Quantum gravity in the sky?

by Abhay Ashtekar and Brajesh Gupt.

Quantum gravity effects in the very early Universe can leave observable imprints.


Abhay Ashtekar (picture taken as a postdoc at Oxford University) is the Eberly Professor of Physics and the Director of the Institute for Gravitation and the Cosmos at the Pennsylvania State University.

The inflationary paradigm traces the genesis of the large-scale structure of the cosmos to astonishingly early times. However, at the onset of inflation spacetime curvature is only about 10-14 times the Planck curvature where quantum gravity effects dominate. Therefore, it is natural to ask if the earlier, pre-inflationary phase of dynamics would change observable predictions of standard inflation. The answer is often assumed to be in the negative. Our CQG paper shows that this conclusion is premature. Specifically, in Loop Quantum Cosmology (LQC) there is an unforeseen interplay between the ultraviolet effects that tame the big bang singularity, and dynamics of infrared modes of cosmological perturbations. As a result, imprints of the quantum spacetime geometry in the Planck regime can manifest themselves at the largest angular scales in the CMB.

In LQC, quantum geometry effects dominate in the Planck regime, replacing the big bang by a quantum bounce, where scalar curvature reaches its finite and universal upper bound. Therefore the radius of curvature has a non-zero lower bound, r_{\rm LQC}. Over the last 7 years, techniques have been developed to describe dynamics of the cosmological perturbations on this quantum background geometry, thereby facing the trans-Planckian issues squarely. Standard inflation assumes that observable modes are in the Bunch-Davies (BD) vacuum at the onset of the slow roll. LQC analysis shows that modes with physical wavelength \lambda > r_{\rm LQC} at the bounce experience curvature as they evolve in the Planck regime. Therefore they have excitations over the BD vacuum. While the use of non-BD states has been considered before, in LQC these states are not postulated, or obtained by tweaking the potential, but arrived at from the Planck scale dynamics. Therefore, quantum gravity effects could manifest themselves in the longest wavelength modes in the CMB. Interestingly, recent CMB observations have revealed anomalies at large angular scales, e.g. suppression of power in temperature anisotropy spectrum at \ell<30. As suggested in PLANCK 2015 XVI paper, although these anomalies have been observed only at a ~2-3 \sigma level, they could be “the visible traces of fundamental physical processes occurring in the early Universe”.


Brajesh Gupt (picture taken as a postdoc at Penn State) is a postdoctoral researcher at the Institute for Gravitation and the Cosmos at the Pennsylvania State University.

The question then is whether modes with \lambda > r_{\rm LQC} at the bounce are in the observable range of CMB. The answer depends on the number of e-folds in the pre-inflationary dynamics.  We use the details of quantum geometry to introduce a new principle to constrain this phase of dynamics. Recall that, because `dark energy’ dominates the late time dynamics, there are cosmological horizons. For observations it suffices to restrict oneself to the interior of the 2-sphere obtained by the intersection of the cosmological horizon with the CMB surface. Given a viable inflationary model –e.g. with the Starobinsky potential– one can trace the evolution of this 2-sphere back in time. At the onset of inflation, the radius is astonishingly small, about 107 Planck lengths; by contrast, the proton radius is ~1020 Planck lengths! In LQC, we can evolve the ball back in time all the way to the bounce. Our principle asks that the radius be the minimum allowed by the smallest non-zero eigenvalue of the area operator, called the area gap. This fixes the pre-inflationary history of the cosmological background; for the Strobinsky potential, for example, there are 17 pre-inflationary e-folds. To specify the initial conditions for cosmological perturbations at the bounce, we use a quantum generalization of Penrose’s Weyl curvature hypothesis (discussed in an accompanying CQG+ article).

With these initial conditions, the existing LQC framework leads to specific predictions.  For the temperature-temperature (TT) correlation function, there is excellent agreement with standard inflation for \ell>30 but there is a power suppression at large angular scales, \ell<30. Consequently, the LQC power spectrum provides a better fit to the data than the standard inflation. Our analysis also predicts specific power suppression in the E-mode polarization spectrum, which will be tested in the upcoming data release by PLANCK mission. Furthermore, predictions involving E-mode polarization are distinct from those of non-primordial mechanisms such as the integrated Sachs-Wolf effect. Thus LQC, together with our principles to fix initial conditions, opens a new window to confront quantum gravity with observations. Finally, there is also a feedback from observations to the fundamental theory. By leaving the area gap as a free parameter, we find the value that would provide a best fit to the observed TT spectrum at all angular scales.  The commonly used value in LQC comes from the black hole entropy calculations. Interestingly, it lies well within the 68% confidence level of the PLANCK data, providing an independent probe into the quantum nature of geometry.

At long last, quantum gravity is ready to leave the pristine perch of mathematical physics and dive into cosmological phenomenology.

[1] Ade, P.A.R., Aghanim, N., Akrami, Y., Aluri, P.K., Arnaud, M., Ashdown, M. and Aumont, J. et al. Planck 2015 results-XVI. Isotropy and statistics of the CMB. Astronomy & Astrophysics. 594, A16 (2016).

Read the full article in Classical and Quantum Gravity:
Quantum gravity in the sky: interplay between fundamental theory and observations
Ashtekar and Gupt 2016. Class. Quantum Grav 34014002

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