Rapid numerical solutions for the Mukhanov-Sasaki equation

Haddadin, W. I. J.; Handley, W. J.

doi:10.48550/arxiv.1809.11095

Cited by 8 publications

(19 citation statements)

References 22 publications

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“…Some modes at low k however always remain far above the horizon and so stay frozen throughout. Figure is based upon Figure 1 in [17].…”

Section: Kinetic Dominance and Inflationmentioning

confidence: 99%

“…We shall consider the following mode initial conditions: Bunch-Davies vacuum (BD) [6], Hamiltonian Diagonalisation (HD) [9], Renormalized Stress Energy Tensor (RSET) [9], Right Handed Mode (RHM) [19], and Frozen Initial Conditions (FIC) [17]. The mathematical definitions of each of these are given in Table I.…”

Section: Initial Condition Definitionmentioning

confidence: 99%

“…Instead FIC are a white-noise state where all modes start with equal magnitude and zero velocity. They were introduced and are briefly explored numerically in [17].…”

Section: Initial Condition Definitionmentioning

confidence: 99%

“…For the initial state we consider a range of alternative initial vacua with the goal of determining if the choice of quantum vacuum may be observationally distinguishable. In addition we investigate an alternative to the paradigm of setting vacuum initial conditions, frozen initial conditions [17], which instead represent a white-noise initial perturbation state at the big-bang singularity. By comparing the observable predictions to the Planck 2018 experimental results [18], we then aim to determine if any of the proposed initial condition can provide an explanation for the features in the CMB spectra not explained by ΛCDM.…”

Section: Introductionmentioning

confidence: 99%

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Constraining Quantum Initial Conditions before Inflation

Gessey-Jones,

Handley

2021

Preprint

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We theoretically and observationally investigate different choices of initial conditions for the primordial mode function that are imposed during an epoch preceding inflation. By deriving predictions for the observables resulting from several alternate quantum vacuum prescriptions we show some choices of vacua are theoretically observationally distinguishable from others. Comparing these predictions to the Planck 2018 observations via a Bayesian analysis shows no significant evidence to favour any of the quantum vacuum prescriptions over the others. In addition we consider frozen initial conditions, representing a white-noise initial state at the big-bang singularity. Under certain assumptions the cosmological concordance model and frozen initial conditions are found to produce identical predictions for the cosmic microwave background anisotropies. Frozen initial conditions may thus provide an alternative theoretic paradigm to explain observations that were previously understood in terms of the inflation of a quantum vacuum.

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“…Some modes at low k however always remain far above the horizon and so stay frozen throughout. Figure is based upon Figure 1 in [17].…”

Section: Kinetic Dominance and Inflationmentioning

confidence: 99%

Section: Initial Condition Definitionmentioning

confidence: 99%

“…Instead FIC are a white-noise state where all modes start with equal magnitude and zero velocity. They were introduced and are briefly explored numerically in [17].…”

Section: Initial Condition Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Constraining Quantum Initial Conditions before Inflation

Gessey-Jones,

Handley

2021

Preprint

Self Cite

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“…Nevertheless, a series of recent results [15][16][17][18] (see also [19]) show that for broad classes of solutions of classical inflationary (INF) models the resulting early Universe is in a state of kinetic dominance (KD). The KD period of inflationary models is a pre-inflationary stage [5,[14][15][16][20][21][22][23][24][25][26][27][28] which occurs when the kinetic energy of the inflaton field dominates over its potential energy, a stage that quickly evolves to the INF stage.…”

Section: Introductionmentioning

confidence: 99%

Kinetic dominance and the wavefunction of the universe

Álvarez,

Alonso,

Medina

2021

Preprint

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We analyze the emergence of classical inflationary universes in a kinetic-dominated stage using a suitable class of solutions of the Wheeler-De Witt equation with a constant potential. These solutions are eigenfunctions of the inflaton momentum operator that are strongly peaked on classical solutions exhibiting either or both a kinetic dominated period and an inflation period. Our analysis is based on semiclassical WKB solutions of the Wheeler-De Witt equation interpreted in the sense of Borel (to perform a correct connection between classically allowed regions) and on the relationship of these solutions to the solutions of the classical model. For large values of the scale factor the WKB Vilenkin tunneling wavefunction and the Hartle-Hawking no-boundary wavefunctions are recovered as particular instances of our class of wavefunctions.

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Primordial power spectra for curved inflating universes

Handley

2019

Phys. Rev. D

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Exact numerical primordial primordial power spectra are computed and plotted for the for the best-fit Planck 2018 curved universe parameters. It is found that the spectra have generic cut-offs and oscillations within the observable window for the level of curvature allowed by current CMB measurements and provide a better fit to current data. Derivations for the Mukhanov-Sasaki equation for curved universes are presented and analysed, and theoretical implications for the quantum and classical initial conditions for inflation are discussed within the curved regime.

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Rapid numerical solutions for the Mukhanov-Sasaki equation

Cited by 8 publications

References 22 publications

Constraining Quantum Initial Conditions before Inflation

Constraining Quantum Initial Conditions before Inflation

Kinetic dominance and the wavefunction of the universe

Primordial power spectra for curved inflating universes

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