Gravitational Radiation from Symmetry Breaking Kate Jones-Smith Harsh
Gravitational Radiation from Symmetry Breaking Kate Jones-Smith Harsh Mathur, Lawrence Krauss CWRU BCCS Workshop December 9 2008 Motivation
Primordial gravity waves a smoking gun of inflation? Similar (scale-invariant) spectrum from symmetry breaking scalar field ( KJS, Mathur &Krauss, PRL,2008; Krauss, Phys.Lett1992) Polarization as probe of symmetry breaking on grand unified scale? Extend to include more general case of gauge field (work in progress)
Symmetry Breaking symmetry broken as field relaxes to ground state minima comprise ground state manifold field free to roam the 2-component field in Mexican hat potential
manifold Idea What happens if symmetry breaking scalar field exists in expanding universe? initially disordered scalar field correlated domains form as horizon grows
As field relaxes and aligns, energy released in the form of gravitational radiation. Symmetry Breaking scalar field equation of motion Generally, only solvable numerically Mazenko (1985), Turok & Spergel (1991) Our Model
N-dimensional scalar field, governed by Lagrangian and subject to non-linear sigma model constraint: , Assumptions Background metric is flat FRW Linearized gravity regime
N is large allows for analytic solution corrections go as 1/N ignore massive mode Key Features For two-point correlator, solution has scaling form with
arising from NLSM constraint. Thus, Field components remain gaussian Four-point and higher correlators via Wicks Theorem In linear regime,
, strain decomposed into scalar, vector, and tensor components: (Gauge-invariant) tensor component obeys sourced wave equation Source hence is transverse stress due to scalar field,
is quadratic in Key Results Scale invariant power spectrum Non-Gaussian Comparison to Inflation
Scale invariant power spectrum =0 scale invariant if gravity waves of all wavelengths produced initially, then just redshift as they enter horizon Source-free evolution Gaussian distributed correlations
Connecting to Observations Observable quantity is polarization Thomson scattering, quadrupole anisotropy yields linearly polarized light Polarization matrix is 2x2 traceless, symmetric E and B modes
Polarization Stokes parameters For linearly polarized light of given intensity, Polarization contd 2x2 traceless, symmetric; can be expressed as 2 scalars
and Like temperature fluctuations, expand in spherical harmonics Boltzmann Equation Describes evolution of energy, polarization of photons Incorporates Thomson scattering Scalar perturbations
Tensor perturbations (gravity waves) Solvable numerically with CMBFast, CAMB, etc. Linear, hence Only tensor perturbations contribute to B mode Compare/Contrast Inflation: D unsourced so correlations
remain Gaussian Weinberg(2007) Our mechanism: D sourced so correlations non-Gaussian Plot coming soon!
Summary & Future Work Summary Analytic solution for symmetry breaking scalar field in expanding universe Scale-invariant power spectrum of gravity waves by virtue of causality (mimics inflation) Constructed code for evolving sourced Einstein equation (more general than CMBFast) Future Work Determine polarization signature from scalar field case (definitely non-Gaussian)
Extend the analysis to include the more general (and interesting) case of gauge field
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