM almost coincides with the best fit for both parametrizations.

  11. The results The equation of state w(z) for TG and FG crosses the PDL (w=-1) It doesn't happen for the SNLS and w(z) remains close and above -1 Thick solid line = best-fit Grey contour = 1σ confidence level around the best-fit.

  12. The results Much better fits to the data The crossing of the PDL (w=-1) seems to be favoured by the Gold SnIa dataset but not by the more recent first year SNLS dataset. Moreover, it has a few problems: • Phantom fields (w<-1) violate the Dominant Energy Condition ρ>0 & ρ + P ≥ 0 • The crossing causes severe gravitational instabilities in the dark energy sector Not fatal! (Caldwell, astro-ph/9908168) For adiabatic perturbations: A. Vikman 2005, astro-ph/0407107 In the context of the Gold data set, what other options do we have?

  13. Another interesting option would be to use a Scalar-Tensor theory of gravity. Potential Kinetic term Non-minimal coupling For minimal coupling: The theory is defined by: For this theory:

  14. Why Scalar-Tensor Theories? 1. Many fundamental theories involving extra dimensions to unify gravity (string theory-dilaton, Kaluza-Klein,...) reduce to scalar-tensor theories 2. The evolution of Fundamental Constants is an appealing idea (eg Dirac large number hypothesis)

  15. The results The Lagrangian: Assuming a homogeneous Φ and varying the action w.r.t. the metric in a RW backround (Jordan frame: Z=1) ... or in terms of redshift: (1) (2)

  16. The results Caution! To compare the theory to observations we shouldn't use the previous relation with the distance modulus nor the lum. distance as now G=G(z) The absolute magnitude will change:

  17. The results The actual G, as measured by Cavendish-type experiments, is related to F by: From Solar test constraints F'(z)~0 Finally the lum. distance is modified: S. Nesseris, L. Perivolaropoulos., astro-ph/0602053

  18. The results To compare theory to observations we considered the following simple polynomial parameterizations for the functions H(z) and G(z) minimally coupled case α=0 From eqs (1), (2) after fitting to the data we will know both the potential U and the kinetic term After minimizing we get: Sc.Tensor Min. Coupled

  19. The results The equation of state w(z) for the best fit parameters: For the minimally coupled case G(z)=const. at all times. Unluckily w(z) again crosses the PDL (w=-1)

  20. Conclusions 1) We have used representativedark energyparametrizations to examine the consistencyamong the three datasets. 2) Thelatest (SNLS) dataset shows distinct trends which are notshared by the other (earlier) datasets (w(z) doesn’t cross w= -1 and favours a flat universemuch more than the Gold datasets). 3) In the context of extended gravity theories we found that in both cases (Scalar-Tensor and minimally coupled) the equation of state crosses the PDL (w= -1). Photo: courtesy of C. Bogdanos

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