The full CMB temperature bispectrum from singlefield inflation
Abstract
We compute the full cosmic microwave background temperature bispectrum generated by nonlinearities after singlefield inflation. By integrating the photon temperature at second order along a perturbed geodesic in Newtonian gauge, we derive an expression for the observed temperature fluctuations that, for the first time, clarifies the separation of the gravitational lensing and timedelay effects from the purely secondorder contributions. We then use the secondorder Boltzmann code CosmoLib$2^{\rm nd}$ to calculate these contributions and their bispectrum. Including the perturbations in the photon path, the numerically computed bispectrum exactly matches the expected squeezed limit. Moreover, the analytic squeezedlimit formula reproduces well the signaltonoise and shape of the full bispectrum, potentially facilitating the subtraction of the bias induced by secondorder effects. For a cosmicvariance limited experiment with $l_{\rm max} = 2000$, the bias on a local signal is $f_{\rm NL}^{\rm loc} =0.73$ negligible for equilateral and orthogonal signals. The signaltonoise ratio is unity at $l_{\rm max} \sim 3000$, suggesting that secondorder effects may hopefully be measured in the future.
 Publication:

arXiv eprints
 Pub Date:
 November 2013
 DOI:
 10.48550/arXiv.1311.6105
 arXiv:
 arXiv:1311.6105
 Bibcode:
 2013arXiv1311.6105H
 Keywords:

 Astrophysics  Cosmology and Extragalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 4 pages, 2 figures