- The paper demonstrates that power-law inflation models face significant constraints due to the reheating phase, characterized by an effective equation-of-state parameter.
- It reveals that the m²φ² (α = 2) model aligns with observations under canonical reheating, while other power-law indices require physically challenging conditions unless ns shifts significantly.
- A derived correlation between reheating temperature and the scalar spectral index underscores that precise ns measurements can decisively differentiate viable inflationary scenarios.
Analysis of Reheating Constraints to Inflationary Models
The paper "Reheating constraints to inflationary models" by Liang Dai, Marc Kamionkowski, and Junpu Wang addresses an essential aspect of cosmology that connects inflationary theories with observational data—analyzing the constraints on inflationary models arisen from the dynamics of the reheating period. Utilizing data from the BICEP2 experiment, the authors investigate how the reheating phase following inflation can influence the parameterization and viability of different inflationary potentials.
Key Findings and Methodology
The paper focuses on the implications of potential inflationary models, specifically power-law potentials characterized by the relation V(ϕ)∝ϕα. The paper examines how these models are affected by reheating, which is depicted by an effective equation-of-state parameter wre. The canonical value for reheating in this framework is wre=0.
The authors demonstrate several points:
- Consistency of α=2: For the α=2 "chaotic" model, consistency is retained with wre=0 for scalar spectral index values ns within the current 1σ observational bounds. However, models where α=1 or α=2/3 require a reheating phase characterized by −1/3<wre<0 unless ns is higher than its 1σ range.
- High α Models: Models where α=4 necessitate wre>1/3, a regime considered physically implausible unless ns lies near the lower limit of the 2σ range.
- Reheat Temperature and ns Relationship: For the α=2 inflation model with canonical reheating, a correlation between the reheating temperature Tre and ns is derived: log10(Tre/106GeV)≃2000(ns−0.96). A higher Tre up to the Grand Unified Theory scale suggests ns nearing 0.965 at the pivot scale k=0.05Mpc−1.
The formalism employs equations linking the number of e-folds from the end of inflation to the present-day observation scale with variables characterizing the reheating and radiation-dominated epochs. Based on current measurements, particularly the scalar spectral index ns, the paper delineates the constraints on Nre, the duration of reheating, and the corresponding reheating temperatures.
Implications
The calculations in this paper reveal critical insights into the nature of power-law potentials for inflaton fields and underline the role of reheating in differentiating amongst these models. The specific case of m2ϕ2 inflation is shown to be reconcilable with simple reheating scenarios, standing favored over other power-law indices in the face of present observational accuracies.
The implications extend to future observational efforts, predominantly focusing on the precise measurement of ns. The refined data could fundamentally aid in distinguishing the most tenable inflation models and enhance understanding of the reheating epoch, offering a complementary avenue to anticipated Cosmic Microwave Background (CMB) observations.
Future Prospects
This work underscores the emerging interplay between theoretical constructs of inflation and the phenomenology of reheating. As empirical techniques advance, the post-inflationary universe, specifically through gravitational wave observations and refined measurement in cosmological parameters such as ns, r (tensor-to-scalar ratio), and Tre, becomes a promising frontier for frontier cosmological analysis.
In summary, the paper establishes groundwork that bridges inflationary theory and observational constraints through reheating dynamics, guiding prospective research towards scrutinized inflationary models and their respective implications on early universe cosmology.