Universit degli Studi di Bari Facolt di Scienze
Università degli Studi di Bari Facoltà di Scienze Matematiche, Fisiche e Naturali Dipartimento di Fisica & INFN Stefano Nicotri Observable (? ) cosmological signatures of superstrings in pre-big bang models of inflation Based on PLB 633 155 (2006), with M. Gasperini 1
Main aim Discriminate between the Type I end the Heterotic superstring model through cross correlated observations of cosmic magnetic fields and primordial gravitationalwaves 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 2
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. 3
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. 4
Problem Conformal invariance of Maxwell lagrangian + Minimal coupling + Conformally flat metric = Fluctuations not coupled to geometry Inflation doesn’t amplificate the fluctuations 5
Possible solution Superstring theory predicts the existence of the dilaton , a scalar field which is nonminimally 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) 6
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 7
Minimal pre-Big Bang Model s = 1/ s 1 = 1/ 1 8
This choice determinates: We can get the physical parameters: Number of pairs produced from the vacuum • • • Pump field Differential Equation ofenergy motiondensity (Bessel equation) Solutions (amplification) Spectral energy density 9
Spectral energy density Photons Gravitons Free (? ) parameters that we shall discuss later Photons spectrum is model dependent while gravitons spectrum is model independent 10
Constraints shared by both spectra: • • • Homogeneity Nucleosyntesis Growing spectrum Constraints for the E. M. spectrum • Seed condition Constraints for the gravitons spectrum • Visibility by Advanced LIGO • Pulsar timing measurement 11
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 • H 1 : value of the Hubble parameter at 1 Ansatz: H 1=Ms=0. 1 Mp 0, and can assume only discrete values 1 = (Ms/Mp)1/2 · 1011 Hz and s are the only two continuous parameter 2 -dimensional parameter space 12
Allowed regions in parameter space 13
Contribution from internal dimensions Internal dimensions do not give any How does superposition region substantial contribution change? 14
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 15
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 An efficient production of magnetic “seeds” is not compatible with the production of relic gravitons detectable by Advanced LIGO 16
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 17
Experiments 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 No detection of relic gravitons by Advanced LIGO = Experimental support to Heterotic superstring model 18
Thanks to R. Anglani, P. Colangelo, F. De Fazio, R. Ferrandes, M. Gasperini, M. Lucente, M. Ruggieri Thank you for patience and attention 19
Interferometer Sensibility 20
Contribute from internal dimensions 21
Photons spectrum 22
Gravitons spectrum 23
Heterotic Photons = 1 24
Type I Photons = 1/2 25
Photons Heterotic + Type I 26
Gravitons (model) independent 27
Solutions Equations of motion Cosmological expansion has NO effect on the fluctuations 28
Pump field Equation of motion in momentum space Solutions 29
Action Contribution coming from the dimensional reduction 30
Action for the fluctuations ? Z( ) is the “pump field” which Evolution apmlificates the equation fluctuations 31
Potential Bessel Equation 32
Equation of motion Potential 33
Homogeneity The energy density of the particles must be small enough to allow linearized treatment of the fluctuations All times and frequencies 34
Nucleosyntesis This constraint is slightly stronger than the previous. It prohibits too intense fields at the epoch of light nuclei formation 35
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 36
Growing spectrum Nucleosyntesis constraint does not allow the spectrum to be decreasing with frequency Model dependent 37
Advanced LIGO Sensibility of Advanced LIGO ’s antennae fixes a lower bound on the energy density of the We are gravitons interestedproduced in the study of relic gravitational waves detectable from next generation interferometers 38
Pulsars timing measurements Energy density must be small Up to now variation ofofthe enough fornofrequencies the pulsar period hasinverse been found order of the of that can be explained observation timeby the presence of relic gravitational waves 39
Growing spectrum Gravitational stability = + Necessity of too a growing Z( ) can’t grow fast in the Growing dilaton condition stringy phase spectrum 40
New parameters 41
- Slides: 41