Constraints from large scale structure

Cosmological constraints on ALPs can be obtained across the range of Eq. 2.11.1. The combined CMB-large scale structure likelihood analysis of [49] has shown that ultra-light fields with mass around 10−32_{– 10}−24_{eV might account for up to 10% of the dark matter abundance. Outside of}

this range, the abundance can be larger21_{. Euclid will be able to place tighter constraints across}

this entire range, and extend the mass range covered.

Ultra-light fields withm _.10−29 _{eV are similar in many ways to massive neutrinos [49], the}

major difference being that their non-thermal production breaks the link between the scale of suppression, km, and the fraction of dark matter, fax, through the dependence of fax on the

initial field value φi. Therefore an accurate measurement of the matter power spectrum in the

low-k region where massive neutrinos corresponding to the WMAP limits on Ων are expected to

suppress structure will determine whether the expected relationship between Ων and km holds.

These measurements will limit the abundance of ultra-light fields that begin oscillations in the matter-dominated era.

Another powerful test of the possible abundance of ultralight fields beginning oscillations in the matter era will be an accurate measure of the position of the turn over in the matter power spectrum, since this gives a handle on the species present at equality. Ultra-light fields with masses in the regime such that they begin oscillations in the radiation-dominated era may suppress structure at scales where the BAO are relevant, and thus distort them. Improving the accuracy of the BAO measurement would place severe limits on ultralight fields in this mass regime.

Recently, [837] showed that with current and next generation galaxy surveys alone it should be possible to unambiguously detect a fraction of dark matter in axions with 10−33 _eV

. m _.

10−29 _{eV of the order of 1% of the total. Furthermore, they demonstrated that the tightest}

constraints on the axion fraction fax come from weak lensing; when combined with a galaxy

21_{Lyman-alpha forest power spectra can push constraints further at the high mass end, although the results in}

10−32 10−31 10−30 10−29 100 101 102 103 104

Fiducial Axion Mass [eV]

Uncertainty in f ax [Percent] CMB GRS WL Total

Figure 50: Marginalized uncertainty infax for CMB (green), a galaxy redshift survey (red), weak

lensing (blue) and the total (black) evaluated for four different fiducial axion masses, for the cosmology ΛCDM+fax+ν. Image reproduced by permission from [837], copyright by APS.

redshift survey, constraining fax to 0.1% should be possible, see Figure 50. The strength of the

weak lensing constraint depends on the photometric redshift measurement, i.e., on tomography. Therefore, lensing tomography will allow Euclid – through the measurement of the growth rate – to resolve the redshift evolution of the axion suppression of small scale convergence power. Further details can be found in [837].

At the heavier end withm_&10−24_{eV axions affect structure formation on scales comparable to}

WDM withmW &0.2 keV [838]. By matching the scale at which the transfer function is suppressed

by factor of 2, one can make a map between axion and WDM masses. This map, adapted from Ref. [838], is shown in Fig. 51. Such a map serves as a guide to the constraining power of Euclid on axions based on WDM forecasts and constraints. However it should be noted that the Jeans scale is dynamical for axions, leading to scale dependent growth, and different non-linear behaviour to WDM, so dedicated studies are needed. For example, constraining mWDM > 2 keV [830] (and

Section 2.6 of this review) can constrain axions to m_&10−21 eV as the main component of the DM. Reaching this level is significant as it approaches the exclusion limits from black hole super radiance [83].

The expected suppression of structure caused by ultralight fields should be properly taken into account inN-body simulations. The nonlinear regime of P(k) needs to be explored further both analytically and numerically for cosmologies containing ultra-light fields, especially to constrain those fields which are heavy enough such that km occurs around the scale where nonlinearities

become significant, i.e., those that begin oscillation deep inside the radiation-dominated regime and are naively degenerate with WDM. For lighter fields the effects in the nonlinear regime should be well-modelled by using the linearP(k) forN-body input, and shifting the other variables such as Ωc accordingly.

Figure 51: Mapping between axion and WDM mass that suppress power by a factor of two at the same scale. This can be used to approximately the axion mass constraint possible with Euclid on based on WDM forecasts.

percent-level constraints on an ultra-light scalar field contribution to the DM over 12 to 13 orders of magnitude in mass in the range 10−33 _eV

.m_.10−20 _eV.

2.12

Dark-matter surrogates in theories of modified gravity