Journal
PHYSICAL REVIEW D
Volume 91, Issue 12, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.91.123518
Keywords
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Funding
- NASA ATP [NNX11AI95G, NNX14AH53G]
- NASA ROSES [12-EUCLID12-0004]
- NSF CAREER [0844825]
- DOE Grant [DE-SC0011838, DE-FG03-91-ER40682]
- Cornell Graduate School
- U.S. Department of Energy (DOE) [DE-SC0011838] Funding Source: U.S. Department of Energy (DOE)
- Division Of Astronomical Sciences
- Direct For Mathematical & Physical Scien [0844825] Funding Source: National Science Foundation
- NASA [682585, NNX14AH53G] Funding Source: Federal RePORTER
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Non-Gaussianity in the distribution of inflationary perturbations, measurable in statistics of the cosmic microwave background (CMB) and large scale structure fluctuations, can be used to probe nontrivial initial quantum states for these perturbations. The bispectrum shapes predicted for generic non-Bunch-Davies initial states are nonfactorizable (nonseparable) and are highly oscillatory functions of the three constituent wave numbers. This can make the computation of CMB bispectra, in particular, computationally intractable. To efficiently compare with CMB data one needs to construct a separable template that has a significant similarity with the actual shape in momentum space. In this paper we consider a variety of inflationary scenarios, with different nonstandard initial conditions, and how best to construct viable template matches. In addition to implementing commonly used separable polynomial and Fourier bases, we introduce a basis of localized piecewise spline functions. The spline basis is naturally nearly orthogonal, making it easy to implement and to extend to many modes. We show that, in comparison to existing techniques, the spline basis can provide better fits to the true bispectrum, as measured by the cosine between shapes, for sectors of the theory space of general initial states. As such, it offers a useful approach to investigate nontrivial features generated by fundamental properties of the inflationary Universe.
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