Probing the inflaton: Small-scale power spectrum constraints from measurements of the CMB energy spectrum (1203.2681v1)

Abstract: In the early Universe, energy stored in small-scale density perturbations is quickly dissipated by Silk-damping, a process that inevitably generates mu- and y-type spectral distortions of the cosmic microwave background (CMB). These spectral distortions depend on the shape and amplitude of the primordial power spectrum at wavenumbers k < 10^4 Mpc^{-1}. Here we study constraints on the primordial power spectrum derived from COBE/FIRAS and forecasted for PIXIE. We show that measurements of mu and y impose strong bounds on the integrated small-scale power, and we demonstrate how to compute these constraints using k-space window functions that account for the effects of thermalization and dissipation physics. We show that COBE/FIRAS places a robust upper limit on the amplitude of the small-scale power spectrum. This limit is about three orders of magnitude stronger than the one derived from primordial black holes in the same scale range. Furthermore, this limit could be improved by another three orders of magnitude with PIXIE, potentially opening up a new window to early Universe physics. To illustrate the power of these constraints, we consider several generic models for the small-scale power spectrum predicted by different inflation scenarios, including running-mass inflation models and inflation scenarios with episodes of particle production. PIXIE could place very tight constraints on these scenarios, potentially even ruling out running-mass inflation models if no distortion is detected. We also show that inflation models with sub-Planckian field excursion that generate detectable tensor perturbations should simultaneously produce a large CMB spectral distortion, a link that could potentially be established by PIXIE.

Probing the Inflaton: Constraints on the Small-Scale Power Spectrum from CMB Energy Spectrum Measurements

This paper investigates a sophisticated approach to constraining the primordial power spectrum on small scales through measurements of the cosmic microwave background (CMB) energy spectrum, specifically $\mu$ and $y$-type spectral distortions. These distortions arise from the dissipation of energy stored in small-scale density perturbations by Silk damping, providing a novel probe into the statistical properties associated with inflationary scenarios.

Key Findings

1. CMB Energy Spectrum as a Constraint: The paper demonstrates how integrated measures of the CMB energy spectrum constrain the primordial power spectrum at wavenumbers $k \lesssim 10^4\,\mathrm{Mpc}^{-1}$. Utilizing data from COBE/FIRAS, the authors establish robust upper limits on the amplitude of the small-scale power spectrum, which are significantly tighter than those derived from primordial black holes within the same range. These constraints can be further tightened with the prospective PIXIE experiment, potentially improving the limits by an additional three orders of magnitude.
2. Model Analysis: Several inflationary models were evaluated, including running-mass inflation models and those entailing episodes of particle production. The paper shows that PIXIE could potentially rule out running-mass inflation models if they fail to predict observed CMB spectral distortions, providing insights into mechanisms with sub-Planckian field excursions. These models link detectable tensor perturbations to large CMB spectral distortions, presenting opportunities for experimental validation.
3. Integral Constraint on Power Spectrum: The discussion on $\mu$ and $y$ window functions in $k$-space offers a computational method for imposing constraints on the power spectrum across a vast range of scales. The equation defining these functions provides a way to translate CMB spectral measurements into specific model constraints, thereby elucidating the trajectory of inflaton dynamics.

Methodology

The authors derived these constraints utilizing numerical simulations and analytical computations focused on the dissipation-induced spectral distortions of the CMB. They accounted for processes such as shear viscosity and thermal conduction within the photon-baryon fluid to compute deviations from a purely blackbody spectra. The constraints are integral by nature, addressing the integrated effect of perturbative modes over extensive periods prior to and during cosmological recombination.

Implications

The constraints established offer several theoretical and observational implications for cosmology:

• Enhanced Model Discrimination: By probing smaller scales, these constraints substantially advance our understanding of inflationary mechanism specifics beyond normal CMB and LSS scale limits.
• Complementary Constraints: The method complement existing observational bounds, including those from primordial black holes (PBHs) and ultracompact minihalos (UCMHs), by providing insights devoid of dependency on particle interactions or deviations from Gaussianity.
• Potential for Discovery: Future prospects pivot on the ability to exploit tools like PIXIE to validate wide-ranging inflationary predictions across scales, thus bridging foundational aspects with empirical observations. This poses an opportunity to address questions regarding the initial conditions for structure formation and particle dynamics in the early Universe.

Conclusion

The paper provides crucial insights into the field of cosmology by advancing methodologies for tracing the primordial power spectrum on scales beyond current observational limits. The proposed approach reinforces the CMB spectrum as a potent vehicle for understanding primordial inflation, laying a comprehensive framework to guide future experimental endeavors in probing the nascent fabric of the Universe.