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Constraining a de Broglie-Bohm quantum bounce cosmology with Planck data

Micol Benetti, Rudnei O. Ramos, Renato Silva, Gustavo S. Vicente

TL;DR

The paper develops a de Broglie-Bohm quantum-bounce cosmology in a flat FLRW universe with a scalar field and derives a scale-dependent distortion in the primordial scalar power spectrum arising from pre-inflationary quantum dynamics. By solving the Mukhanov–Sasaki equation across a three-phase history (Bounce, Transition, Inflation) and carefully matching solutions, it produces a closed-form correction Δ_k to the standard spectrum and expresses it in terms of model parameters, notably the bounce scale $k_B$ and a dimensionless parameter $c$. Confronting the distorted spectrum with Planck 2018 data via CAMB/Cobaya yields strong upper bounds on $k_B$ for representative $c$ values and shows only a marginal improvement over ΛCDM, though the model hints at an anti-correlation between $H_0$ and $\sigma_8$ that could alleviate current tensions. The work demonstrates that Planck-scale quantum gravity effects can leave observable imprints in the CMB and provides testable predictions for future cosmological surveys.

Abstract

This work investigates a singularity-free early Universe within the paradigm of quantum cosmology. We develop a bouncing model where the singularity is resolved via the de Broglie-Bohm interpretation of quantum mechanics, which provides a deterministic trajectory for the scale factor through a quantum bounce. The primordial power spectrum for scalar perturbations is derived, incorporating a characteristic modulation (distortion function) imprinted by the non-standard quantum gravitational dynamics near the bounce. We confront this model with the Planck 2018 cosmic microwave background data, establishing its strong compatibility with observations. Our analysis places a stringent upper bound on the fundamental scale of the bounce, $k_B$, constraining the parameter space of such quantum cosmological scenarios. Furthermore, the model's specific scale-dependent anti-correlation between the spectral index and amplitude of perturbations offers a potential mechanism for mitigating the $H_0$-$σ_8$ tension, presenting a testable signature for future cosmological surveys.

Constraining a de Broglie-Bohm quantum bounce cosmology with Planck data

TL;DR

The paper develops a de Broglie-Bohm quantum-bounce cosmology in a flat FLRW universe with a scalar field and derives a scale-dependent distortion in the primordial scalar power spectrum arising from pre-inflationary quantum dynamics. By solving the Mukhanov–Sasaki equation across a three-phase history (Bounce, Transition, Inflation) and carefully matching solutions, it produces a closed-form correction Δ_k to the standard spectrum and expresses it in terms of model parameters, notably the bounce scale and a dimensionless parameter . Confronting the distorted spectrum with Planck 2018 data via CAMB/Cobaya yields strong upper bounds on for representative values and shows only a marginal improvement over ΛCDM, though the model hints at an anti-correlation between and that could alleviate current tensions. The work demonstrates that Planck-scale quantum gravity effects can leave observable imprints in the CMB and provides testable predictions for future cosmological surveys.

Abstract

This work investigates a singularity-free early Universe within the paradigm of quantum cosmology. We develop a bouncing model where the singularity is resolved via the de Broglie-Bohm interpretation of quantum mechanics, which provides a deterministic trajectory for the scale factor through a quantum bounce. The primordial power spectrum for scalar perturbations is derived, incorporating a characteristic modulation (distortion function) imprinted by the non-standard quantum gravitational dynamics near the bounce. We confront this model with the Planck 2018 cosmic microwave background data, establishing its strong compatibility with observations. Our analysis places a stringent upper bound on the fundamental scale of the bounce, , constraining the parameter space of such quantum cosmological scenarios. Furthermore, the model's specific scale-dependent anti-correlation between the spectral index and amplitude of perturbations offers a potential mechanism for mitigating the - tension, presenting a testable signature for future cosmological surveys.
Paper Structure (12 sections, 51 equations, 5 figures, 1 table)

This paper contains 12 sections, 51 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background Cosmological Model
  3. Classical model
  4. Quantum model: de Broglie-Bohm Interpretation
  5. Primordial Scalar Perturbations
  6. Bounce phase
  7. Transition phase
  8. Inflationary phase
  9. Matching the solutions
  10. Power Spectrum
  11. Analysis and Results
  12. Conclusions

Figures (5)

  • Figure 1: Comparison between the exact function ${\cal V}(T)$, given by Eq. (\ref{['VT']}), and its Pöschl-Teller approximation ${\cal V}_{\rm PT}(T)$ for the representative parameters $\lambda=m_{\rm Pl}$, $T_0=m_{\rm Pl}^{-1}$ and $a_{\rm B}=1$.
  • Figure 2: The primordial power spectrum as a function of the scale (in units of Mpc$^{-1}$), assuming $c=0.03$ and for different values for $k_B$.
  • Figure 3: The CMB temperature anisotropy power spectrum fixing $c=0.03$ and varying $k_B$ (in units of Mpc$^{-1}$).
  • Figure 4: Confidence regions from our analysis using CMB Planck 2018 $TTTEEE$+$lowE$+lensing data Planck:2019nip.
  • Figure 5: The bounce scale $k_B$ posterior (in units of Mpc$^{-1}$) using the CMB Planck 2018 $TTTEEE$+$lowE$+lensing data Planck:2019nip.