Generation of Gravitational Waves due to Magnetohydrodynamic - PowerPoint PPT Presentation

Generation of Gravitational Waves due to Magnetohydrodynamic Turbulence in the Early Universe PhD Final Examination Alberto Roper Pol (PhD candidate) Faculty Advisor: Brian Argrow Research Advisor: Axel Brandenburg Collaborators: Tina Kahniashvili, Arthur Kosowsky & Sayan Mandal University of Colorado at Boulder Laboratory for Atmospheric and Space Physics (LASP) May 8, 2020 A. Roper Pol et al., Geophys. Astrophys. Fluid Dyn. 114 , 130. arXiv:1807.05479 (2020) A. Roper Pol et al., submitted to Phys. Rev. D arXiv:1903.08585 (2020) Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 1 / 52

Overview Introduction and Motivation 1 Evidence of primordial magnetic fields 2 Magnetohydrodynamics 3 Gravitational waves 4 Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 2 / 52

Introduction and Motivation Generation of cosmological gravitational waves (GWs) during phase transitions and inflation Electroweak phase transition ∼ 100 GeV Quantum chromodynamic (QCD) phase transition ∼ 100 MeV Inflation Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 3 / 52

Introduction and Motivation Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 4 / 52

Introduction and Motivation Generation of cosmological gravitational waves (GWs) during phase transitions and inflation Electroweak phase transition ∼ 100 GeV Quantum chromodynamic (QCD) phase transition ∼ 100 MeV Inflation GW radiation as a probe of early universe physics Possibility of GWs detection with Space-based GW detector LISA Pulsar Timing Arrays (PTA) B -mode of CMB polarization Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 5 / 52

Introduction and Motivation Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 6 / 52

Introduction and Motivation LISA Laser Interferometer Space Antenna (LISA) is a space–based GW detector LISA is planned for 2034 LISA was approved in 2017 as one of the main research missions of ESA LISA is composed by three spacecrafts in a distance of Figure: Artist’s impression of LISA from 2.5M km Wikipedia Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 7 / 52

Orbit of LISA Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 8 / 52

Introduction and Motivation Generation of cosmological gravitational waves (GWs) during phase transitions and inflation Electroweak phase transition ∼ 100 GeV Quantum chromodynamic (QCD) phase transition ∼ 100 MeV Inflation GW radiation as a probe of early universe physics Possibility of GWs detection with Space-based GW detector LISA Pulsar Timing Arrays (PTA) B -mode of CMB polarization Magnetohydrodynamic (MHD) sources of GWs: Hydrodynamic turbulence from phase transition bubbles nucleation Primordial magnetic fields Numerical simulations using Pencil Code to solve: Relativistic MHD equations Gravitational waves equation Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 9 / 52

Introduction and Motivation 1 Evidence of primordial magnetic fields 2 Magnetohydrodynamics 3 Gravitational waves 4 Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 10 / 52

Evidence of primordial magnetic fields There are different astrophysical evidences that indicate the presence of a large scale coherent magnetic field. 1 Fermi blazar observations Gamma rays from blazars ( ∼ 1 TeV) interact with extragalactic background light Generation of electron - positron beam Observed power removal from gamma-ray beam 1L. M. Widrow Rev. of Mod. Phys. , 74 775–823 (2002) Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 11 / 52

Evidence of primordial magnetic fields Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 12 / 52

Evidence of primordial magnetic fields Solution Large scale (intergalactic) magnetic fields could deviate the electron-positron from beam in opposite directions Recombination does not happen leading to lose of energy Strength ∼ 10 − 16 G, scale ∼ 100 kpc 2 Origin Intergalactic magnetic fields could have been originated from: Astrophysical or Cosmological seed fields subsequently amplified during structure formation 2A. M. Taylor, I. Vovk, and A. Neronov Astron. & Astrophys. , 529 A144, (2011) Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 13 / 52

Evidence of primordial magnetic fields Helicity Magnetic helicity is observed in present astrophysical objects Fractional magnetic helicity is required in cosmological seed fields Primordial helical magnetic fields require a first order phase transition: Electroweak phase transition (EWPT) t ∼ 10 − 12 s Quantum chromodynamics (QCD) phase transtion t ∼ 10 − 6 s Definition (Magnetic Helicity) � ∇× ) − 1 B � ∇ H = B B · ( ∇ B B B = � A A A · B B B � Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 14 / 52

