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CMB at 2x2 order: the dissipation of primordial acoustic waves and the observable part of the associated energy release (1202.0057v2)

Published 1 Feb 2012 in astro-ph.CO, gr-qc, and hep-th

Abstract: Silk damping of primordial small-scale perturbations in the photon-baryon fluid due to diffusion of photons inevitably creates spectral distortions in the CMB. With the proposed CMB experiment PIXIE it might become possible to measure these distortions and thereby constrain the primordial power spectrum at comoving wavenumbers 50 Mpc{-1} < k < 104 Mpc{-1}. Since primordial fluctuations in the CMB on these scales are completely erased by Silk damping, these distortions may provide the only way to shed light on otherwise unobservable aspects of inflationary physics. A consistent treatment of the primordial dissipation problem requires going to second order in perturbation theory, while thermalization of these distortions necessitates consideration of second order in Compton scattering energy transfer. Here we give a full 2x2 treatment for the creation and evolution of spectral distortions due to the acoustic dissipation process, consistently including the effect of polarization and photon mixing in the free streaming regime. We show that 1/3 of the total energy (9/4 larger than previous estimates) stored in small-scale temperature perturbations imprints observable spectral distortions, while the remaining 2/3 only raises the average CMB temperature, an effect that is unobservable. At high redshift dissipation is mainly mediated through the quadrupole anisotropies, while after recombination peculiar motions are most important. During recombination the damping of the higher multipoles is also significant. We compute the average distortion for several examples using CosmoTherm, analyzing their dependence on parameters of the primordial power spectrum. For one of the best fit WMAP7 cosmologies, with n_S=1.027 and n_run=-0.034, the cooling of baryonic matter practically compensates the heating from acoustic dissipation in the mu-era. (abridged)

Citations (177)

Summary

Overview of "CMB at 2×2 order: the dissipation of primordial acoustic waves and the observable part of the associated energy release"

This paper by Chluba, Khatri, and Sunyaev focuses on spectral distortions in the Cosmic Microwave Background (CMB) caused by the damping of primordial acoustic waves. The primary mechanism responsible for these distortions is known as Silk damping, which occurs when small-scale photon-baryon perturbations dissipate due to photon diffusion. These distortions offer a unique window into inflationary physics beyond what is accessible through direct observations of primordial fluctuations, which are erased on small scales due to Silk damping.

The authors emphasize the necessity of a consistent second-order perturbation theory to thoroughly address this primordial dissipation problem. Specifically, they explore both the creation and evolution of spectral distortions arising from acoustic dissipation processes, distinctly incorporating polarization effects and photon mixing in a free-streaming regime. Through this refined analysis, the paper reveals that approximately one-third of the total energy initially stored in small-scale temperature perturbations yields observable spectral distortions, with the remainder only manifesting as a rise in the average CMB temperature.

Theoretical and Empirical Contributions

The paper contributes both theoretically and empirically. On the analytical side, the authors derive and generalize previous work, embedding the second-order effects into the photon Boltzmann equation, including a detailed treatment of photon scattering with energy transfer. Their approach yields expressions for temperature-dependent corrections to the Compton scattering collision integral, and they approximate anisotropic Bremsstrahlung and double Compton emissions.

Empirically, the work uses cosmological parameters from WMAP7, tracking the evolution of these distortions through recombination and free-streaming epochs via the cosmological thermalization code, CosmoTherm. The insightful computation shows that for some cosmologies, such as the WMAP7 best fit, negative μ\mu-distortions (indicative of Bose-Einstein condensation) effectively cancel the positive distortions due to acoustic dissipation.

Key Numerical Insights

  • Energy Contributions: The paper quantitatively asserts that one-third of the dissipated energy results in measurable spectral distortions while two-thirds simply elevate the CMB temperature.
  • Distortion Types: Despite the diverse processes that can result in yy-type distortions (e.g., from reionization and intracluster heating), μ\mu-type distortions are exclusive to high redshift energy injections (z104106z \sim 10^4 - 10^6), making them a critical focus.

Implications for Technology and Future Research

The proposed PIXIE experiment could articulate these distortions, constraining the primordial power spectrum at scales of 50Mpc1k104Mpc150\,{\rm Mpc}^{-1} \lesssim k \lesssim 10^4\,\rm{Mpc}^{-1}. Should this become feasible, it provides the only direct observational approach for probing inflationary dynamics in this range. This has profound implications for understanding structure formation and the Universe's initial conditions.

Additionally, this research implies that further advancements in second-order perturbation theory and computational modeling are necessary, considering additional energy injection scenarios and the potential discovery of fractional pre-recombination distortions.

Conclusion

Overall, while the paper carefully avoids sensationalist claims, it nonetheless underscores a significant advancement in our understanding of CMB spectral distortions resulting from the dissipation of primordial acoustic waves. By elucidating these second-order processes and their observable imprints, it offers a strong theoretical foundation for future experimental endeavors and stimulates further evolution of computational techniques in cosmological studies. The next generation of CMB experiments, such as PIXIE, will be critical in validating these theoretical predictions and potentially unlocking new pathways in cosmological and fundamental physics research.