The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology

Navascués, Beatriz Elizaga; Blas, Daniel Martín de; Marugán, Guillermo A. Mena

doi:10.3390/universe4100098

Cited by 29 publications

(33 citation statements)

References 93 publications

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“…(Gupt and Singh, 2012;Gupt and Singh, 2013; and references therein.]. In particular, the last two approaches have been widely studied and found that they are all consistent with current cosmological observations (Agullo and Morris, 2015;de Blas and Olmedo, 2016;Castelló Gomar et al, 2017;Agullo et al, 2018;Elizaga Navascués et al, 2018;Navascues et al, 2018;Wu et al, 2018;Zhu et al, 2018). In addition, within the framework of the dressed metric approach recently it has been also shown that some anomalies from the CMB data (Akrami and Planck collaboration, 2020;Akrami and Planck collaboration, 2020;Schwarz et al, 2016) can be reconciled purely due to the quantum geometric effects (Ashtekar et al, 2020;Ashtekar et al, 2021).…”

Section: Introductionsupporting

confidence: 58%

Phenomenological Implications of Modified Loop Cosmologies: An Overview

Singh

Wang

2021

Front. Astron. Space Sci.

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In this paper, we first provide a brief review of the effective dynamics of two recently well-studied models of modified loop quantum cosmologies (mLQCs), which arise from different regularizations of the Hamiltonian constraint and show the robustness of a generic resolution of the big bang singularity, replaced by a quantum bounce due to non-perturbative Planck scale effects. As in loop quantum cosmology (LQC), in these modified models the slow-roll inflation happens generically. We consider the cosmological perturbations following the dressed and hybrid approaches and clarify some subtle issues regarding the ambiguity of the extension of the effective potential of the scalar perturbations across the quantum bounce, and the choice of initial conditions. Both of the modified regularizations yield primordial power spectra that are consistent with current observations for the Starobinsky potential within the framework of either the dressed or the hybrid approach. But differences in primordial power spectra are identified among the mLQCs and LQC. In addition, for mLQC-I, striking differences arise between the dressed and hybrid approaches in the infrared and oscillatory regimes. While the differences between the two modified models can be attributed to differences in the Planck scale physics, the permissible choices of the initial conditions and the differences between the two perturbation approaches have been reported for the first time. All these differences, due to either the different regularizations or the different perturbation approaches in principle can be observed in terms of non-Gaussianities.

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Section: Introductionsupporting

confidence: 58%

Phenomenological Implications of Modified Loop Cosmologies: An Overview

Singh

Wang

2021

Front. Astron. Space Sci.

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“…within the Hybrid Quantization Approach [32] in order to deal with (both scalar and fermionic) perturbations in quantum cosmology (see, for instance, Refs. [100][101][102][103][104][105][106][107]).…”

Section: Discussionmentioning

confidence: 99%

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

2020

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In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lemaître-Robertson-Walker, de Sitter, and Bianchi I spacetimes. These results are attained by imposing the criteria of symmetry invariance and of unitary implementability of the dynamics. This powerful combination of criteria allows not only to address the ambiguity in the representation of the canonical commutation relations, but also to single out a preferred set of fundamental variables. For the sake of clarity and completeness in the presentation (essentially as a background and complementary material), we first review the classical and quantum theories of a scalar field in globally hyperbolic spacetimes. Special emphasis is made on complex structures and the unitary implementability of symplectic transformations. * jacq@ciencias.unam.mx † mena@iem.cfmac.csic.es ‡ jvelhi@ubi.pt(2.1)By taking the direct sum of these two spaces, we get the complex vector space V + J ⊕ V − J , the elements of which can be written as (J turns out to be the same as V C , so that the complex vector spaces defined in Eq. (2.1) provide a splitting for the complexification of V . Besides, notice that every v in V can be decomposed asClearly, different complex structures will lead to distinct splittings for V C and, consequently, to different decompositions for v ∈ V . By extending the action of J from V to V C by complex linearity, we obtain that v + and v − are eigenvectors of J with eigenvalues i and −i,Given another complex structure, sayJ, its eigenvectors will satisfy relationships (2.2) with J replaced withJ. The eigenvectors ofJ and J are related byṽ. , x m , y 1 , . . . , y m )}. The standard (also called canonical) symplectic form is then. Equivalently, the standard symplectic form defines a skew-symmetric bilinear function on V [1], on C, and where we have used that Jv − = Jv + . A straightforward inspection shows that v, w J defines a Hermitian inner product on V + J ; that is,is a Hermitian inner product. This, together with the fact that any element of V + J is uniquely represented by an element of V (and vice versa), implies that the complex vector space V , with Hermitian inner product (2.7), and the complex vector space V + J , with Hermitian inner product (2.8), are (essentially) the same inner product spaces.B. The scalar field: Classical theory the unit function [see Eq. (2.11)]. Since observables on (S, Ω) can be obtained by taking linear combinations of products of natural observables Ω(φ, · ) and the unit function I (which provides the constant functions on S), the subspace 4 {I, Ω(φ, · ) | φ ∈ S} R of O qualifies as an admissible set of basic observables. This, together with the "naturalness and simplicity" of our choice, leads us to select the commented subspace as the set O 0 of fundamental (basic, or elementary) classical observables.By equipping the phase space (S, Ω) with a compatible complex structure J, the fi...

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“…The final article I would like to discuss concerns a study of primordial fluctuations in a hybrid loop quantum cosmology (HLQC) model [15]. HLQC models are extensions of LQC where small anisotropies and inhomogeneities are included, in such a way that the dominant effects of quantum geometry are studied using the standard quantization of LQC.…”

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confidence: 99%

“…The opposite situation characterizes the slow-roll inflationary phase. The work of [15] shows explicitly that the primordial power spectrum depends strongly on the choice of vacuum. In general, the adiabatic spectra are suppressed at large scales, but exhibit rapid oscillations at intermediate scales.…”

mentioning

confidence: 99%