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Superstring Cosmological Signatures: Magnetic Fields and Gravitational Waves

This study aims to discriminate between Type I and Heterotic superstring models by observing cosmic magnetic fields and primordial gravitational waves. Theoretical constraints and experimental confrontations are performed to determine the allowed parameter space.

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Superstring Cosmological Signatures: Magnetic Fields and Gravitational Waves

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

  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 gravitons • Theoretical and phenomenological constraints • Plot of the allowed regions in the parameter space • Confrontation of the two models by experiments

  3. Cosmic magnetic fields • Magnetic fields on galactic and intergalactic scales: • Amplitude ~ 10-6 Gauss • 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. Seeds 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. Problem Conformal invariance of Maxwell lagrangian + Conformally flat metric Minimal coupling + = Fluctuations not coupled to geometry Inflation doesn’t amplificate the fluctuations

  6. Possible solution 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 We compare the cases =1 (Heterotic superstring) and  =1/2 (Type I superstring)

  7. Action Internal space isotropy Ten dimensional space-time Action for the fluctuation fields i Equation of motion “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

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

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

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

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

  12. Free parameters • 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 • : 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 •  : 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 • H1 : value of the Hubble parameter at 1 Ansatz: H1=Ms=0.1Mp 1 = (Ms/Mp)1/2 ·1011Hz  and s are the only two continuous parameter 0,  and  can assume only discrete values 2-dimensional parameter space

  13. Allowed regions in parameter space

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

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

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

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

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

  20. Interferometer Sensibility

  21. Contribute from internal dimensions

  22. Photons spectrum

  23. Gravitons spectrum

  24. Heterotic Photons  = 1

  25. Type I Photons  = 1/2

  26. PhotonsHeterotic + Type I

  27. Gravitons  (model) independent

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

  29. Pump field Equation of motion in momentum space Solutions

  30. Action Contribution coming from the dimensional reduction

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

  32. Potential Bessel Equation

  33. Equation of motion Potential

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

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

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

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

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

  41. New parameters

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