Oscillations in the inflaton potential: Complete numerical treatment and comparison with the recent and forthcoming CMB datasets

Moumita Aich, Dhiraj Kumar Hazra, L. Sriramkumar, and Tarun Souradeep

Phys. Rev. D 87, 083526 – Published 26 April 2013

Abstract

Amongst the multitude of inflationary models currently available, models that lead to features in the primordial scalar spectrum are drawing increasing attention, since certain features have been found to provide a better fit to the cosmic microwave background data than the conventional, nearly scale invariant, primordial spectrum. In this work, we carry out a complete numerical analysis of two models that lead to oscillations over all scales in the scalar power spectrum. We consider the model described by a quadratic potential which is superposed by a sinusoidal modulation and the recently popular axion monodromy model. Since the oscillations continue even on to arc minute scales, in addition to the WMAP data, we also compare the models with the small scale data from ACT. Though, both the models, broadly, result in oscillations in the spectrum; interestingly, we find that, while the monodromy model leads to a considerably better fit to the data in comparison to the standard power law spectrum, the quadratic potential superposed with a sinusoidal modulation does not improve the fit to a similar extent. We also carry out forecasting of the parameters using simulated Planck data for both the models. We show that the Planck mock data performs better in constraining the model parameters as compared to the presently available cosmic microwave background datasets.

Received 20 June 2011

DOI:https://doi.org/10.1103/PhysRevD.87.083526

Authors & Affiliations

Moumita Aich^1,*, Dhiraj Kumar Hazra^2,†, L. Sriramkumar^2,‡, and Tarun Souradeep^1,§

¹IUCAA, Post Bag 4, Ganeshkhind, Pune 411007, India
²Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India

^*Present address: Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Durban, South Africa. aich@ukzn.ac.za
^†Present address: Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk 790-784, Korea. dhiraj@hri.res.in
^‡Present address: Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India. sriram@physics.iitm.ac.in
^§tarun@iucaa.ernet.in

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Vol. 87, Iss. 8 — 15 April 2013

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Images

Figure 1
The difference in $χ_{eff}^{2}$ with respect to the reference model, i.e., $Δ χ_{eff}^{2} = [χ_{eff}^{2} (model) - χ_{eff}^{2} (power law)]$ , in the case of the axion monodromy model has been plotted as a function of the multipole moment for the WMAP seven year data, after binning in the multipole space with $ℓ_{bin} = 10$ . While the figure on top corresponds to the WMAP seven year $T T$ data (for $ℓ > 32$ ), the lower one is for the $T E$ data (for $ℓ > 24$ ).Reuse & Permissions
Figure 2
The scalar power spectra corresponding to the best fit values of the WMAP seven year data for the two inflationary models that we have considered. The solid red and the blue lines (highly oscillating) describe the scalar power spectra in the cases of the chaotic model with a sinusoidal modulation and the axion monodromy model, respectively. The spectrum corresponding to the best fit power law model would essentially be the same as in the chaotic model with sinusoidal modulations, but without any oscillations. The inset highlights the extraordinary extent of persistent oscillations in the case of the monodromy model.Reuse & Permissions
Figure 3
The CMB $T T$ angular power spectra corresponding to the best fit values of the different models for the WMAP seven year data. The red (dots), green (dashed), and the black (solid) curves correspond to the power law model, the chaotic model with sinusoidal modulation and the axion monodromy model, respectively. The gray circles with error bars denote the WMAP seven year unbinned data. The inset highlights the difference in the angular power spectrum between the monodromy model and the power law case. In the case of the axion monodromy model, the tiny and continued oscillations in the power spectrum lead to small improvements in the fit to the data over a wide range of multipoles, which eventually add up to a good extent.Reuse & Permissions
Figure 4
The CMB $T E$ and the $E E$ angular power spectra corresponding to the best fit values of the different models for the WMAP seven year data. The red (dots), green (dashed), and the black (solid) curves represent the $T E / E E$ spectrum (in fact, magnitude of $T E$ spectrum) in the power law case, the chaotic model with sinusoidal modulations and the axion monodromy model, respectively. As in the earlier figure, the insets highlight the difference in the $T E / E E$ spectrum between the monodromy model and the power law case.Reuse & Permissions
Figure 5
One dimensional distributions of the inflationary model parameters from the WMAP-7 (dot-dashed), $WMAP − 7 + ACT$ (dashed), and the Planck (solid) simulated data. We have plotted the constraints on the parameters $m$ , $α$ , $β$ , and $δ$ of the chaotic model with sinusoidal modulations (on the left column) and the parameters $λ$ , $α$ , $β$ , and $δ$ for the axion monodromy model (on the right column). It is evident that the simulated Planck data tightens the bounds on the parameters substantially.Reuse & Permissions
Figure 6
The joint two dimensional constraints on the inflationary model parameters from the WMAP-7, $WMAP − 7 + ACT$ and the Planck simulated data. The figure on top illustrates the joint constrains on the parameters $m$ and $β$ that characterize the chaotic model with sinusoidal modulations, while the lower figure displays the joint constraints on the parameters $λ$ and $β$ that describe the axion monodromy model. Note that the red contours (unfilled with thick dashed lines) are the $1 − σ$ and the $2 − σ$ constraints from WMAP-7, the blue contours (filled) are from $WMAP − 7 + ACT$ , while the small green contours (filled, shaded) are from the simulated Planck data. It is again clear that the simulated Planck data constrains the parameters considerably more than the available data.Reuse & Permissions

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