Gravitational Fluctuations as an Alternative to Inflation III. Numerical Results

Abstract

<jats:p>Power spectra play an important role in the theory of inflation, and their ability to reproduce current observational data to high accuracy is often considered a triumph of inflation, largely because of a lack of credible alternatives. In previous work we introduced an alternative picture for the cosmological power spectra based on the nonperturbative features of the quantum version of Einstein’s gravity, instead of currently popular inflation models based on scalar fields. The key ingredients in this new picture are the appearance of a nontrivial gravitational vacuum condensate (directly related to the observed cosmological constant), and a calculable renormalization group running of Newton’s G on cosmological scales. More importantly, one notes the absence of any fundamental scalar fields in this approach. Results obtained previously were largely based on a semi-analytical treatment, and thus, while generally transparent in their implementation, often suffered from the limitations of various approximations and simplifying assumptions. In this work, we extend and refine our previous calculations by laying out an updated and extended analysis, which now utilizes a set of suitably modified state-of-the-art numerical programs (ISiTGR, MGCAMB and MGCLASS) developed for observational cosmology. As a result, we are able to remove some of the approximations employed in our previous studies, leading to a number of novel and detailed physical predictions. These should help in potentially distinguishing the vacuum condensate picture of quantum gravity from that of other models such as scalar field inflation. Here, besides the matter power spectrum P m ( k ) , we work out, in detail, predictions for what are referred to as the TT, TE, EE, BB angular spectra, as well as their closely related lensing spectra. However, the current limited precision of observational data today (especially on large angular scales) does not allow us yet to clearly prove or disprove either set of ideas. Nevertheless, by exploring in more details the relationship between gravity and cosmological matter and radiation both analytically and numerically, together with an expected future influx of increasingly accurate observational data, one can hope that the new quantum gravitational picture can be subjected to further stringent tests in the near future.</jats:p>

Dyson’s Equations for Quantum Gravity in the Hartree–Fock Approximation

“…Here, in this section, the main concern will be the inclusion of the effects of a running of Newton's G, as given in Equations ( 163), (164), and (161) in the matter power spectrum, as measured for example in current CMB data. Modifications to the matter power spectrum P m (k) at small k originating in a running G(k) can be done either analytically using the transfer function [123,124] or by relying on more comprehensive numerical programs [125]. Analytically, the effect of a running Newton's constant (Equation (163)) can be included via dimensional analysis for the correct factors of G to include, P m (k) → (G 0 /G(k)) 2 P m (k) [124].…”

“…Analytically, the effect of a running Newton's constant (Equation (163)) can be included via dimensional analysis for the correct factors of G to include, P m (k) → (G 0 /G(k)) 2 P m (k) [124]. Here, we will focus instead on the more comprehensive, and more accurate, results that can be obtained by consistently incorporating the running of G in all relevant cosmological equations, and in many more cosmological observables, such as temperature and polarization correlations [125].…”

“…The fact that it exhibits a gentler dip at small k perhaps also provides support for a potentially smaller lattice running coefficient of Equation (164) of approximate value c 0 ≈ 2.29. More details for the most recent constraints on this lattice parameter c 0 are discussed in [124,125]. after all (as discussed earlier, the lowest order Hartree-Fock approximation can be extended to higher order, by including increasingly complex higher loop diagrams, with dressed propagators and vertices still determined self-consistently by a truncated version of the Schwinger-Dyson equations).…”

“…(164) of approximate value c 0 ≈ 2.29. More details for the most recent constraints on this lattice parameter c 0 are discussed in [124,125]. Following similar analysis to determining P m (k), other spectra such as the angular temperature spectrum C T T l , should be fully derivable from the primordial function R o k , or specifically n s , which is set by the scaling of gravitational curvature fluctuations ν.…”

Post-Editorial of “Universe: 5th Anniversary” Special Volume

“…Among the consequences of their approach treated with the classical Riemannian geometric methods, they deal with the geodesic motion under the influence of DM. H. Hamber et al [21] study numerically gravitational fluctuations as a possible alternative to cosmic inflation. In particular, they propose to explain the accurate cosmological power spectra data by means of nonperturbative features of the quantum version of Einstein's gravity.…”