BINGO: a code for the efficient computation of the scalar bi-spectrum

Hazra, Dhiraj Kumar; Sriramkumar, L.; Martin, Jérôme

doi:10.1088/1475-7516/2013/05/026

Cited by 103 publications

(186 citation statements)

References 147 publications

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“…ground and the perturbation equations using BINGO [20] without any approximations. We search for the best fit in the vicinity of the ζ ∼ 1.2 (to generate a Tanh step like scalar PPS) and ζ ∼ 2 (to generate a broken scalar PPS) using Powell's BOBYQA minimization algorithm.…”

Section: Resultsmentioning

confidence: 99%

“…However this model is interesting, since it is able to provide a balance between Planck low-ℓ suppression and BICEP2 B-mode data. For the evaluation of background and perturbation equations for the potential we have used the publicly available code BINGO [20]. The potential that we are using from [5] is very similar to [12] in the limit ζ = 1.…”

Section: Formalismmentioning

confidence: 99%

See 1 more Smart Citation

Ruling out the power-law form of the scalar primordial spectrum

Hazra

Shafieloo

Smoot

et al. 2014

J. Cosmol. Astropart. Phys.

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Abstract. Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than 3σ CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the form of the primordial scalar perturbation spectrum, similar to what we studied recently analyzing Planck data [4], can address both Planck and BICEP2 results simultaneously. Our findings also indicate that the data may require more flexibilities than what running of scalar spectral index can provide. Finally we show that an inflaton potential, originally appeared in [5], can generate both the step and the break model of scalar primordial spectrum in two different limits. The discussed potential is found to be favored by Planck data but marginally disfavored by BICEP2 results as it produces slightly lower amplitude of tensor primordial spectrum. Hence, if the tensor-to-scalar ratio (r) quoted by BICEP2 persists, it is of importance that we generate inflationary models with large r and at the same time provide suppression in scalar primordial spectrum at large scales.

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Section: Resultsmentioning

confidence: 99%

Section: Formalismmentioning

confidence: 99%

Ruling out the power-law form of the scalar primordial spectrum

Hazra

Shafieloo

Smoot

et al. 2014

J. Cosmol. Astropart. Phys.

Self Cite

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show abstract

“…We have introduced a cut-off of the form exp [−κ k/(a H)] and have worked with κ = 0.1, which is known to lead to consistent results [25,38]. We should mention here that we have made the latest version of BINGO publicly available at the URL: http://www.physics.iitm.ac.in/~sriram/bingo/bingo.html.…”

Section: F Nl For An Arbitrary Triangular Configuration Of the Wavenumentioning

confidence: 99%

On the scalar consistency relation away from slow roll

Vijayakumar

Hazra

Sriramkumar

2015

J. Cosmol. Astropart. Phys.

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Abstract. As is well known, the non-Gaussianity parameter f NL , which is often used to characterize the amplitude of the scalar bi-spectrum, can be expressed completely in terms of the scalar spectral index n s in the squeezed limit, a relation that is referred to as the consistency condition. This relation, while it is largely discussed in the context of slow roll inflation, is actually expected to hold in any single field model of inflation, irrespective of the dynamics of the underlying model, provided inflation occurs on the attractor at late times. In this work, we explicitly examine the validity of the consistency relation, analytically as well as numerically, away from slow roll. Analytically, we first arrive at the relation in the simple case of power law inflation. We also consider the non-trivial example of the Starobinsky model involving a linear potential with a sudden change in its slope (which leads to a brief period of fast roll), and establish the condition completely analytically. We then numerically examine the validity of the consistency relation in three inflationary models that lead to the following features in the scalar power spectrum due to departures from slow roll: (i) a sharp cut off at large scales, (ii) a burst of oscillations over an intermediate range of scales, and (iii) small, but repeated, modulations extending over a wide range of scales. It is important to note that it is exactly such spectra that have been found to lead to an improved fit to the CMB data, when compared to the more standard power law primordial spectra, by the Planck team. We evaluate the scalar bi-spectrum for an arbitrary triangular configuration of the wavenumbers in these inflationary models and explicitly illustrate that, in the squeezed limit, the consistency condition is indeed satisfied even in situations consisting of strong deviations from slow roll. We conclude with a brief discussion of the results.

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“…where is the imaginary part and we evaluate the integral from τ 0 to τ e , where τ e is some time sufficiently long after the Hubble crossing horizon, when the modes are frozen [14,15,34,36,37]. It is common to study non-Gaussianity using the parameter f NL defined by…”

Section: Calculation Of the Bispectrummentioning

confidence: 99%

“…If the perturbations followed a perfectly Gaussian distribution the two points correlation function would be enough, but even the most recent observations are compatible with some non-Gaussianity corresponding to f local NL = 2.5 ± 5.7 and f equil NL = −16 ± 70 [8,11], motivating the theoretical study of the conditions which could have generated it. Some recent developments in the study of models which could generate non-Gaussianity and in the detection can be found for example in [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Effects of discontinuities of the derivatives of the inflaton potential

Cadavid

Romano

2015

Eur. Phys. J. C

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We study the effects of a class of features of the inflaton potential, corresponding to discontinuities in its derivatives. We perform fully numerical calculations and derive analytical approximations for the curvature perturbations spectrum and the bispectrum which are in good agreement with the numerical results. The spectrum of primordial perturbations has oscillations around the scale k 0 which leaves the horizon at the time τ 0 when the feature occurs, with the amplitude and phase of the oscillations determined by the size and the order of the discontinuity. The large scale bispectrum in the squeezed and equilateral limits have a very similar form and are linearly suppressed. Both in the squeezed and the equilateral small scale limit the bispectrum has an oscillatory behavior whose phase depends on the parameters determining the discontinuity, and whose amplitude is inversely proportional to the scale. Given the generality of this class of features they could be used to model or classify phenomenologically different types of non-Gaussian features encountered in observational data such as the cosmic microwave background radiation or large scale structure.

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BINGO: a code for the efficient computation of the scalar bi-spectrum

Cited by 103 publications

References 147 publications

Ruling out the power-law form of the scalar primordial spectrum

Ruling out the power-law form of the scalar primordial spectrum

On the scalar consistency relation away from slow roll

Effects of discontinuities of the derivatives of the inflaton potential

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