5. Impact of inhomogeneities on slowly rolling quintessence: implications for the local variations of the fine-structure constant

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Context: The explanation of dark energy coming from a cosmological constant as a model of vacuum energy is difficult to justify. I, along with Leonardo Giani and Oliver Piattella, have developed a new way to constrain one of the most common model of dark energy, the Quintessence model. This theory proposes local variations of the fine-structure constant \(\alpha\), which can be constrained by spectroscopic measurements of stars near the supermassive black hole in our galaxy’s center.

Method: To investigate a dynamic fine-structure constant \(\alpha\), we combined a quintessential scalar field with Maxwell electromagnetism in a FLRW universe filled with dust. We analysed scalar perturbations in the Newtonian gauge and assumed a spherically symmetrical, static density contrast, and a slowly rolling scalar field. By assuming a static gravitational potential \(\phi\), we established the relationship between perturbations of the quintessence field \(\delta \phi\). We then used this information to determine the dependence for a non-static potential. Finally, we calculated the relative variation of \(\alpha\) through its connection to the electromagnetic coupling and the quintessential field’s fluctuations.

Results:

• In both static and non-static configurations, the gravitational potential generated by a stable structure leads to perturbations inversely proportional to the distance, i.e. \(\delta \phi \propto 1/r\)…
• … which induces a spatial dependence of the fine-structure “constant”, i.e. the relative variation of two objects A and B goes as \(\Delta A /\Delta B = r_B / r_A\).
• Using spectroscopic observations of five stars orbiting around SgrA*, the strongest constraint obtained is a variation of \(0.4 \pm 2.5\) for the couple (S0-12,S1-5).