Is Cosmic Acceleration Slowing Down? Invisible Universe-UNESCO-Paris 29 th June-3 rd July 2009 Arman Shafieloo Theoretical Physics, University of Oxford

Current cosmological observations indicate that the universe expands today with acceleration. The driving agent of this acceleration is what is called “dark energy”, a uniformly distributed component constituting about 70% of total energy density and having negative pressure. The nature of the “dark-energy” phenomenon remains to be unknown and is one of the biggest puzzles in modern cosmology. ACCELERATING UNIVERSE AND DARK ENERGY

Dark Energy Models Cosmological constant Quintessence and k-essence (scalar fields) Exotic matter (Chaplygin gas, phantom, etc.) Braneworlds (higher-dimensional theories) ….. But which one is really responsible for the acceleration of the expanding universe?!

The most direct indication for the current accelerating expansion of the universe comes from the accumulating type Ia supernovae data: Most general form Dark Energy Supernovae Ia as Standard Candles

Y. Gong, JCAP 2005

Dealing with observational uncertainties in matter density Small uncertainties in the value of matter density may affect the reconstruction exercise quiet dramatically. Hubble parameter is not affected to a very high degree by the value of matter density. Any uncertainties in matter density is bound to affect the reconstructed w(z).

V. Sahni, A. Shafieloo, A. Starobinsky, PRD 2008

Instead of trying to find out w(z) and exact properties of dark energy with current status of data, we can concentrate on a more reasonable problem: OR NOT

V. Sahni, A. Shafieloo, A. Starobinsky, PRD 2008

Om diagnostic LCDM Phantom Quintessence V. Sahni, A. Shafieloo, A. Starobinsky, PRD 2008 arXive: Also look at: C. Zunckel & C. Clarkson, PRL 2008 arXive:

QuintessencePhantom Simulated results for 1000 realization of SNAP data, using smoothing method. A. Shafieloo et al, MNRAS 2006 A. Shafieloo, MNRAS 2007 V. Sahni, A. Shafieloo, A. Starobinsky, PRD 2008

SNLS data, CPL parameterization

Union data, CPL parameterization

Tracker Models V. Sahni, A. Shafieloo, A. Starobinsky, PRD 2008

Constitution SN data + BAO, CPL parameterization 90 new low redshift (z<0.08) SnIa data from CfA survey SnIa SnIa+ BAO

Constitution SN data + BAO + CMB, CPL parameterization SnIa+ BAO+CMB

Constitution SN data + BAO + CMB, CPL parameterization A. Shafieloo, V. Sahni, A. Starobinsky, arXiv:

CPL parametrization is strained to fit the data simultaneously at low and high redshifts. A. Shafieloo, V. Sahni, A. Starobinsky, arXiv:

Toy Model with respect to CPL A. Shafieloo, V. Sahni, A. Starobinsky, arXiv:

Summary: Om can be derived directly from the Hubble parameter and not its derivatives. Errors in the reconstruction of Om are smaller than those appearing in the EOS. Om is not sensitive to the value of matter density. Om can be determined using parametric as well as non- parametric reconstruction methods. Om and can be applied on non-uniform data.

Low redshift supernovae are very important in cosmological parameter estimation. CPL parameterization is strained to fit the data at low and high redshifts simultaneously. If w is assumed to be constant, then |1+w| < 0.06 (1 \sigma) from independent tests. If the latter (not justified) assumption is omitted, many unexpected and interesting things may occur at recent z < 0.3. previously, we thought that this may be temporal phantom DE behaviour, but new data, if interpreted cosmologically, points to just the opposite direction. significant increase of “Om”, “q” and “w” as compared to the LCDM, possible decay of DE into something else.

NewScientist April 2009

BUT!  The observed luminosity distances of supernovae are not so accurate.  To calculate the Hubble parameter and the equation of state of dark energy, we should use the first and second derivatives of this data, which enlarges the errors by huge factors.  Even future supernovae data (like SNAP) will not be that accurate to be used directly to calculate these cosmological parameters.

Some dark energy models consistent with the Union data. V. Sahni, A. Shafieloo, A. Starobinsky, PRD 2008

Union SN data + BAO + CMB, CPL parameterization

Summary: Om can be derived directly from the Hubble parameter and not its derivatives. Errors in the reconstruction of Om are smaller than those appearing in the EOS. Om is not sensitive to the value of matter density. Om can be determined using parametric as well as non- parametric reconstruction methods. Acceleration probe depend upon the value of Hubble parameter and the look-back time. Om and acceleration probe can be applied on non-uniform data.

Acceleration Probe Acceleration probe is the mean value of the deceleration parameter:

Union SN data, CPL parameterization

Shafieloo et al, MNRAS 2006, Sahni & Starobinsky 2007 Real Matter density = 0.3 Assumed Matter density = 0.2

The w-Probe It is possible to obtain more information on the equation of state of dark energy from the reconstructed Hubble parameter by considering a weighted average of the equation of state.

The reconstructed w-prob for 3 fiducial models realizations

Robustness of the The w-Probe to observational uncertainties in Matter density. W=1 W= -1/1+z Marginalizing over matter density Shafieloo et al, MNRAS 2006

Conclusion: The proposed reconstruction method by smoothing the SN data appears to be sufficiently accurate and when applied to SNAP-type observations, should be able to distinguish between evolving dark energy models and a cosmological constant. Reconstructed results are not biased by any functional fitting form or any assumed theoretical model. Reconstructed results at any redshift rely mostly on the supernovae data points at the same redshift range. w-probe provides us with an excellent diagnostic of dark energy. w- probe is robust to small uncertainties in the value of matter density. w-probe can be used by any reconstruction method that accurately calculates either the dark energy density or Hubble parameter.

Conclusion: SN Ia observations, Gold and SNLS, are consistence with the results of detection of the baryon acoustic peak in a range of matter density between and 0.299, without assuming any theoretical model. In the derivation of q(z) and w(z), we found disagreement between Gold and SNLS datasets. Gold data suggest the red-shift of the commence of acceleration at z ≃ 0.42 while SNLS suggest z ≃ 0.80 The derived form of w(z) from SNLS dataset, is in good concordance with LCDM, while Gold dataset prefers an evolving form of dark energy. The large error-bars at the high redshifts for the reconstructed results, reflect the significant lack of data points. It limits our ability to say much about the behavior of the universe at the early stages at high redshifts.

Ongoing Works: Making the method error-sensitive Reanalysis of SNLS and ESSENCE data Working on w-probe and q-probe

Refinement of the method:

Variable Delta Refinement of the method:

Accuracy of the results and the relation with the quality and quantity of the data M. Tegmark, PRD 2002 Tegmark et al, astro-ph/ In this method, a large value of delta produces a smooth result, but the accuracy of reconstruction worsens, while a small delta gives a more accurate, but noisy result. Bias: Shafieloo et al, MNRAS 2006

Smoothing function (error-sensitive) The Method of Smoothing error-sensitive

WMAP 5 E. Komatsu et al, APJS 2008