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Constraining Lorentz Violation using 21cm and CMB Cross Correlations

Bhuwan Joshi, Rahul Kothari, Shyam Chaudhary

Abstract

Lorentz symmetry is a fundamental pillar of modern Physics, yet high-energy theories often predict its violation. One potential signature of such a violation is cosmic birefringence - rotation of the polarization plane of photons due to Chern-Simons coupling in Maxwell's electrodynamics. This rotation angle, aka birefringence angle, depends upon the distance travelled by the photon and is thus different for CMB and 21cm photons. While the rotation angle in CMB, i.e., $α_\mathrm{CMB}$, has been tightly constrained by CMB experiments, the potential of the 21cm cosmological signal to constrain this parameter, as well as constrain $α_\mathrm{21cm}$, remains largely unexplored. In this work, we provide constraints on both these angles by cross-correlating 21cm and CMB signals. Using the Fisher matrix formalism, we give our forecasts for 21cm experiments, including SKA, HIRAX, and PUMA, and Planck like CMB experiment. We find that best constraints $σ_{α_\mathrm{CMB}} \sim 4.4^\circ$ and $σ_{α_\mathrm{21cm}} \sim 100^\circ$ are found using $C_\ell^{T_{21} B_\mathrm{CMB}}$ and $C_\ell^{T_{21} B_{21}}$ respectively. Since birefringence hasn't yet been detected in 21cm, we choose the fiducial value $α_\mathrm{21cm}^\mathrm{fid}=0$ assuming the null hypothesis.

Constraining Lorentz Violation using 21cm and CMB Cross Correlations

Abstract

Lorentz symmetry is a fundamental pillar of modern Physics, yet high-energy theories often predict its violation. One potential signature of such a violation is cosmic birefringence - rotation of the polarization plane of photons due to Chern-Simons coupling in Maxwell's electrodynamics. This rotation angle, aka birefringence angle, depends upon the distance travelled by the photon and is thus different for CMB and 21cm photons. While the rotation angle in CMB, i.e., , has been tightly constrained by CMB experiments, the potential of the 21cm cosmological signal to constrain this parameter, as well as constrain , remains largely unexplored. In this work, we provide constraints on both these angles by cross-correlating 21cm and CMB signals. Using the Fisher matrix formalism, we give our forecasts for 21cm experiments, including SKA, HIRAX, and PUMA, and Planck like CMB experiment. We find that best constraints and are found using and respectively. Since birefringence hasn't yet been detected in 21cm, we choose the fiducial value assuming the null hypothesis.
Paper Structure (12 sections, 33 equations, 2 figures, 1 table)

This paper contains 12 sections, 33 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Modifying Maxwell Electrodynamics for testing Lorentz Violation
  3. CMB and 21cm Line as cosmological probes
  4. CMB Temperature Anisotropies and Polarization
  5. CMB Noise Power Spectra
  6. Brightness Temperature and Polarization of 21cm Line
  7. Instrumental Noise for 21cm Signal
  8. Cross Correlations for studying Lorentz Violation
  9. Fisher Forecasts
  10. Effects of 21cm Foregrounds and Window Function
  11. Results and Discussion
  12. Conclusion and Outlook

Figures (2)

  • Figure 1: Cumulative error on the birefringence angle $\alpha_\mathrm{CMB}$ (in degrees) as a function of redshift using various correlations. In these plots, we have used $\alpha_\mathrm{CMB}^\mathrm{fid} = 0.3\degree$. The bin-width for the Dirac window function is chosen to be $\Delta z= 0.1$. The correlations considered are left:$C_{\ell}^{T_{21} B_{\mathrm{CMB}}}$ and right:$C_{\ell}^{E_{21} B_{\mathrm{CMB}}}$. It is clear that $C_{\ell}^{T_{21} B_{\mathrm{CMB}}}$ gives the best constraint on $\alpha_\mathrm{CMB}$.
  • Figure 2: Cumulative error on birefringence angle $\alpha_\mathrm{21cm}$ (in degrees) as a function of redshift using various correlations. Here, we've used $\alpha_\mathrm{21cm}^\mathrm{fid} = 0$ (for discussion, see § \ref{['sec:cross_cor_def_eq']}). Row 1: left $C_{\ell}^{T_{21}B_{21}}$ and right:$C_{\ell}^{E_{21}B_{21}}$, Row 2:left:$C_{\ell}^{T_{\mathrm{CMB}} B_{21}}$ and right:$C_{\ell}^{E_{\mathrm{CMB}} B_{21}}$. It is clear that $C_{\ell}^{T_{21}B_{21}}$ has the best constraining power out of all possibilities.