# $$\Xi > 0$$: The expansion shifts toward coasting

There is already some empirical evidence in favor of the parameter $$Xi$$ being greater than zero.

The parameter would, if great enough, force the expansion of the universe to become close to a linear one, $$a(\tau) \sim \tau$$.

This can be seen quite easily, it is sufficient to assume that the term with $$\Xi$$ in the Friedman equation $3 \left(\frac{a'}{a}\right)^2 = -\Upsilon a^{-6} + 3 \Xi a^{-2} + \Lambda + \varepsilon$ would be in some intermediate region the most important one in comparison with all others. Then the evolution equation would approximately follow the following law: $3 \left(\frac{a'}{a}\right)^2 \approx 3 \Xi a^{-2}$ or, in other words, $a' \approx \sqrt{\Xi}$ so that $$a(\tau) \approx \sqrt{\Xi} \tau$$. Such a linear expansion of the universe is named "coasting".

## Empirical evidence in favor of expansion closer to coasting

The early ($$10 \le z \le 1000$$) universe allows to obtain some information which depends on the deceleration of the universe at that time. The expansion of the universe decelerates strongly in the standard $$\Lambda$$CDM universe, while with a large $$\Xi$$ it could be as close as one likes to coasting $$a(\tau) \sim \tau$$. This difference leads to different path lengths across the epochs when one expects 21cm absorption of the background radiation by hydrogen: The absorption is predicted to be a factor of $$\sim 2$$ greater for coasting than in the $$\Lambda$$CDM. This has been shown for a theory without cold dark matter (which would also be much more close to coasting) by McGaugh:

We consider the 21cm absorption signal expected at high redshift in cosmologies with and without non-baryonic cold dark matter. The expansion of the early universe decelerates strongly with dark matter, but approximately coasts without it. This results in a different path length across the epochs when absorption is expected, with the consequence that the absorption is predicted to be a factor of $$\sim$$ 2 greater without dark matter than with it.
$$\dots$$
Fortunately, the physics of the 21cm absorption is straightforward, depending only on atomic physics and the fact that the universe is expanding. This provides the opportunity to outline some very general expectations. Generically, we expect a universe devoid of non-baryonic dark matter (NoCDM) to be low density, and thus experience less deceleration at early times [31] than the conventional ΛCDM [32] universe. As a consequence, there is a greater path length to the surface of last scattering that leads to a stronger absorption signal. [ McGaugh 2018]

Once the argument depends only on the difference between $$\Lambda$$CDM and coasting, not on the other details of the considered theory, this will hold for GLET with large enough $$\Xi$$ too.

The expected absorption at cosmic dawn has recently been detected by EDGES.

A comparison of the $$\Lambda$$CDM prediction (dotted red), the NoCDM prediction, which would be close to GLET for large enough $$\Xi$$ (blue) and the EDGES measurements have been given in figure 1 of McGaugh 2018:

## References

1. McGaugh, S.S. (2018). Predictions for the Sky-Averaged Depth of the 21 cm Absorption Signal at High Redshift in Cosmologies with and without Nonbaryonic Cold Dark Matter, Phys. Rev. Lett. 121, 081305, arxiv:1808.02532.
2. Bowman, J.D., Rogers, A.E.E. Monsalve, R.A., Mozdzen, T.J., Mahesh, N. (2018). An absorption profile centred at 78 megahertz in the sky-averaged spectrum, Nature 555, 67–70, arxiv:1810.05912.