Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

Hamber, Herbert W.; Yu, Lu

doi:10.3390/universe5110216

Cited by 3 publications

(27 citation statements)

References 101 publications

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“…The amount of flexibility for inflation has thus led many to question the predictability and ultimate naturalness of such scalar-field based solutions [57,58,59,60,61]. Although the original model of inflation was invented to explain the flatness and horizon problem, it has been convincingly argued that it is not a necessary ingredient to do so [62][63][64][65][66][67][68]. We have argued therefore that the gravitational picture provides a more concrete and natural explanation to the origin and distribution of cosmological matter fluctuations.…”

Section: Resultsmentioning

confidence: 99%

“…Here we note that it is of some interest to explore analytical (as opposed to numerical) methods related to the running of Newton's constant G. One possibility briefly mentioned earlier is the 2 + expansion [38,39,40], which provides an estimate for the scaling exponent ν −1 to be between 2 and 4.4, through a one-and two-loop double expansion (in G and the dimension) respectively, giving additional confidence in the numerically computed value ν −1 3. Similar estimates for the exponent ν are found within a set of truncated RG equations, directly in four dimensions [43][44][45][46][47][48].…”

Section: Constraining the Running Of G From Cosmologymentioning

confidence: 94%

“…For the present discussion, we will mention that the nonperturbative treatment of quantum gravity via Wilson's 2 + double expansion (in G and the dimension) and the Regge-Wheeler lattice path integral formulation [23] both reveal the existence of a new quantum phase, involving a nontrivial gravitational vacuum condensate [16]. Along with this comes a nonperturbative characteristic correlation length scale, ξ, and a new set of non-trivial scaling exponents, as is common for well-studied perturbatively non-renormalizable theories ν [24][25][26][27][28][29][30][31]. Together, these two parameters characterize quantum corrections to physical observables such as the long-distance behavior of invariant correlation functions, as well as the renormalization group (RG) running of Newton's constant G. In particular, in can be shown [16,32]…”

Section: Nonperturbative Approach To Quantum Gravitymentioning

confidence: 98%

“…The combination that is most naturally identified with ξ would be ξ ∼ 3/λ 5300 Mpc [37,16]. The other key quantity, the universal scaling dimension ν, can be evaluated via a number of methods, many of which are summarized in [36,[38][39][40][41][42][43][44][45][46][47][48]. Multiple avenues point to an indication of ν −1 3, which here will serve as a good working value for this parameter.…”

Section: Nonperturbative Approach To Quantum Gravitymentioning

confidence: 99%

“…The conventional explanation of the shape of these power spectra is provided by inflation, which is based on the hypothesis of additional primordial scalar fields called inflatons [11,12,13]. The shape of the power spectrum is thus derived from quantum fluctuation of these primordial inflaton fields, and the agreement of this prediction with observations to high accuracy has been widely regarded as a great triumph and confirmation for inflation [14].…”

Section: Introductionmentioning

confidence: 99%

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Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

Hamber¹,

Yu²

2019

Preprint

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Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum $ P(k) $ and the CMB temperature angular power spectrum $ C_l $’s to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of inflation models based on scalar fields. In this work, we review the basic concepts and provide further in-depth investigations. We first update the analysis with more recent data sets and error analysis, and then extend our predictions to the CMB angular spectrum coefficients $ C_l $, which we did not consider previously. Then we investigate further the potential freedoms and uncertainties associated with the fundamental parameters that are part of this picture, and show how recent cosmological data provides significant constraints on these quantities. Overall, we find good general consistency between theory and data, even potentially favoring the gravitationally-motivated picture at the largest scales. We summarize our results by outlining how this picture can be tested in the near future with increasingly accurate astrophysical measurements.

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Section: Resultsmentioning

confidence: 99%

Section: Constraining the Running Of G From Cosmologymentioning

confidence: 94%

Section: Nonperturbative Approach To Quantum Gravitymentioning

confidence: 98%

Section: Nonperturbative Approach To Quantum Gravitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

Hamber¹,

Yu²

2019

Preprint

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

Hamber

2021

Symmetry

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Unlike scalar and gauge field theories in four dimensions, gravity is not perturbatively renormalizable and as a result perturbation theory is badly divergent. Often the method of choice for investigating nonperturbative effects has been the lattice formulation, and in the case of gravity the Regge–Wheeler lattice path integral lends itself well for that purpose. Nevertheless, lattice methods ultimately rely on extensive numerical calculations, leaving a desire for alternate methods that can be pursued analytically. In this work, we outline the Hartree–Fock approximation to quantum gravity, along lines which are analogous to what is done for scalar fields and gauge theories. The starting point is Dyson’s equations, a closed set of integral equations which relate various physical amplitudes involving graviton propagators, vertex functions, and proper self-energies. Such equations are in general difficult to solve, and as a result they are not very useful in practice, but nevertheless provide a basis for subsequent approximations. This is where the Hartree–Fock approximation comes in, whereby lowest order diagrams get partially dressed by the use of fully interacting Green’s function and self-energies, which then lead to a set of self-consistent integral equations. The resulting nonlinear equations for the graviton self-energy show some remarkable features that clearly distinguish it from the scalar and gauge theory cases. Specifically, for quantum gravity one finds a nontrivial ultraviolet fixed point in Newton’s constant G for spacetime dimensions greater than two, and nontrivial scaling dimensions between d=2 and d=4, above which one obtains Gaussian exponents. In addition, the Hartree–Fock approximation gives an explicit analytic expression for the renormalization group running of Newton’s constant, suggesting gravitational antiscreening with Newton’s constant slowly increasing on cosmological scales.

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Gravitational Fluctuations as an Alternative to Inflation III. Numerical Results

Hamber

Kankanamge

2020

Universe

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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.

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Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

Cited by 3 publications

References 101 publications

Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

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

Gravitational Fluctuations as an Alternative to Inflation III. Numerical Results

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