1. 1 Observable (?) cosmological signatures of superstrings in pre-big bang models of inflation Università degli Studi di Bari Facoltà di Scienze Matematiche, Fisiche e Naturali Dipartimento di Fisica & INFN Facoltà di Scienze Matematiche, Fisiche e Naturali Dipartimento di Fisica & INFN Based on PLB 633 155 (2006), with M. Gasperini Stefano Nicotri

2. 2 Main aim Discriminate between the Type I end the Heterotic superstring model through cross correlated observations of cosmic magnetic fields and primordial gravitational- waves background Spectral energy density for photons (two models) Spectral energy density for photons (two models) Spectral energy density for gravitons Spectral energy density for gravitons Theoretical and phenomenological constraints Theoretical and phenomenological constraints Plot of the allowed regions in the parameter space Plot of the allowed regions in the parameter space Confrontation of the two models by experiments Confrontation of the two models by experiments Spectral energy density for photons (two models) Spectral energy density for photons (two models) Spectral energy density for gravitons Spectral energy density for gravitons Theoretical and phenomenological constraints Theoretical and phenomenological constraints Plot of the allowed regions in the parameter space Plot of the allowed regions in the parameter space Confrontation of the two models by experiments Confrontation of the two models by experiments

3. 3 Cosmic magnetic fields Magnetic fields on galactic and intergalactic scales: Magnetic fields on galactic and intergalactic scales: Amplitude ~ 10 -6 Gauss Amplitude ~ 10 -6 Gauss Coherence scale > 10 Kpc Coherence scale > 10 Kpc Magnetic fields on galactic and intergalactic scales: Magnetic fields on galactic and intergalactic scales: Amplitude ~ 10 -6 Gauss Amplitude ~ 10 -6 Gauss Coherence scale > 10 Kpc Coherence scale > 10 Kpc Possible mechanism of production Galactic Dynamo (Parker et al., 1973) It needs some “seed” magnetic field to be started up, that is a field which is strong enough to be amplificated by this mechanism.

4. 4SeedsSeeds Even in vacuum F   0 (quantum fluctuations) Inflationary expansion can amplificate quantum fluctuations Identification of the amplified quantum fluctuations with the seeds fields required by the dynamo to be started up.

5. 5 Problem Conformally flat metric Conformal invariance of Maxwell lagrangian ++ == Fluctuations not coupled to geometry ++ Minimal coupling Inflation doesn’t amplificate the fluctuations

6. 6 Superstring theory predicts the existence of the dilaton , a scalar field which is non- minimally coupled to the E.M. field: e -  F  F   depends on superstring model Possible solution We compare the cases  =1 (Heterotic superstring) and  =1 /2 (Type I superstring)

7. 7 ActionAction Ten dimensional space-time Internal space isotropy Action for the fluctuation fields  i “pump field” which amplificates the fluctuations in the inflationary phase. It depends on the dilaton coupling and on the choice of the model of cosmological evolution, through the scale factors “pump field” which amplificates the fluctuations in the inflationary phase. It depends on the dilaton coupling and on the choice of the model of cosmological evolution, through the scale factors Equation of motion

8. 8 Minimal pre-Big Bang Model  s = 1/  s  1 = 1/  1

9. 9 This choice determinates: Pump field Pump field Equation of motion (Bessel equation) Equation of motion (Bessel equation) Solutions (amplification) Solutions (amplification) Pump field Pump field Equation of motion (Bessel equation) Equation of motion (Bessel equation) Solutions (amplification) Solutions (amplification) We can get the physical parameters: Number of pairs produced from the vacuum Differential energy density Spectral energy density

10. 10 Spectral energy density PhotonsPhotons GravitonsGravitons Photons spectrum is model dependent while gravitons spectrum is model independent Free (?) parameters that we shall discuss later

11. 11 ConstraintsConstraints Constraints shared by both spectra: Homogeneity Homogeneity Nucleosyntesis Nucleosyntesis Growing spectrum Growing spectrum Homogeneity Homogeneity Nucleosyntesis Nucleosyntesis Growing spectrum Growing spectrum Constraints for the E.M. spectrum Seed condition Seed condition Constraints for the gravitons spectrum Visibility by Advanced LIGO Visibility by Advanced LIGO Pulsar timing measurement Pulsar timing measurement Visibility by Advanced LIGO Visibility by Advanced LIGO Pulsar timing measurement Pulsar timing measurement

