Semiclassical cosmology with backreaction: The Friedmann-Schrödinger equation and inflation

Husain, Viqar; Singh, S. Somorendro

doi:10.1103/physrevd.99.086018

Cited by 6 publications

(3 citation statements)

References 25 publications

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“…There are a few broader features of coupled classicalquantum systems where the quantum part evolves unitarily and the classical one via Hamilton equations. The SC equations are well defined as a dynamical system whether physically valid or not, and the corresponding effective Hamiltonian is conserved; the same holds for the semiclassical Einstein equation at least for model systems [11]. This raises questions for the type of analysis presented in [18], where the question of energy conservation is raised.…”

Section: Spins On Classical (Oscillator) Background (Cb)mentioning

confidence: 99%

“…This is a nonperturbative hybrid classicalquantum equation; it raises many questions, such as what is the physical interpretation of the metric corresponding to a linear or entangled combination of matter states, and how exactly the right-hand side is to be defined if the metric is not known explicitly [8]. There are other hybrid models of this type: the so-called Newton-Schrodinger equation [9,10], a Friedman-Schrodinger generalization to cosmology and related work [11,12], and linear state evolution models using generalizations of the Lindblad equation [13].…”

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confidence: 99%

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Dynamics and entanglement in quantum and quantum-classical systems: lessons for gravity

Husain,

Javed,

Singh

2022

Preprint

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Motivated by quantum gravity, semiclassical theory, and quantum theory on curved spacetime, we study the system of an oscillator coupled to two spin-1/2 particles. This simple model provides a prototype for comparing three types of dynamics: the full quantum theory, the classical oscillator with spin backreaction, and spins propagating on a fixed oscillator background. From nonperturbative calculations of oscillator and entanglement entropy dynamics, we find that (i) entangled tripartite states produce novel oscillator trajectories, (ii) the three systems give equivalent dynamics for sufficiently weak oscillator-spin couplings, and (iii) spins driven by a classical oscillator, with or without backreaction, can produce entangled spin states. The latter result suggests a counterpoint to claims that gravity must be quantized to produce entangled matter states.

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Section: Spins On Classical (Oscillator) Background (Cb)mentioning

confidence: 99%

mentioning

confidence: 99%

Dynamics and entanglement in quantum and quantum-classical systems: lessons for gravity

Husain,

Javed,

Singh

2022

Preprint

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“…Note that a Hamiltonian picture characterizing formally the backreaction of QFT on gravity for a Friedman-Roberson-Walker Universe and a single foliation of spacetime was developed by Husain and Singh in [26,27]. Our formalism diverges from theirs both in the mathematical formalism (we add the quantum Hermitian connection and the geometric-dependent measure and Hilbert spaces, the use of the superset of Hida distributions and the symplectic geometry and Poisson structures for this space of quantum states) and physical implications (its application to generic spacetimes, norm conservation, relating non-unitarily equivalent Hilbert spaces, potential effects of the quantum connection in relation with particle creation), but the spirit is similar.…”

Section: Introductionmentioning

confidence: 99%

Hybrid geometrodynamics: a Hamiltonian description of classical gravity coupled to quantum matter

Alonso,

Bouthelier-Madre,

Clemente-Gallardo

et al. 2024

Class. Quantum Grav.

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We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by a classical metric tensor field over a spatial hypersurface and its associated momentum. Thus, in our approach there is no non-dynamic background structure, apart from the manifold of events, and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled. Given the Hamiltonian nature of the framework, we work with the generators of hypersurface deformations over the manifold of quantum states. The construction relies heavily on the differential geometry of a fibration of the set of quantum states over the set of gravitational variables. An important mathematical feature of this work is the use of Minlos’s theorem to characterize Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schr¨odinger wave functional picture of QFT in curved spacetime. This allows us to relate states within different Hilbert spaces in the case of vacuum states or measures that depend on the gravitational degrees offreedom, as the ones associated to Ashtekar’s complex structure. This is achieved through the inclusion of a quantum Hermitian connection for the fibration, which will have profound physical implications. The most remarkable physical features of theconstruction are norm conservation of the quantum state (even if the total dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on geometry and viceversa, which shall modify the physical properties the gravitational field would have in the absence of backreaction.

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Quantum backreaction on a classical universe

Husain

Singh

2021

Phys. Rev. D

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Semiclassical cosmology with backreaction: The Friedmann-Schrödinger equation and inflation

Cited by 6 publications

References 25 publications

Dynamics and entanglement in quantum and quantum-classical systems: lessons for gravity

Dynamics and entanglement in quantum and quantum-classical systems: lessons for gravity

Hybrid geometrodynamics: a Hamiltonian description of classical gravity coupled to quantum matter

Quantum backreaction on a classical universe

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