Magnetic field generation during inflation Chiara Caprini IPhT - PowerPoint PPT Presentation

Magnetic field generation during inflation Chiara Caprini IPhT CEA-Saclay Lorenzo Sorbo and CC arXiv:1407.2809

Cosmological magnetic fields • magnetic fields of microGauss amplitude observed in galaxies, clusters and high redshift objects ( z < 4)

Cosmological magnetic fields • magnetic fields of microGauss amplitude observed in galaxies, clusters and high redshift objects ( z < 4) • correlated on scales of the order of the object size : difficult to explain

Cosmological magnetic fields • magnetic fields of microGauss amplitude observed in galaxies, clusters and high redshift objects ( z < 4) • correlated on scales of the order of the object size : difficult to explain • lower bound on magnetic field amplitude in the intergalactic medium from observation of blazars with gamma ray telescopes B Mpc > 6 · 10 − 18 G Vovk et al 1112.2534 ( B λ ∝ λ − 1 / 2 )

Cosmological magnetic fields • magnetic fields of microGauss amplitude observed in galaxies, clusters and high redshift objects ( z < 4) • correlated on scales of the order of the object size : difficult to explain • lower bound on magnetic field amplitude in the intergalactic medium from observation of blazars with gamma ray telescopes B Mpc > 6 · 10 − 18 G Vovk et al 1112.2534 ( B λ ∝ λ − 1 / 2 ) • the origin is not understood: after recombination (related to structure formation) or primordial?

Primordial magnetic fields • a primordial field permeates the universe: it could explain - observations in all structures and at high redshift - the lower bound in the intergalactic medium

Primordial magnetic fields • a primordial field permeates the universe: it could explain - observations in all structures and at high redshift - the lower bound in the intergalactic medium • many proposed generation mechanisms but no preferred one

Primordial magnetic fields • a primordial field permeates the universe: it could explain - observations in all structures and at high redshift - the lower bound in the intergalactic medium • many proposed generation mechanisms but no preferred one • phase transitions, MHD turbulence, CAUSAL : charge separation + vorticity... • problem: small correlation length and blue spectrum too small seeds on cosmologically relevant scales

Primordial magnetic fields • a primordial field permeates the universe: it could explain - observations in all structures and at high redshift - the lower bound in the intergalactic medium • many proposed generation mechanisms but no preferred one • INFLATION NON CAUSAL : • generation at all scales, spectrum can be red

Primordial magnetic fields • a primordial field permeates the universe: it could explain - observations in all structures and at high redshift - the lower bound in the intergalactic medium • many proposed generation mechanisms but no preferred one • INFLATION NON CAUSAL : • generation at all scales, spectrum can be red L = − 1 4 F µ ν F µ ν need to break conformal invariance otherwise no amplification of vacuum fluctuations

Simple model for MF generation − f 2 ( φ ) ✓ ◆ Z Turner and Widrow 1988 d 4 x √− g S = F µ ν F µ ν Ratra 1992 4 • test field that does not change the background evolution F µ ν

Simple model for MF generation − f 2 ( φ ) ✓ ◆ Z Turner and Widrow 1988 d 4 x √− g S = F µ ν F µ ν Ratra 1992 4 • test field that does not change the background evolution F µ ν • a model for the function: f ( φ ) → f ( τ ) = a ( τ ) n Martin and Yokoyama 0711.4307 Demozzi et al 0907.1030

Simple model for MF generation − f 2 ( φ ) ✓ ◆ Z Turner and Widrow 1988 d 4 x √− g S = F µ ν F µ ν Ratra 1992 4 • test field that does not change the background evolution F µ ν • a model for the function: f ( φ ) → f ( τ ) = a ( τ ) n • equation of motion for the gauge field ✓ ◆ k 2 − n ( n + 1) ¨ A σ + A σ = 0 τ 2

Simple model for MF generation − f 2 ( φ ) ✓ ◆ Z Turner and Widrow 1988 d 4 x √− g S = F µ ν F µ ν Ratra 1992 4 • test field that does not change the background evolution F µ ν • a model for the function: f ( φ ) → f ( τ ) = a ( τ ) n • equation of motion for the gauge field ✓ ◆ k 2 − n ( n + 1) ¨ A σ + A σ = 0 τ 2 amplification at same equation for both helicities large scales � k τ ⌧ 1 parameter n controls the EM field spectrum

Simple model for MF generation − f 2 ( φ ) ✓ ◆ Z Turner and Widrow 1988 d 4 x √− g S = F µ ν F µ ν Ratra 1992 4 • test field that does not change the background evolution F µ ν • a model for the function: f ( φ ) → f ( τ ) = a ( τ ) n • equation of motion for the gauge field ✓ ◆ k 2 − n ( n + 1) ¨ A σ + A σ = 0 τ 2 • generates EM field : after reheating, conductivity in the universe is very large, E-field dissipates away and B-field stays

Simple model for MF generation ✓ k ◆ f ( n ) � d ρ B • MF power spectrum = H 4 � � d ln k H � end

