We show that, by using resummation techniques based on the extension of the methods of Yennie, Frautschi and Suura to Feynman's formulation of Einstein's theory, we get quantum field theoretic predictions for the UV fixed-point values of the dimensionless gravitational and cosmological constants. Connections to the phenomenological asymptotic safety analysis of Planck scale cosmology by Bonanno and Reuter are discussed.
Planck Scale Cosmology and Asymptotic Safety in Resummed Quantum Gravity
在Weinberg的渐近安全方法中，一个UV稳定不动点的有限维临界面产生了一个具有有限个物理参数的量子引力理论。我们认为，在费曼的原始配方的理论的延伸，我们恢复这个不动点UV行为从一个确切的重新安排各自的微扰系列。我们的结果与Alberter { \it et al.}并与Kreimer的最近的Hopf-代数Dyson-Schwinger重整化理论结果进行了比较。我们得到了无量纲引力常数和宇宙学常数的第一性原理预言，我们的结果支持了Bonanno和Schmidter的普朗克尺度宇宙学.最后，我们对目前观测到的宇宙学常数值进行了估计。
We investigate the observational signatures of quantum cosmology in the Cosmic Microwave Background data provided by Planck collaboration. We apply the warm inflationary paradigm with a tachyon scalar field to the loop quantum cosmology. In this context, we first provide the basic cosmological functions in terms of the tachyon field. We then obtain the slow-roll parameters and the power spectrum of scalar and tensor fluctuations respectively. Finally, we study the performance of various warm inflationary scenarios against the latest Planck data and we find a family of models which are in agree…
We present an overview of the phenomenological implications of the theory of resummed quantum gravity. We discuss its prediction for the cosmological constant in the context of the Planck scale cosmology of Bonanno and Reuter, its relationship to Weinberg's asymptotic safety idea, and its relationship to Weinberg's soft graviton resummation theorem. We also discuss constraints and consistency checks of the theory.
Taking into account a fractal structure for the black hole horizon, Barrow argued that the area law of entropy is modified due to quantum-gravitational effects (Barrow in Phys Lett B 808:135643, https://doi.org/10.1016/j.physletb.2020.135643, 2020). Accordingly, the corrected entropy takes the form $S \sim A^{1+\mathrmΔ/2}$, where $0\leq\mathrmΔ\leq1$, indicates the amount of the quantum-gravitational deformation effects. In this paper, based on Barrow entropy, we first derive the modified gravitational field equations through the Clausius relation. We then consider the Friedmann-Lemaître-Robe…
I provide some philosophical groundwork for the recently proposed 'trans-Planckian censorship' conjecture in theoretical physics. In particular, I argue that structure formation in early universe cosmology is, at least as we typically understand it, autonomous with regards to quantum gravity, the high energy physics that governs the Planck regime in our universe. Trans-Planckian censorship is then seen as a means of rendering this autonomy an empirical constraint within ongoing quantum gravity research.
For most initial conditions, cosmologically relevant physical modes were trans-planckian at the bounce time, often by many magnitude orders. We improve the usual loop quantum cosmology calculation of the primordial power spectra -- in the inflationary framework -- by accounting for those trans-planckian effects through modified dispersion relations. This can induce drastic changes in the spectrum, making it either compatible or incompatible with observational data, depending on the details of the choices operated.
A new perspective on the Cosmological Constant Problem (CCP) is proposed and discussed within the multiverse approach of Quantum Cosmology. It is assumed that each member of the ensemble of universes has a characteristic scale $a$ that can be used as integration variable in the partition function. An averaged characteristic scale of the ensemble is estimated by using only members that satisfy the Einstein field equations. The averaged characteristic scale is compatible with the Planck length when considering an ensemble of solutions to the Einstein field equations with an effective cosmologica…
In minisuperspace quantum cosmology, the Lorentzian path integral formulations of the no-boundary and tunneling proposals have recently been analyzed. But it has been pointed out that the wave function of linearized perturbations around a homogeneous and isotropic background is of an inverse Gaussian form and thus that their correlation functions are divergent. In this paper, we revisit this issue and consider the problem of perturbations in Lorentzian quantum cosmology by modifying the dispersion relation based on trans-Planckian physics. We consider two modified dispersion relations, the gen…
We study quasi-matter bounce cosmology in light of Planck cosmic microwave background (CMB) angular anisotropy measurements along with the BICEP2/Keck Array data. We propose a new primordial scalar power spectrum by considering a linear approximation of the equation of state $w\cong w_0+κ(η-η_0)$ for quasi-matter field in the contracting phase of the universe. Using this new primordial scalar power spectrum, we constrain the zeroth-order approximation of the equation of state $w_0= -\,0.00340\pm 0.00044$ and first-order correction $10^{4} ζ= -1.67^{+1.50}_{-0.83}$ at the $1σ$ confidence level …
We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, no…
We summarize our investigations of the second-order perturbations in loop quantum cosmology (LQC). We shall discuss, primarily, two aspects. Firstly, whether the second-order contributions arising from the cosmic bounce, occurring at Planck scale, could be large enough to break the validity of perturbation theory. Secondly, the implications of the upper bounds on primordial non-Gaussianity, arrived at by the Planck collaboration, on the LQC phenomenology.
