Effects of quantum fluctuations of metric on the universe

1. Effects of quantum fluctuations of metric on the universe Rongjia Yang (杨荣佳) Hebei University(河北大学) Based on arXiv:1506.02889 2015.6.11，中国科学技术大学

2. Outline • Motivation • Modified gravitational field equations • Cosmological applications • Conclusions

3. Motivation Quantized Gravity Canonical quantization: LQG Path integral quantization Heisenberg's nonperturbative quantization

4. Motivation Heisenberg's technique offers one possibility to solve this operator equation by average it over all possible products of the metric operator

5. Decompose the metric operator into a sum of an average metric and a fluctuating part

6. Motivation The modified Lagrangian density can be written as

7. Modified gravitational field equations • Lagrangian density takes the form We consider the simplest case:

8. Modified gravitational field equations Varying Lagrangian density with respect to

9. Modified gravitational field equations Assuming that the Lagrangiandensity of matter depends only on the metric tensor components

10. Modified gravitational field equations We obtain the gravitational field equations Then we have

11. Modified gravitational field equations The divergence of the stress-energy tensor gives

12. Cosmological applications Considering a FLRW spacetime and a perfect fluid specified by the stress energy tensor

13. Cosmological applications We get the expression Taking the Lagrangian for matter as

14. Cosmological applications The Friedmann equations are modified as

15. Cosmological applications The conservation equation takes forms Here we consider a spatial flat FLRW spacetime

16. Cosmological applications A bounce universe can be obtained, which can not be realized in general relativity with normal matter. The effects of the quantum fluctuation of metric on the very early universe

17. Cosmological applications The effects of the quantum fluctuation of metric on inflation

18. Cosmological applications The two slow-roll parameters are modified as

19. Cosmological applications The spectral index and the spectrum of the primordial curvature perturbation are modified as, respectively

20. Cosmological applications which can be integrated as For a constant EoS，the conservation equation takes forms

21. Cosmological applications The expansion of the universe will be accelerated even in a radiation-dominated period For a radiation-dominated epoch

22. Cosmological applications The expansion of the universe will be accelerated even in a dust-dominated period For a dust-dominated epoch

23. Cosmological applications A decelerated expansion will be obtained due to the quantum fluctuations of metric For a dark energy dominated epoch, assuming a constant EoS, we find that for

24. Cosmological applications we find See, for example, taking

25. Cosmological applications we find See, for example, taking

26. Conclusions and discussions A model of modified gravity is proposed We have investigated effects of quantum fluctuations of metric on the universe. Due to the quantum fluctuations a bounce universe can be obtained and a decelerated expansion can also possibly be obtained even in a dark energy dominated epoch Other cases, see, for example， are also worth discussing

27. Thanks