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Whole post-bounce tensor spectra in presence of the holonomy corrections. Green points comes from the numerical simulations. Black line is the analytical spectrum from the model given by Eq. 66. Dashed (red and blue) lines represents UV and IR behaviours, in both cases PT ∝ k 2 .
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In this paper we consider tensor perturbations produced at a bounce phase in the presence of holonomy corrections. Here, the bounce phase and holonomy corrections originate from loop quantum cosmology. We rederive formulas for the corrections of a model with scalar field content. Background dynamics with a free scalar field and multifluid potential...
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... In particular we are interested in the tensor mode, which is known as gravitational waves (GWs). The power spectrum of such primordial GWs in LQC has been calculated in previous studies using analytical and numerical approaches [22][23][24]. Those studies used the Bogoliubov transformations to evolve the GWs in LQC. ...
... This enables us to evolve the GWs from the parent universe through the possible deflation, the quantum bounce, the inflation, and any epoch of our interest. In particular, we discuss GWs with the holonomy corrections [23,27,28]. Our formalism is so transparent that we are able to resolve, for example, the IR suppression problem. ...
... The simplest case is to consider a scalar-field free cosmological background during the quantum bounce epoch. An exact form of such an effective mass was derived as a function of proper time in Ref. [23]. Its corresponding 'approximated' function of the conformal time was then provided but only in the classical limit where |t| → ∞ [23]. ...
With the observational advance in recent years, primordial gravitational waves (GWs), known as the tensor-mode cosmic perturbations, in the Loop Quantum Cosmology (LQC) are becoming testable and thus require better framework through which to bridge between the observations and the theories. In this work we present a new formalism that employs the transfer functions to bring the GWs from any epoch, even before the quantum bounce, to a later time, including the present. The evolutionary epochs considered here include the possible deflation, quantum bounce, and inflation. This formalism enables us to predict more accurately the GW power spectrum today. With the ADM formalism for the LQC background dynamics, our approach is equivalent to the commonly used Bogoliubov transformations for evolving the primordial GWs, but more transparent for discussions and easier to calculate due to its nature of being linear algebra dealing with linear perturbations. We utilize this advantage to have resolved the IR suppression problem. We also propose the field-free approximation for the effective mass in the quantum bounce epoch to largely improve the accuracy in the predicted GW power spectrum. Our transfer-function formalism is general in dealing with any linear problems, and thus expected to be equally useful under other context with linearity.
... The criticism is harsh, but until one really knows admissible early universe geometry one cannot rule out the Rovelli [63] approach, or confirm it. In addition, Jakub Mielczarek [65] (2009) considered tensor perturbations produced at a bounce phase in presence of the holonomy corrections. Here bounce phase and holonomy corrections originate from Loop Quantum Cosmology What comes to the fore are corrections due to what is called quantum holonomy, l.. ...
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... The criticism is harsh, but until one really knows admissible early universe geometry one cannot rule out the Rovelli approach, or confirm it. In addition, Jakub Mielczarek [47] (2009) considered tensor gravitational perturbations produced at a bounce phase in presence of the holonomy corrections. Here bounce phase and holonomy corrections originate from Loop Quantum Cosmology . ...
This document will out line what the authors suppose is relevant to squeezed states of initial space time and how that affects both the composition of relic GW, and also gravitons. A side issue to consider is if gravitons can be configured as semi classical "particles" , which is akin to the Pilot model of Quantum Mechanics as embedded in a larger non linear 'deterministic' background. In addition, as the main author has discussed with Stuart Allen in long evening talks, the relative classical embedding of QM will be linkable to upper bounds to the graviton mass, for reasons brought up in the manuscript.
... The criticism is harsh, but until one really knows admissible early universe geometry one cannot rule out the Rovelli approach, or confirm it. In addition, Jakub Mielczarek (2009) ...
In the 12th Marcel Grossmann Meeting, July 9 th , 2009, the author raised the issue of whether early graviton production could affect non-Gaussian contributions to DM density profiles. Non gaussianity of evolving cosmological states is akin to asking if there is a way to get quantum contributions due to squeezed initial vacuum states which act highly non classscially. If particle counting algorithms in graviton production is important as for entropy, and if entropy perturbations affects the density profile of dark matter clumping prifiles, then there is room to ask to what degree initial perturbations affecting structure formation are due to classical/ non linear processes, or more quantum theoretic states. If squeezing of the initial vacuum states is essential in the relic conditions, then quantization is unavoidable. If squeezing is not essential, then coherent initial vacuum states may contribute in semi classical ways to GW production . The end result of this stated inquiry may be answering if or not gravity in the onset of inflation is a quantized field. Or if a highly non linear set of complex initial conditions for gravity can be stated using purely classical models, as T"Hooft, Corda, and others believe. Note, also that Bojowald as of 2008 has left the degree of squeezing of initial vacuum states in the region of space as an open problem. In Bojowald"s model of a cosmological bounce, the degree of squeezing is a measure of what strength the "bounce" from an initial configuration of the universe takes, and how strongly quantum effects contribute to the evolution of the LQG cosmos, after inflation commences. Similar questions are being raised as to the necessity of squeezing of initial vacuum states and if or not coherency of initial states is initially largely achievable, before the rapid expansion of the universe commences. Finally, and not least is a series of questions as to what conditions which would either require high or low frequencies as to relic signals from the big bang. As it is, large spatial dimensions which could induce far lower initial frequencies for relic signals are popular in many string theory models. The author views this assumption as of debatable validity, as well as the assumption made by Arkani Hamid that largely does away with coherency of initial vacuum states and specifies highly quantum , low frequency generation of relic GW.
General relativity has been the dominant paradigm theory of gravity for the last century, it manages to explain a plethora of astronomical and cosmological observations with high accuracy. A major challenge faced by general relativity is, that it predicts a singularity as the beginning of our universe. In this paper, we shall explore a well-known idea in the literature that of the emergent universe and its viability according to Planck 2018 data and BBN constraints.
The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review, prepared within the COST Action CA18108 “Quantum gravity phenomenology in the multi-messenger approach”, is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers.
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is done not only for didactic purposes but also as a (hopefully temporary) necessity in active research. For instance, it is natural to consider the big-bang and cosmological constant problems in an expanding cosmological background. In such a setting, one does not employ the full machinery of general theories of quantum gravity and a number of simplifications take place. We apply the procedure of symmetry reduction to canonical gravity and quantum cosmological scenarios, first in the Wheeler–DeWitt approach in ADM variables (Sect. 10.2) and then within loop quantum cosmology (Sect. 10.3).
We derive the primordial power spectra, spectral indices and runnings of both
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quantum gravitational corrections to the standard inflationary spectra and
spectral indices to the second-order of the slow-roll parameters, and obtain
the observational constraints on the inverse-volume corrections from Planck
2015 data for various values of $\sigma$. Using these constraints we discuss
whether these quantum gravitational corrections lead to measurable signatures
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contributions to inflationary spectra from the inverse-volume corrections could
be well within the range of the detectability of the forthcoming generation of
experiments.
