Recent cosmological measurements suggest the possibility of an anisotropic universe. As a result, the Bianchi Type I metric, being the simplest anisotropic extension to the standard Friedmann-Lemaître-Robertson-Walker metric has been extensively studied. In this work, we show how the recombination history should be modified in an anisotropic universe and derive observables by considering the null geodesic. We then constrain the locally rotationally symmetric Bianchi type I model by performing Markov chain Monte Carlo with the acoustic scales in cosmic microwave background and baryon acoustic oscillation data, together with local measurements of $H(z)$ and pantheon supernova data. Our results reveal that the anisotropic model is not statistically preferred over the $\mathrm{\Lambda }$ cold dark matter model, and we obtain a tight constraint on the anisotropy that generally agrees with previous studies under a maximum temperature anisotropy fraction of $2\times {10}^{-5}$. Besides, we also present constraints based on a relaxed maximum temperature anisotropy. We stress that there is a significant difference between the geodesic-based observables and the naive isotropic analogies when there is a noticeable anisotropy. However, the changes in recombination history are insignificant even under the relaxed anisotropy limit.

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• Baryon acoustic oscillations
• Cosmic microwave background
• Cosmological parameters
• Cosmology
• Evolution of the Universe