[Paper Review] Redshift and redshift-drift in $\Lambda = 0$ quasi-spherical Szekeres cosmological models and the effect of averaging

Priti Mishra, Marie-Noëlle Célérier|arXiv (Cornell University)|Mar 20, 2014

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper derives the redshift and redshift-drift equations for general quasi-spherical Szekeres (QSS) models without dark energy, applying them to the Bolejko-Sussman (BSQSS) model. It finds that the BSQSS model predicts a cosmological blueshift—unobserved in reality—thus ruling it out, while showing that averaging such models can yield physically viable alternatives to ΛCDM that are distinguishable via redshift-drift measurements.

ABSTRACT

Since the advent of the accelerated expanding homogeneous universe model, some other explanations for the supernova Ia dimming have been explored, among which there are inhomogeneous models constructed with exact $\Lambda = 0$ solutions of Einstein's equations. They have been used either as one patch or to build Swiss-cheese models. The most studied ones have been the Lema\^itre-Tolman-Bondi (LTB) models. However, these models being spatially spherical, they are not well designed to reproduce the large scale structures which exhibit clusters, filaments and non spherical voids. This is the reason why Szekeres models, which are devoid of any symmetry, have recently come into play. In this paper, we give the equations and an algorithm to compute the redshift-drift for the most general quasi-spherical Szekeres (QSS) models with no dark energy. We apply it to a QSS model recently proposed by Bolejko and Sussman (BSQSS model) who averaged their model to reproduce the density distribution of the Alexander and collaborators' LTB model which is able to fit a large set of cosmological data without dark energy. They concluded that their model represents a significant improvement over the observed cosmic structure description by spherical LTB models. We show here that this QSS model is ruled out by a negative cosmological redshift, i.e. a blueshift, which is not observed in the Universe. We also compute a positive redshift and the redshift-drift for the Alexander et al.'s model and compare this redshift-drift to that of the $\Lambda$CDM model. We conclude that the process of averaging an unphysical QSS model can lead to obtain a physical model able to reproduce our observed local Universe with no dark energy need and that the redshift-drift can discriminate between this model and the $\Lambda$CDM model. For completeness, we also compute the blueshift-drift of the BSQSS model.

Motivation & Objective

• To derive the general equations for redshift and redshift-drift in quasi-spherical Szekeres models with no dark energy.
• To apply these equations to the Bolejko-Sussman (BSQSS) model, a spatially averaged QSS model reproducing Alexander et al.'s LTB-like density profile.
• To test whether the averaging process transforms unphysical features (like blueshift) into physically acceptable ones.
• To compare the redshift-drift of the averaged BSQSS model and Alexander et al.'s LTB model with that of the ΛCDM model.
• To assess the potential of redshift-drift as a discriminant between inhomogeneous models and ΛCDM, despite small signal amplitudes.

Proposed method

• Derives the differential equations for redshift and redshift-drift in the most general quasi-spherical Szekeres (QSS) models using exact solutions of Einstein's equations with dust only.
• Develops a numerical algorithm to integrate the redshift and redshift-drift equations along null geodesics in the QSS geometry.
• Applies the algorithm to the BSQSS model, a spatially averaged QSS model designed to mimic the Alexander et al. LTB model’s density profile.
• Computes redshift and redshift-drift for both the BSQSS model and the original Alexander et al. LTB model using consistent numerical methods.
• Compares the resulting redshift-drift curves with those of the ΛCDM model to assess distinguishability.
• Evaluates the measurability of the redshift-drift signal using future instruments like CODEX/EXPRESSO and DECIGO/BBO.

Experimental results

Research questions

• RQ1 Does the Bolejko-Sussman quasi-spherical Szekeres model (BSQSS) predict a cosmological redshift or blueshift, and is this consistent with observations?
• RQ2 Can the process of spatial averaging transform an unphysical QSS model (with blueshift) into a physically viable cosmological model?
• RQ3 How does the redshift-drift of the averaged BSQSS model compare quantitatively to that of the ΛCDM model?
• RQ4 Can redshift-drift measurements at high redshift (z > 2) distinguish between the averaged QSS model and ΛCDM?
• RQ5 What is the expected amplitude of the redshift-drift signal in the BSQSS and Alexander et al. models, and is it measurable with future instruments?

Key findings

• The BSQSS model predicts a cosmological blueshift (negative redshift), which is not observed in the Universe, thus ruling it out as a physical model.
• The averaging process transforms the unphysical blueshift of the BSQSS model into a physical cosmological redshift consistent with observations.
• The redshift-drift of the averaged BSQSS model is distinguishable from that of the ΛCDM model in principle, despite small signal amplitudes.
• The redshift-drift signal in the Alexander et al. LTB model is positive and very small, with a ten-year variation of only |δz| ∼ 2.10−11 at z ∼ 0.085.
• The redshift-drift signal in the BSQSS model is also extremely small, making it unmeasurable with current or near-future instruments like CODEX/EXPRESSO.
• The study suggests that more complex, non-symmetric Swiss-cheese models based on QSS could, in principle, be tested via redshift-drift if they reach higher redshifts (z > 2) and produce measurable signals.