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Cosmological Constraints on the Generalized Uncertainty Principle from Redshift-Space Distortions

Andronikos Paliathanasis

Abstract

We investigate the imprints of the Generalized Uncertainty Principle on cosmological scales by using redshift-space distortion measurements in combination with background cosmological data to determine constraints on the deformation parameter $β$. We consider the modified Poisson bracket related to the existence of a minimal length, which leads to a modified Raychaudhuri equation for the standard $Λ$CDM model and gives rise to a phenomenological one-parameter dynamical dark energy scenario. Through this modification, we can reveal the effects of the minimal length on the late-time structure of the universe. We employ the $f$ and $fσ_8$ measurements of the growth rate combined with background data, including cosmic chronometers, baryon acoustic oscillations and Type Ia supernova observations. The observational constraints reveal a systematically negative value for the deformation parameter $β$, with the $Λ$CDM limit lying within the 95\% credible interval. When supernova data are included, the Akaike Information Criterion indicates weak-to-strong support in favour of the GUP-modified model depending on the SNIa catalogue, while the Bayesian evidence suggests a weak preference.

Cosmological Constraints on the Generalized Uncertainty Principle from Redshift-Space Distortions

Abstract

We investigate the imprints of the Generalized Uncertainty Principle on cosmological scales by using redshift-space distortion measurements in combination with background cosmological data to determine constraints on the deformation parameter . We consider the modified Poisson bracket related to the existence of a minimal length, which leads to a modified Raychaudhuri equation for the standard CDM model and gives rise to a phenomenological one-parameter dynamical dark energy scenario. Through this modification, we can reveal the effects of the minimal length on the late-time structure of the universe. We employ the and measurements of the growth rate combined with background data, including cosmic chronometers, baryon acoustic oscillations and Type Ia supernova observations. The observational constraints reveal a systematically negative value for the deformation parameter , with the CDM limit lying within the 95\% credible interval. When supernova data are included, the Akaike Information Criterion indicates weak-to-strong support in favour of the GUP-modified model depending on the SNIa catalogue, while the Bayesian evidence suggests a weak preference.

Paper Structure

This paper contains 10 sections, 16 equations, 9 figures, 5 tables.

Table of Contents

  1. Introduction
  2. GUP-modified Cosmology
  3. GUP-modified FLRW Cosmology
  4. Observational Data
  5. Observational Constraints of the Quadratic GUP
  6. Without SNIa
  7. With SNIa
  8. Statistical Comparison
  9. Observational Constraints of the Power-law GUP
  10. Conclusions

Figures (9)

  • Figure 1: Confidence space for the posterior parameters GUP-modified model for the data sets without SNIa.
  • Figure 2: Marginalized constraints on the deformation parameter $\beta$ for the different dataset combinations. We observe that when the supernova data are introduced, there is a consistent preference for a negative value of $\beta$ at the $68\%$ confidence level.
  • Figure 3: Confidence space for the posterior parameters GUP-modified model for the data sets combined with the PP catalogue.
  • Figure 4: Confidence space for the posterior parameters GUP-modified model for the data sets combined with the U3 catalogue.
  • Figure 5: Confidence space for the posterior parameters GUP-modified model for the data sets combined with the DD catalogue.
  • ...and 4 more figures