Quantization ambiguities and the robustness of effective descriptions of primordial perturbations in hybrid Loop Quantum Cosmology
Quantization ambiguities and the robustness of effective descriptions of primordial perturbations in hybrid Loop Quantum Cosmology
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DOI：
10.1088/1361-6382/ac3b9b
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Beatriz Elizaga Navascu'es;G. A. M. Marug'an
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文献类型：
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作者：
Beatriz Elizaga Navascu'es;G. A. M. Marug'an
我们研究的印记，某些量子化的模糊性可能会留下有效的制度的混合环量子描述的宇宙学扰动。更具体地说，在标量微扰的情况下，我们研究如何重建Mukhanov-Sasaki场的有效制度圈量子宇宙学，作为量子化的一个典型的制定具有不同的动力学的其他微扰规范不变量的起点。这种量子理论的表述，除了Mukhanov-Sasaki的变量之外，对于获得具有良好行为的量子哈密顿量至关重要，避免了量子场论中典型的定义不明确的哈密顿算符的问题。在Mukhanov-Sasaki场的重建中，我们要求有效的Mukhanov-Sasaki方程采用类似的形式，并显示与经典方程相同的哈密顿结构，这是过去十年来在圈量子宇宙学研究中广泛假设的属性。这个条件实际上限制了某些量化模糊性所固有的自由度。一旦这些模糊性被消除，Mukhanov-Sasaki场的重建自然地确定了有效方程的一组正频率解，从而确定了扰动的初始条件。我们的分析构成了一个重要的和必要的测试的鲁棒性标准的有效描述在圈量子宇宙学，沿着他们的观测预测的原始功率谱，考虑到他们应该是一个更基本的量子理论的后果，一个定义良好的哈密顿量，在狄拉克的长期思想的精神。
We study the imprint that certain quantization ambiguities may leave in effective regimes of the hybrid loop quantum description of cosmological perturbations. More specifically, in the case of scalar perturbations we investigate how to reconstruct the Mukhanov-Sasaki field in the effective regime of Loop Quantum Cosmology, taking as starting point for the quantization a canonical formulation in terms of other perturbative gauge invariants that possess different dynamics. This formulation of the quantum theory, in terms of variables other than the Mukhanov-Sasaki ones, is crucial to arrive at a quantum Hamiltonian with a good behavior, elluding the problems with ill defined Hamiltonian operators typical of quantum field theories. In the reconstruction of the Mukhanov-Sasaki field, we ask that the effective Mukhanov-Sasaki equations adopt a similar form and display the same Hamiltonian structure as the classical ones, a property that has been widely assumed in Loop Quantum Cosmology studies over the last decade. This condition actually restricts the freedom inherent to certain quantization ambiguities. Once these ambiguities are removed, the reconstruction of the Mukhanov-Sasaki field naturally identifies a set of positive-frequency solutions to the effective equations, and hence a choice of initial conditions for the perturbations. Our analysis constitutes an important and necessary test of the robustness of standard effective descriptions in Loop Quantum Cosmology, along with their observational predictions on the primordial power spectrum, taking into account that they should be the consequence of a more fundamental quantum theory with a well-defined Hamiltonian, in the spirit of Dirac’s long-standing ideas.