Introduction and Motivation 1 Evidence of primordial magnetic fields 2 Magnetohydrodynamics 3 Gravitational waves 4 Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 15 / 52

MHD description Right after the electroweak phase transition we can model the plasma using continuum MHD Quark-gluon plasma Charge-neutral, electrically conducting fluid Relativistic magnetohydrodynamic (MHD) equations Ultrarelativistic equation of state p = ρ c 2 / 3 Friedmann–Lemaˆ ıtre–Robertson–Walker model g µν = diag {− 1 , a 2 , a 2 , a 2 } Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 16 / 52

Stress–energy tensor Contributions to the stress-energy tensor γ − 1 T µν = p / c 2 + ρ U µ U ν + pg µν + F µγ F ν 4 g µν F λγ F λγ , � � From fluid motions From magnetic fields: p / c 2 + ρ � � γ 2 u i u j + p δ ij T ij = T ij = − B i B j + δ ij B 2 / 2 Relativistic equation of state: p = ρ c 2 / 3 4–velocity U µ = γ ( c , u i ) 4–potential A µ = ( φ/ c , A i ) 4–current J µ = ( c ρ e , J i ) Faraday tensor F µν = ∂ µ A ν − ∂ ν A µ Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 17 / 52

MHD equations Conservation laws T µν ; ν = 0 Relativistic MHD equations are reduced to 3 MHD equations ∂ ln ρ = − 4 1 J 2 � � 3 ( ∇ ∇ · u ∇ u + u u · ∇ ∇ ∇ ln ρ ) + u · ( J J × B B ) + η J u u u u J B J ∂ t ρ c 2 Du Dt = 1 u u ∇ ln ρ ) − u u u − 1 ∇ ln ρ + 3 B +2 � B ) + η J 2 � 4 c 2 ∇ 3 u ( ∇ ∇ ∇ · u u u + u u · ∇ u ∇ u u u · ( J J J × B B ∇ 4 ρ J J J × B B ρ ∇ ∇ ∇· ( ρν S S S ) ρ c 2 for a flat expanding universe with comoving and normalized p = a 4 p phys , ρ = a 4 ρ phys , B i = a 2 B i , phys , u i , and conformal time t . 3A. Brandenburg, K. Enqvist, and P. Olesen, Phys. Rev. D 54 , 1291 (1996) Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 18 / 52

MHD equations Electromagnetic fields are obtained from Faraday tensor as E = −∇ φ − ∂ A B = ∇ × A , ∂ t Generalized Ohm’s law E = η J − u × B Maxwell equations ∇ · E = ρ e c 2 , ∇ · B = 0 ∇ × B = J + ✚✚✚ ❩❩❩ ✚ ∂ B 1 ∂ E ∂ t = −∇ × E ❩ c 2 ∂ t Maxwell equations + Ohm’s law combined: ∂ B B B ∇ ∂ t = ∇ ∇ × ( u u u × B B B − η J J J ) Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 19 / 52

Evolution of magnetic strength and correlation length Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 20 / 52

Introduction and Motivation 1 Evidence of primordial magnetic fields 2 Magnetohydrodynamics 3 Gravitational waves 4 Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 21 / 52

Gravitational waves equation GWs equation for an expanding flat Universe Assumptions: isotropic and homogeneous Universe ıtre–Robertson–Walker (FLRW) metric γ ij = a 2 δ ij Friedmann–Lemaˆ Tensor-mode perturbations above the FLRW model: g ij = a 2 � � δ ij + h phys ij GWs equation is 4 ❆ a ′′ ✁ h ij = 16 π G � a − c 2 ∇ 2 � ✁ ∂ 2 a c 2 T TT t − ❆ ij ✁ ❆ h ij are rescaled h ij = ah phys ij Comoving spatial coordinates ∇ = a ∇ phys Conformal time d t = a d t phys Comoving stress-energy tensor components T ij = a 4 T phys ij Radiation-dominated epoch such that a ′′ = 0 4L. P. Grishchuk, Sov. Phys. JETP , 40, 409-415 (1974) Alberto Roper Pol (University of Colorado) Gravitational Waves from the early-universe May 8, 2020 22 / 52