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Constraints on a Bianchi type I spacetime extension of the standard $Λ$CDM model

Ozgur Akarsu, Suresh Kumar, Shivani Sharma, Luigi Tedesco

TL;DR

The paper investigates a simple anisotropic extension of ΛCDM by adopting a Bianchi type-I background and adding a stiff-fluid–like term $\Omega_{\sigma0} a^{-6}$ to the expansion history, so that $\frac{H^2}{H_0^2}=\Omega_{\sigma0} a^{-6}+\Omega_{r0} a^{-4}+\Omega_{m0} a^{-3}+\Omega_{\Lambda0}$. Using late-time data ($H(z)$, Pantheon) and then including BAO and Planck CMB data, the authors find $\Omega_{\sigma0}\lesssim 4.6\times10^{-4}$ (95% CL) from $H(z)$ alone and $\lesssim$ a few $\times10^{-15}$ (95% CL) when BAO/CMB are included, with Bayesian evidence decisively favouring the anisotropic model. A BBN-based bound tightens the constraint to $\Omega_{\sigma0}\lesssim10^{-23}$, implying negligible impact on the CMB quadrupole despite a theoretical possibility of a few–tens of microkelvin temperature shifts. Overall, the work shows that current data tightly bound expansion anisotropy in this simple GR framework, while providing a robust method to test similar anisotropic cosmologies.

Abstract

We consider the simplest anisotropic generalization, as a correction, to the standard $Λ$CDM model, by replacing the spatially flat Robertson-Walker metric by the Bianchi type-I metric, which brings in a new term $Ω_{σ0}a^{-6}$ (mimicking the stiff fluid) in the average expansion rate $H(a)$ of the Universe. From Hubble and Pantheon data, relevant to the late Universe ($z\lesssim 2.4$), we obtain the constraint $Ω_{\sigma0}\lesssim10^{-3}$, in line with the model-independent constraints. When the baryonic acoustic oscillations and cosmic microwave background (CMB) data are included, the constraint improves by 12 orders of magnitude, i.e., $Ω_{\sigma0}\lesssim10^{-15}$. We find that this constraint could alter neither the matter-radiation equality redshift nor the peak of the matter perturbations. Demanding that the expansion anisotropy has no significant effect on the standard big bang nucleosynthesis (BBN), we find the constraint $Ω_{\sigma0}\lesssim10^{-23}$. We show explicitly that the constraint from BBN renders the expansion anisotropy irrelevant to make a significant change in the CMB quadrupole temperature, whereas the constraint from the cosmological data in our model provides the temperature change up to $\sim11\, \rm mK$, though it is much beyond the CMB quadrupole temperature.

Constraints on a Bianchi type I spacetime extension of the standard $Λ$CDM model

TL;DR

The paper investigates a simple anisotropic extension of ΛCDM by adopting a Bianchi type-I background and adding a stiff-fluid–like term to the expansion history, so that . Using late-time data (, Pantheon) and then including BAO and Planck CMB data, the authors find (95% CL) from alone and a few (95% CL) when BAO/CMB are included, with Bayesian evidence decisively favouring the anisotropic model. A BBN-based bound tightens the constraint to , implying negligible impact on the CMB quadrupole despite a theoretical possibility of a few–tens of microkelvin temperature shifts. Overall, the work shows that current data tightly bound expansion anisotropy in this simple GR framework, while providing a robust method to test similar anisotropic cosmologies.

Abstract

We consider the simplest anisotropic generalization, as a correction, to the standard CDM model, by replacing the spatially flat Robertson-Walker metric by the Bianchi type-I metric, which brings in a new term (mimicking the stiff fluid) in the average expansion rate of the Universe. From Hubble and Pantheon data, relevant to the late Universe (), we obtain the constraint , in line with the model-independent constraints. When the baryonic acoustic oscillations and cosmic microwave background (CMB) data are included, the constraint improves by 12 orders of magnitude, i.e., . We find that this constraint could alter neither the matter-radiation equality redshift nor the peak of the matter perturbations. Demanding that the expansion anisotropy has no significant effect on the standard big bang nucleosynthesis (BBN), we find the constraint . We show explicitly that the constraint from BBN renders the expansion anisotropy irrelevant to make a significant change in the CMB quadrupole temperature, whereas the constraint from the cosmological data in our model provides the temperature change up to , though it is much beyond the CMB quadrupole temperature.

Paper Structure

This paper contains 15 sections, 52 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Basic Equations and the Model
  3. Bayesian Inference
  4. Data and likelihoods
  5. $H(z)$
  6. BAO
  7. CMB
  8. Pantheon supernovae type Ia
  9. Methodology
  10. Results and Discussion
  11. Further Discussions
  12. Matter-radiation equality
  13. Big bang nucleosynthesis
  14. CMB quadrupole problem
  15. Conclusions

Figures (4)

  • Figure 1: One-dimensional and two-dimensional marginalized confidence regions (68% and 95% C.L.) for the anisotropic $\Lambda$CDM parameters $H_0$, $\Omega_{\rm m0}$ and $\Omega_{\sigma 0}$ from $H(z)$ and $H(z)$ + Pantheon data.
  • Figure 2: One-dimensional and two-dimensional marginalized confidence regions (68% and 95% C.L.) for the anisotropic $\Lambda$CDM model parameters $H_0$, $\Omega_{\rm m0}$ and $\Omega_{\sigma 0}$ from $H(z)$, CMB, BAO and Pantheon data combinations.
  • Figure 3: 68% confidence intervals of $H_0$ and $\Omega_{\rm m0}$ for the anisotropic $\Lambda$CDM in comparison with the $\Lambda$CDM model.
  • Figure 4: Summary of the Bayesian evidence for the anisotropic $\Lambda$CDM model in comparison with the $\Lambda$CDM model.