Simple model for MF generation ✓ k ◆ f ( n ) � d ρ B • MF power spectrum = H 4 � � d ln k H � end • interesting regime: scale invariant spectrum ◆ 2 ✓ T reh B Mpc ' 10 − 5 Gauss M pl high values of B-field at large scales for high scale inflation! T reh ' 10 16 GeV B ' 10 − 11 Gauss

Simple model for MF generation ✓ k ◆ f ( n ) � d ρ B • MF power spectrum = H 4 � � d ln k H � end • interesting regime: scale invariant spectrum HOWEVER THERE ARE CONSTRAINTS

Simple model for MF generation ✓ k ◆ f ( n ) � d ρ B • MF power spectrum = H 4 � � d ln k H � end • interesting regime: scale invariant spectrum HOWEVER THERE ARE CONSTRAINTS • avoid strong coupling of the theory : f ≥ 1 n < 0 → − f 2 ✓ ◆ ∂ µ + iA µ 4 F µ ν F µ ν → − 1 4 F µ ν F µ ν + i ¯ ψγ µ ψ f Demozzi et al 0907.1030

Simple model for MF generation ✓ k ◆ f ( n ) � d ρ B • MF power spectrum = H 4 � � d ln k H � end • interesting regime: scale invariant spectrum HOWEVER THERE ARE CONSTRAINTS • avoid strong coupling of the theory : f ≥ 1 n < 0 → • avoid back-reaction of the EM field ρ EM ≤ ρ inf → n > − 2 energy density on the background: Martin and Yokoyama 0711.4307

Simple model for MF generation ✓ k ◆ f ( n ) � d ρ B • MF power spectrum = H 4 � � d ln k H � end • interesting regime: scale invariant spectrum HOWEVER THERE ARE CONSTRAINTS • avoid strong coupling of the theory : f ≥ 1 n < 0 → • avoid back-reaction of the EM field ρ EM ≤ ρ inf → n > − 2 energy density on the background: the spectrum is blue B Mpc < 10 − 32 Gauss T reh ' 10 16 GeV

Simple model for MF generation two methods to reduce back-reaction: 1. lower the scale of inflation 2. reduce the duration of EM field production

Simple model for MF generation two methods to reduce back-reaction: 1. lower the scale of inflation 2. reduce the duration of EM field production Ferreira et al 1305.7151 inflation at 10 MeV + magnetogenesis active only when O(Mpc) scales exit the horizon = MF produced can fulfil lower bound in the IGM

Simple model for MF generation two methods to reduce back-reaction: 1. lower the scale of inflation 2. reduce the duration of EM field production Ferreira et al 1305.7151 inflation at 10 MeV + problem: magnetogenesis active only when O(Mpc) scales exit the horizon too low-scale inflation for BICEP2 = MF produced can fulfil lower bound in the IGM

Problems and possible solutions decouple amplitude from in the previous model the spectrum: spectrum can vary (parameter n) try to increase the EM field but the amplitude is fixed amplitude keeping a MF spectrum as red as possible very low scale inflation is required to enhance the MF the gauge field sources the amplitude and make the tensor perturbations spectrum redder: problem with BICEP2

Add helicity to magnetogenesis ✓ ◆ − 1 4 F µ ν F µ ν − ξ 8 nF µ ν ˜ L = f 2 ( τ ) F µ ν

Add helicity to magnetogenesis ✓ ◆ − 1 4 F µ ν F µ ν − ξ 8 nF µ ν ˜ L = f 2 ( τ ) F µ ν f ( τ ) = a ( τ ) n − 2 < n < 0 1. avoid strong coupling 2. avoid strong back-reaction by the EM 3. get the most red spectrum possible

Add helicity to magnetogenesis ✓ ◆ − 1 4 F µ ν F µ ν − ξ 8 nF µ ν ˜ L = f 2 ( τ ) F µ ν add axial coupling : f ( τ ) = a ( τ ) n 1. controls the EM field amplitude ξ 2. the MF generated is helical so it − 2 < n < 0 evolves by inverse cascade 1. avoid strong coupling 2. avoid strong back-reaction by the EM 3. get the most red spectrum possible the evolution through inverse cascade amplifies the magnetic field at large scales : brings energy there where we need it!

Add helicity to magnetogenesis ✓ ◆ − 1 4 F µ ν F µ ν − ξ 8 nF µ ν ˜ L = f 2 ( τ ) F µ ν • equation of motion in this case : ✓ ◆ τ − n ( n + 1) k 2 + 2 σ ξ k ¨ A σ + A σ = 0 τ 2

Add helicity to magnetogenesis ✓ ◆ − 1 4 F µ ν F µ ν − ξ 8 nF µ ν ˜ L = f 2 ( τ ) F µ ν • equation of motion in this case : ✓ ◆ τ − n ( n + 1) k 2 + 2 σ ξ k ¨ A σ + A σ = 0 τ 2 exponential amplification of only one helicity mode at horizon crossing: generation of helical MF