Breakdown of the semiclassical approximation during the early stages of preheating

Anderson, Paul R.; Molina-Parı́s, Carmen; Sanders, Dillon H.

doi:10.1103/physrevd.92.083522

Cited by 6 publications

(11 citation statements)

References 34 publications

(46 reference statements)

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“…Our numerical results predict a crucial role of quantum fluctuations in the back-reaction effect of particle production onto the inflaton field: not only does the emission of dipole and Golstone excitations leads to an effective damping of the breathing mode as predicted by a semiclassical picture, but is also responsible for a quick decoherence of its initially in-phase excitation. The generality of the microscopic processes underlying our numerically observed results highlights the importance of going beyond semiclassical approaches [56,57] and including quantum fluctuation features in the description of back-reaction phenomena in gravitation and cosmology. Future work will extend the study to the elusive back-reaction phenomena that are responsible for black hole evaporation under the effect of Hawking emission.…”

mentioning

confidence: 62%

Numerical studies of back-reaction effects in an analog model of cosmological pre-heating

Butera¹,

Carusotto²

2022

Preprint

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We theoretically propose an atomic Bose-Einstein condensate as an analog model of back-reaction effects during the pre-heating stage of early Universe. In particular, we address the out-ofequilibrium dynamics where the initially excited inflaton field decays by parametrically exciting the matter fields. We consider a two-dimensional, ring-shaped BEC under a tight transverse confinement whose transverse breathing mode and the Goldstone and dipole excitation branches simulate the inflaton and quantum matter fields, respectively. A strong excitation of the breathing mode leads to an exponentially-growing emission of dipole and Goldstone excitations via parametric pair creation: our numerical simulations of the BEC dynamics show how the associated back-reaction effect not only results in an effective friction of the breathing mode but also in a quick loss of longitudinal spatial coherence of the initially in-phase excitations. Implications of this result on the validity of the usual semiclassical description of back-reaction are finally discussed.

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confidence: 62%

Numerical studies of back-reaction effects in an analog model of cosmological pre-heating

Butera¹,

Carusotto²

2022

Preprint

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“…Perturbing the semiclassical backreaction equation yields the linear response equation which contains this two-point correlation function and describes the time evolution of perturbations about a given semiclassical solution. A criterion for the validity of the semiclassical approximation was originally developed for semiclassical gravity 9 and modified for preheating in chaotic inflation 8 . This criterion was applied to semiclassical electrodynamics 1 and states: the semiclassical approximation will break down if any linearized gauge invariant quantity constructed from solutions to the linear response equation with finite non-singular initial data grows rapidly for some period of time.…”

Section: Validity Criterion For the Semiclassical Approximationmentioning

confidence: 99%

“…This included solving the necessary backreaction equations for scalar and spin 1 ⁄2 fields coupled to two different classical source profiles, one which led to an asymptotically constant electric field and the other being the Sauter pulse. To wit, a criterion was implemented to assess the validity of the semiclassical approximation which had been previously applied to the process of preheating in models of chaotic inflation 8 , with an earlier version applied to semiclassical gravity 9 . This criterion involves the behavior of solutions to the linear response equation, which can be derived by perturbing the semiclassical backreaction equation about a background field solution.…”

Section: Introductionmentioning

confidence: 99%

“…In general, the linear response equation is a second order integro-differential equation which can be cumbersome to solve numerically. Therefore a method was developed 8 to approximate solutions to the linear response equation which involves the difference between solutions to the semiclassical backreaction equation with similar initial conditions. For early times, this difference is expected to act as an approximate solution to the linear response equation as long as the exact solution is relatively small.…”

Section: Introductionmentioning

confidence: 99%

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Validity of the Semiclassical Approximation in 1+1 Electrodynamics: Numerical Solutions to the Linear Response Equation

Newsome¹

2021

Preprint

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From previous work 1 , the semiclassical backreaction equation in 1+1 dimensions was solved and a criterion was implemented to assess the validity of the semiclassical approximation in this case. The criterion involves the behavior of solutions to the linear response equation which describes perturbations about solutions to the semiclassical backreaction equation. The linear response equation involves a time integral over a two-point correlation function for the current induced by the quantum field and it is expected that significant growth in this two-point function (and therefore in quantum fluctuations) will result in significant growth in solutions to the linear response equation. It was conjectured for early times that the difference of two nearby solutions to the semiclassical backreaction equation, with similar initial conditions, can act as an approximate solution to the linear response equation. A comparative analysis between the approximate and numerical solutions to the linear response equation, for the critical scale for particle production, will be presented for the case of a massive, quantized spin 1 ⁄2 field in order to determine how robust the approximation method is for representing its solutions.

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“…The semiclassical approximation breaks down if quantum fluctuations are too large. We use a criterion for the validity of the semiclassical approximation that has been previously applied to the process of preheating in models of chaotic inflation [20]. An earlier version of the criterion has also been used to study the validity of the semiclassical approximation for free scalar fields in flat space when the fields are in the Minkowski vacuum state [21] and for the conformally invariant scalar field in the Bunch-Davies state in de Sitter space in the usual spatially flat cosmological coordinates [22].…”

Section: Introductionmentioning

confidence: 99%

Pair production due to an electric field in 1+1 dimensions and the validity of the semiclassical approximation

et al. 2021

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Solutions to the backreaction equation in 1 þ 1-dimensional semiclassical electrodynamics are obtained and analyzed when considering a time-varying homogeneous electric field initially generated by a classical electric current, coupled to either a quantized scalar field or a quantized spin-1 2 field. Particle production by way of the Schwinger effect leads to backreaction effects that modulate the electric field strength. Details of the particle production process are investigated along with the transfer of energy between the electric field and the particles. The validity of the semiclassical approximation is also investigated using a criterion previously implemented for chaotic inflation and, in an earlier form, semiclassical gravity. The criterion states that the semiclassical approximation will break down if any linearized gauge-invariant quantity constructed from solutions to the linear response equation, with finite nonsingular data, grows rapidly for some period of time. Approximations to homogeneous solutions of the linear response equation are computed and it is found that the criterion is violated when the maximum value, E max , obtained by the electric field is of the order of the critical scale for the Schwinger effect, E max ∼ E crit ≡ m 2 =q, where m is the mass of the quantized field and q is its electric charge. For these approximate solutions the criterion appears to be satisfied in the extreme limits qE max m 2 ≪ 1 and qE max m 2 ≫ 1.

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Breakdown of the semiclassical approximation during the early stages of preheating

Cited by 6 publications

References 34 publications

Numerical studies of back-reaction effects in an analog model of cosmological pre-heating

Numerical studies of back-reaction effects in an analog model of cosmological pre-heating

Validity of the Semiclassical Approximation in 1+1 Electrodynamics: Numerical Solutions to the Linear Response Equation

Pair production due to an electric field in 1+1 dimensions and the validity of the semiclassical approximation

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