1 / 27

Effects of quantum fluctuations of metric on the universe

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. Outline. Motivation Modified gravitational field equations Cosmological applications Conclusions. Motivation. Quantized Gravity.

darleneb
Download Presentation

Effects of quantum fluctuations of metric on the universe

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related