Forecasting constraints from the cosmic microwave background on eternal inflation

Stephen M. Feeney, Franz Elsner, Matthew C. Johnson, and Hiranya V. Peiris

Phys. Rev. D 92, 083515 – Published 16 October 2015

Abstract

We forecast the ability of cosmic microwave background (CMB) temperature and polarization data sets to constrain theories of eternal inflation using cosmic bubble collisions. Using the Fisher matrix formalism, we determine both the overall detectability of bubble collisions and the constraints achievable on the fundamental parameters describing the underlying theory. The CMB signatures considered are based on state-of-the-art numerical relativistic simulations of the bubble collision spacetime, evolved using the full temperature and polarization transfer functions. Comparing a theoretical cosmic-variance-limited experiment to the WMAP and Planck satellites, we find that there is no improvement to be gained from future temperature data, that adding polarization improves detectability by approximately 30%, and that cosmic-variance-limited polarization data offer only marginal improvements over Planck. The fundamental parameter constraints achievable depend on the precise values of the tensor-to-scalar ratio and energy density in (negative) spatial curvature. For a tensor-to-scalar ratio of 0.1 and spatial curvature at the level of $1 0^{- 4}$ , using cosmic-variance-limited data it is possible to measure the width of the potential barrier separating the inflating false vacuum from the true vacuum down to $M_{Pl} / 500$ , and the initial proper distance between colliding bubbles to a factor $π / 2$ of the false vacuum horizon size (at three sigma). We conclude that very near-future data will have the final word on bubble collisions in the CMB.

Received 15 June 2015

DOI:https://doi.org/10.1103/PhysRevD.92.083515

Authors & Affiliations

Stephen M. Feeney^1,*, Franz Elsner^2,†, Matthew C. Johnson^3,4,‡, and Hiranya V. Peiris^2,§

¹Astrophysics Group, Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, United Kingdom
²Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
³Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
⁴Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada

^*s.feeney@imperial.ac.uk
^†f.elsner@ucl.ac.uk
^‡mjohnson@perimeterinstitute.ca
^§h.peiris@ucl.ac.uk

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Issue

Vol. 92, Iss. 8 — 15 October 2015

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Images

Figure 1
An example of a potential giving rise to eternal inflation with two possible types of bubbles. The components of the potential determining the various parameters in Eq. (1) are labeled.
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Figure 2
In the left panel, we show the geometry of a bubble collision on the surface of last scattering. Shaded regions are affected by the collision, while unshaded regions are not. The observer is located at the origin, and the circle represents their past light cone. In the right panel, we show the mapping between the observed angular radius of the collision $θ_{c}$ in degrees and the comoving position of the collision boundary $x_{c}$ in Mpc.
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Figure 3
The induced signal in the three-dimensional curvature perturbation (left panel, shown on shells centered on the observer out to the last scattering surface) results in radially symmetric features in the CMB. Right panel: With the direction of the bubble collision in the center of the plot, we show Mollweide projections of the corresponding templates in temperature (upper half) and polarization (lower half) in dimensionless units.
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Figure 4
Contour plots of the fractional marginalized uncertainty on the Lagrangian parameters (dashed, red to orange) for signatures with $x_{c} = 1$ (left column) and 13 Gpc (right column). Regions of parameter space in which different components are distinguishable from zero at $3 σ$ are indicated by shading. In dark grey regions, none of the amplitudes is detectable; in mid-grey regions, $R_{0}$ is detectable but $R_{0}^{L}$ and $R_{0}^{Q}$ are not; in light grey hatched regions, $R_{0}^{L}$ is detectable in addition to $R_{0}$ ; in light grey hatched regions, $R_{0}^{Q}$ is detectable in addition to $R_{0}$ . In white regions all amplitudes are detectable.
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Figure 5
Amplitudes detectable at $3 σ$ using temperature-only (left), polarization-only (center) and combined temperature and polarization (right) data from WMAP7 (orange), Planck (red) and a cosmic-variance-limited experiment (dark red). Detectable values of $R_{0}$ are indicated with solid lines, $R_{0}^{L}$ with long-dashed lines and $R_{0}^{Q}$ with short-dashed lines.
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Figure 6
At large scales, the temperature and polarization transfer functions behave qualitatively differently. While for polarization, they remain positive over the full width of the last scattering surface (black solid line, scale shown on the right y-axis), for temperature, a change of sign occurs, leading to partial cancellation of the curvature perturbation contribution to the template signal (blue solid line, scale shown on the left y-axis).
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