Oral Defense: A Truncated Primordial Power Spectrum and Its Impact on Inflation

Abstract: Large-scale anomalies in the Cosmic Microwave Background (CMB), including the lack of large-angle correlations in the temperature correlation function and the low power anomaly of the temperature angular power spectrum, have been significant challenges to the standard model for two decades. One likely solution to these anomalies is to introduce a hard cutoff k_min at the large-scale end of the primordial power spectrum. The evidence for the existence of k_min, provided by the temperature fluctuations in the CMB, is already quite compelling.

Based on this, in this thesis, we show that k_min is not just a statistical feature of the primordial power spectrum; it actually implies a delayed initiation of inflation. k_min can be used as a strong constraint to limit the initial conditions of inflation. We begin our study with a systematic analysis of the impact of k_min on slow-roll inflationary models, demonstrating that most, if not all, slow-roll models cannot solve the horizon problem with this new constraint. We then take a further step, co-analyzing the impact of k_min and several other severe post Planck challenges to conventional models. The results show that without some exotic modification to the conventional inflation picture, it is impossible to solve all the difficulties, implying that the conventional picture needs significant revision or perhaps it simply never happened.

To support such a strong statement associated with k_min, we systematically study the impact of k_min on CMB measurements across all the temperature and polarization measurements. In all cases where we have measurements to compare to, introducing k_min significantly reduces the discrepancies between the theoretical predictions and the data. As for the B mode, although we have no data to compare to, our analysis shows that k_min affects the B mode angular power spectrum and angular correlation function in measurable ways, particularly if the tensor-to-scalar ratio “r” is not much smaller than its current upper limit. This can be used to confirm or deny the existence of k_min. 

In summary, our results show that the new constraint from k_min, combined with other post Planck constraints, rules out the conventional inflationary models. On the other hand, our results confirm the existence of k_min with the current measurements and highlight the importance and potential of using upcoming B mode observations to verify or deny the existence of k_min.

Zoom Link: https://arizona.zoom.us/j/4222006763?omn=88510137178 Password: inflation