12. 12 Free parameters  1 : frequency inverse of the transition time from pre-bb to post-bb phase  1 : frequency inverse of the transition time from pre-bb to post-bb phase  s : frequency inverse of the transition time from dilaton to string phase  s : frequency inverse of the transition time from dilaton to string phase  : phenomenological parameter that possibly takes into account the effects of the higher order corrections to the effective action  : phenomenological parameter that possibly takes into account the effects of the higher order corrections to the effective action  0 : exponent of the external scale factor  0 : exponent of the external scale factor  : exponent of the internal scale factor  : exponent of the internal scale factor  : quantity that parametrizes the coupling of the dilaton with the E.M field in the two superstring models we have considered  : quantity that parametrizes the coupling of the dilaton with the E.M field in the two superstring models we have considered H 1 : value of the Hubble parameter at  1 H 1 : value of the Hubble parameter at  1  1 : frequency inverse of the transition time from pre-bb to post-bb phase  1 : frequency inverse of the transition time from pre-bb to post-bb phase  s : frequency inverse of the transition time from dilaton to string phase  s : frequency inverse of the transition time from dilaton to string phase  : phenomenological parameter that possibly takes into account the effects of the higher order corrections to the effective action  : phenomenological parameter that possibly takes into account the effects of the higher order corrections to the effective action  0 : exponent of the external scale factor  0 : exponent of the external scale factor  : exponent of the internal scale factor  : exponent of the internal scale factor  : quantity that parametrizes the coupling of the dilaton with the E.M field in the two superstring models we have considered  : quantity that parametrizes the coupling of the dilaton with the E.M field in the two superstring models we have considered H 1 : value of the Hubble parameter at  1 H 1 : value of the Hubble parameter at  1 Ansatz:Ansatz: H 1 =M s =0.1M p  1 = (M s /M p ) 1/2 ·10 11 Hz  0,  and  can assume only discrete values  and  s are the only two continuous parameter 2-dimensional parameter space

13. 13 Allowed regions in parameter space

14. 14 Contribution from internal dimensions How does superposition region change? Internal dimensions do not give any substantial contribution

15. 15 RemarksRemarks Superposition between Type I photons and gravitons allowed regions Superposition between Type I photons and gravitons allowed regions No superposition between Heterotic photons and gravitons allowed regions No superposition between Heterotic photons and gravitons allowed regions These considerations are substanially not influenced by internal dimensions contributions These considerations are substanially not influenced by internal dimensions contributions Superposition between Type I photons and gravitons allowed regions Superposition between Type I photons and gravitons allowed regions No superposition between Heterotic photons and gravitons allowed regions No superposition between Heterotic photons and gravitons allowed regions These considerations are substanially not influenced by internal dimensions contributions These considerations are substanially not influenced by internal dimensions contributions

16. 16 Physical interpretation Presence of a superposition region between gravitons and Type I photons An efficient production of magnetic “seeds” is compatible with the production of relic gravitons detectable by Advanced LIGO Absence of a superposition region between gravitons and Heterotic photons An efficient production of magnetic “seeds” is not compatible with the production of relic gravitons detectable by Advanced LIGO

17. 17 ConclusionsConclusions Direct experimental information on the primordial intensity of the photon-dilaton coupling and on the superstring model that best describes primordial cosmological evolution can be obtained Direct experimental information on the primordial intensity of the photon-dilaton coupling and on the superstring model that best describes primordial cosmological evolution can be obtained

18. 18 ExperimentsExperiments Experimental confirmation of the production of primordial magnetic seeds as predicted by pre-Big Bang models ++ Detection of relic gravitons by Advanced LIGO == Experimental support to Type I superstring model Experimental support to Heterotic superstring model No detection of relic gravitons by Advanced LIGO ==

19. 19 Thanks to R. Anglani, P. Colangelo, F. De Fazio, R. Ferrandes, M. Gasperini, M. Lucente, M. Ruggieri R. Anglani, P. Colangelo, F. De Fazio, R. Ferrandes, M. Gasperini, M. Lucente, M. Ruggieri Thank you for patience and attention

20. 20 Interferometer Sensibility

21. 21 Contribute from internal dimensions

22. 22 Photons spectrum

23. 23 Gravitons spectrum

24. 24 Heterotic Photons  =1 =1 =1 =1

25. 25 Type I Photons  = 1/2

26. 26 Photons Heterotic + Type I

27. 27GravitonsGravitons  (model) independent

28. 28 Equations of motion SolutionsSolutions Cosmological expansion has NO effect on the fluctuations

29. 29 Pump field Equation of motion in momentum space SolutionsSolutions

30. 30ActionAction Contribution coming from the dimensional reduction

31. 31 Action for the fluctuations Z(  ) is the “pump field” which apmlificates the fluctuations Evolution equation Evolution equation ?

32. 32 PotentialPotential Bessel Equation

33. 33 Equation of motion PotentialPotential

34. 34 HomogeneityHomogeneity The energy density of the particles must be small enough to allow linearized treatment of the fluctuations All times and frequencies

35. 35 NucleosyntesisNucleosyntesis This constraint is slightly stronger than the previous. It prohibits too intense fields at the epoch of light nuclei formation

36. 36 Seed condition Lower buond on energy density. It’s the minimal intensity that allows the dynamo to be started up. Well defined time and frequency

37. 37 Growing spectrum Nucleosyntesis constraint does not allow the spectrum to be decreasing with frequency Model dependent

38. 38 Advanced LIGO We are interested in the study of relic gravitational waves detectable from next generation interferometers Sensibility of Advanced LIGO ’s antennae fixes a lower bound on the energy density of the gravitons produced

39. 39 Pulsars timing measurements Up to now no variation of the pulsar period has been found that can be explained by the presence of relic gravitational waves Energy density must be small enough for frequencies of the order of the inverse of observation time

40. 40 Growing spectrum Gravitational stability Z(  ) can’t grow too fast in the stringy phase ++ Growing dilaton condition == Necessity of a growing spectrum

41. 41 New parameters