The recent Planck Legacy 2018 release has confirmed the presence of an enhanced lensing amplitude in CMB power spectra compared to that predicted in the standard $Λ$CDM model. A closed universe can provide a physical explanation for this effect, with the Planck CMB spectra now preferring a positive curvature at more than $99 \%$ C.L. Here we further investigate the evidence for a closed universe from Planck, showing that positive curvature naturally explains the anomalous lensing amplitude and demonstrating that it also removes a well-known tension within the Planck data set concerning the val…
Loop Quantum Gravity and the The Planck Regime of Cosmology
非常早期的宇宙提供了我们目前测试量子引力理论的最佳舞台。暴胀范式成功地解释了观测到的宇宙微波背景的不均匀性，这在一定程度上已经说明了这一点，因为暴胀范式是基于弯曲宇宙时空的量子场论。然而，这种分析排除了普朗克时代，因为背景时空满足爱因斯坦方程，一直回到大爆炸奇点。利用圈量子引力的技术，这个范式现在已经扩展到从普朗克状态到暴胀开始的自洽理论，涵盖了大约11个数量级的曲率。此外，对于一个狭窄的窗口的初始条件，有偏离标准的范例，与新的效果，如修改的一致性关系，涉及标量和张量功率谱和一个新的来源的非高斯性。因此，宇宙大尺度结构的起源可以追溯到量子引力波动\emph{in the Planck regime}。本报告为广义相对论界提供了这些发展的鸟瞰图。
In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any standard effective field theoretical description will miss part of the degrees of freedom and thus break unitarity. Here we show that these expectations can be made precise in loop quantum cosmology. Concretely, even when loop quantum cosmology is unitary at the fundamental level, when microscopic degrees of freedom, irrelevant to low-energy cosmological observers, are suitably ignored, pure states in the effective description evolve into mixed states due to …
In this paper, using a qualitative theory of dynamical systems, we study the stability of a unified dark matter-dark energy framework known as quartessence Chaplygin model (QCM) with three different equation-of-states within ultraviolet (UV) deformed Friedmann-Robertson-Walker (FRW) cosmologies without Big-Bang singularity. The UV deformation is inspired by the non-commutative (NC) Snyder spacetime approach in which by keeping the transformation groups and rotational symmetry there is a dimensionless, Planck scale characteristic parameter $μ_0$ with dual implications dependent on its sign that…
We consider five dimensional conformal gravity theory which describes an anisotropic extra dimension. Reducing the theory to four dimensions yields Brans-Dicke theory with a potential and a hidden parameter $z$ which implements the anisotropy between the four dimensional spacetime and the extra dimension. We find that a range of value of the parameter $z$ can address the current dark energy density compared to the Planck energy density. Constraining the parameter $z$ and the other cosmological model parameters using the recent observational data consisting of the Hubble parameters, type Ia sup…
Constraining a de Broglie--Bohm quantum bounce cosmology with Planck data
Scuola Superiore Meridionale（南方高等学院）；INFN Sez. di Napoli（那不勒斯 INFN 分部）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）；Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro（里约热内卢州立大学技术学院）
We analyze the spectrum of time observable in noncommutative cosmological model introduced in [5], defined by $(ρ, s=\frac 12)\,$ representation of the de Sitter group. We find that time has peculiar property: it is not self-adjoint, but appropriate restrictions to the space of physical states give self-adjoint extensions. Extensions have discrete spectrum with logarithmic distribution of eigenvalues, $\,t_n \sim \ell\, \log\, n$+const, where $\ell$ characterizes noncommutativity and the usual assumption is $\,\ell=\ell_{Planck}$. When calculated on physical states, radius of the universe is b…
We extend the phenomenology of loop quantum cosmology (LQC) to second order in perturbations. Our motivation is twofold. On the one hand, since LQC predicts a cosmic bounce that takes place at the Planck scale, the second order contributions could be large enough to jeopardize the validity of the perturbative expansion on which previous results rest. On the other hand, the upper bounds on primordial non-Gaussianity obtained by the Planck Collaboration are expected to play a significant role on explorations of the LQC phenomenology. We find that the bounce in LQC produces an enhancement of non-…
