Detecting relic gravitational waves using pulsar timing arrays

1. Detecting relic gravitational waves using pulsar timing arrays Minglei Tong National Time Service Center Chinese Academy of Sciences

2. Outline • Introduction of gravitational waves • Relic gravitational waves (RGWs) in the accelerating universe. • Detection of RGWs using pulsar timing • Summary

3. The theoretical prediction of GWs • In 1915, Einstein found a solution of Einstein Equation in the weak field approximation--GWs. • In 1950s, Bondi found the strict solution of GWs.Then, the existence of GWs was accepted completely from theories.

4. The indirect evidence of GWs Nobel Prize Physics 1993 Hulse & Taylor Hulse Taylor PRS 1913+16

5. The basics of GWs In vacuum the solution is the superposition of plane waves: GWs only have two polarizations h+ h×

6. New window IR Radio CMB x-ray GRBs g-ray Gravitational Waves will give us a non electromagnetic view of the universe, and open a new window for observations. From GWs, one can learn the physics of binary compact stars, spinning neutron stars, colliding massive bodies, and gain further insights in the early universe. GW sky?

7. Relic gravitational waves are generated by the quantum fluctuations and amplified by inflation. Relic gravitational waves could serve as the unique tool to study the early universe before the recombination Gravitational waves can escape from earliest moments of the universe

8. The analytic solutions of relicGWs In the flat FRW spacetime, the GW equation is Decompose into the Fourier modes of the comoving wave number and the polarization state Then one has For , the general analytic solution is

9. The scale factor in various phases • Inflation stage • Reheating stage • Radiation-dominant stage • Matter-dominant stage • Accelerating stage

10. Spectra of RelicGWs The variance The spectrum The energy density parameter The energy spectrum

11. Approximate solutions of relicGWs M.Tong, CQG, 29, 155006 (2012)

12. The increases of the scale factor • The accelerating history • The matter-dominant history • The radiation-dominant history • where and count the effective number • of relativistic degrees of freedom for the entropy density at the preheartin • g stage and the present day, respectively. • The prehearting history (Conservation of the entropy)

13. The slow-roll inflation model • In the frame of the slow-roll inflation with a scalar filed potential • one obtain • This result depends sensitively on the forms of V, and the relative error is • large! Furthermore, if we do not consider the quantum normalization • condition(not necessary ), the values of and do not affect the • spectrum of RGWs in the detecting window of pulsar timing arrays. J. Mielczarek, PRD, 83, 023502 (2011)

14. The slow-roll inflation model • In the frame of the slow-roll inflation with a scalar filed potential • one obtain • This result depends sensitively on the forms of V, and the relative error is • large! Furthermore, if we do not consider the quantum normalization • condition(not necessary ), the values of and do not affect the • spectrum of RGWs in the detecting window of pulsar timing arrays. J. Mielczarek, PRD 83, 023502 (2011)

15. Normalizations of RGWs CMB The tensor-to-scalar ratio E. Komatsu, ApJS, 192, 18 (2011) Quantum Normalization M.Tong, CQG, 29, 155006 (2012)

16. No quantum normalization

17. Limitations from PPTA The characteristic strain F.A. Jenet et al, ApJ,653,1571 (2006)

18. Limitations from PPTA F.A. Jenet et al, ApJ,653,1571 (2006)

19. Limitations from PPTA The current PPTA: The future PPTA:

20. Withquantum normalization

21. Limitation of the early universe For The current PPTA: The future PPTA:

22. Dimensional evaluation of RGWs detection

23. Summary • We give the complete approximate solutions of RGWs including the consideration of the present accelerating universe. • We give the limitations of by the current PPTA and the potential future PPTA which depend on r , without considering the quantum normalization. • Consider the validity of quantum normalization, we could study the expansion histories of the very early universe including the preheating stage and the radiation-dominant stage using pulsar timing technique. • As an dimensional evaluation, we make a comparison of the complete PPTA and the planned SKA with the theoretical RGWs. We found SKA is easy to detect RGWs.

24. Thank you!