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Direct Evidence of acceleration from a distance modulus- redshift graph

Direct Evidence of acceleration from a distance modulus- redshift graph. Yungui Gong 龚云贵 College of Mathematics and Physics Chongqing University of Posts and Telecommunications 重庆邮电大学数理学院. String Theory and Cosmology Workshop ， KITPC, 10/22/2007. Outlines. Introduction SN Ia Evidence

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Direct Evidence of acceleration from a distance modulus- redshift graph

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  1. Direct Evidence of acceleration from a distance modulus-redshift graph Yungui Gong 龚云贵 College of Mathematics and Physics Chongqing University of Posts and Telecommunications 重庆邮电大学数理学院 String Theory and Cosmology Workshop，KITPC, 10/22/2007

  2. Outlines • Introduction • SN Ia Evidence • Introduction to numerical Fitting • Dark Energy Parameterization • Conclusion

  3. Dark Energy

  4. Quintessence?

  5. Dark Energy

  6. Type Ia Supernova Observation • Observational Data: Redshift-Luminosity distance • For a given cosmological model, calculate Luminosity distance-redshift relation • To fit observation data, need to assume a model and then fit the parameters in the model

  7. Dark Energy

  8. SN Ia Evidence • Model: Cosmological constant • Model independent Way? Energy Condition

  9. Friedmann Equation • Friedmann Equation

  10. Acceleration and Energy Conditions

  11. Energy Conditions in Distance graph • Strong Energy Condition

  12. Results? • The SEC was first violated billions of years ago, at z~1.1 (Santos etal., PRD 74 (06) 067301; PRD 75(07) 083523）.

  13. CDM Model • Deceleration to Acceleration Transition happened at z<0.8

  14. How to interpret? • Gong and Wang, JCAP 0708 (07) 018; PLB 652 (07) 63 • Key Points: SEC and the derived luminosity conditions are not equivalent!

  15. Reasons • Integration Effect

  16. Key Points • SEC leads to upper bound on the luminosity distance • Violation of the upper bound means violation of SEC • Violation of the upper bound at z does not necessarily mean the violation of SEC at the same z • Satisfaction of the upper bound up to z does not mean no violation of SEC up to z

  17. Conclusion • Energy condition can be used to give direct and model-independent evidence of cosmic acceleration • No detailed information about the acceleration can be given • No information on dark energy can be given

  18. Parameter Degeneracy • At Low Red-shift (z<0.1), Almost the same (z)–z relation • To the first order, • w(z=0)

  19. Numerical Fitting • For a given cosmological model, we can calculate the luminosity distance (or distance modulus) with given parameters P • Find out the parameters that gives the minimum value of • Parameter space: grid (point to point search), Monte Carlo Markov Chain method

  20. Toy Model (Essence Data)

  21. The error of w(z=0)

  22. The sweet spot

  23. 结论 • Energy condition can be used to give direct and model-independent evidence of cosmic acceleration • The luminosity distance is almost independent of cosmological models at low redshift, so the value of w(z=0) may not be well determined.

  24. Thank you！

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