PHYSICAL REVIEW D 101, 063030 (2020) Cosmological evolution of light dark photon dark matter Samuel D. McDermott 1 and Samuel J. Witte 2 1Theoretical Astrophysics Group, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 2Instituto de Física Corpuscular (IFIC), CSIC-Universitat de Val`encia, 46980 Paterna, Spain (Received 20 November 2019; accepted 9 March 2020; published 27 March 2020) Light dark photons are subject to various plasma effects, such as Debye screening and resonant oscillations, which can lead to a more complex cosmological evolution than is experienced by conventional cold dark matter candidates. Maintaining a consistent history of dark photon dark matter requires ensuring that the superthermal abundance present in the early Universe (i) does not deviate significantly after the formation of the cosmic microwave background (CMB), and (ii) does not excessively leak into the Standard Model plasma after big band nucleosynthesis (BBN). We point out that the role of nonresonant absorption, which has previously been neglected in cosmological studies of this dark matter candidate, produces strong constraints on dark photon dark matter with mass as low as 10−22 eV. Furthermore, we show that resonant conversion of dark photons after recombination can produce excessive heating of the intergalactic medium (IGM) which is capable of prematurely reionizing hydrogen and helium, leaving a distinct imprint on both the Ly-α forest and the integrated optical depth of the CMB. Our constraints surpass existing cosmological bounds by more than 5 orders of magnitude across a wide range of dark photon masses. DOI: 10.1103/PhysRevD.101.063030 I. INTRODUCTION additional model complexity [19]. The work of [12] provided a compelling alternative production mechanism As many once-favored models of particle dark matter due to fluctuations of the metric during a period of early- become increasingly constrained (see e.g., [1–5]), candi- Universe inflation, but the nonobservation of primordial dates other than those resulting from weak-scale thermal gravitational waves constrain this mechanism from pro- freeze-out have been the subject of growing focus and ducing a viable dark matter population if m 0 ≲ μeV. More development. One candidate of recent interest is the dark A recently, [13–17] showed that a dark photon coupled to a photon, A0 [6–19], which arises from an Abelian group hidden sector (pseudo)scalar field can generate the entire outside of the Standard Model (SM) gauge group. This −20 dark matter with masses as light as m 0 ∼ 10 eV. This particle may “kinetically mix” with the SM photon via the A μν 0 superthermal population of dark photons is generated by renormalizable operator ϵF Fμν=2 [20], with “natural” ϵ 10−16 10−2 – temperature-dependent instabilities or defects in the values of typically ranging from to [21 23]. (pseudo)scalar field. Given that various works have now Historically, one of the more problematic features of provided more compelling mechanisms to generate what light vector dark matter has been the identification of a had perhaps previously been a more speculative dark matter simple, well-motivated production mechanism. Early work candidate, we find it timely to revisit old, and develop on the subject suggested that such a candidate could be novel, cosmological constraints on (and potential signa- produced via the misalignment mechanism [10], similar to tures of) light dark photon dark matter. that of axion dark matter (see e.g., [24,25]), but it was later The observational signatures of dark photon dark matter pointed out that this mechanism is inefficient at generating are quite distinct from canonical weak-scale particles. the desired relic abundance unless one also introduces a Various cosmological effects of light dark photon dark R large nonminimal coupling to the curvature [11,12,18]. matter have been investigated over the years, typically Such a coupling, however, can introduce ghost instabilities focusing exclusively on the observational consequences – in the longitudinal modes [26 28]; while it may be possible arising from the resonant transition between dark and visible to avoid this feature, proposed solutions come at the cost of photons that occurs when the plasma frequency ωp is approximately equal to the mass of the dark photon mA0 [11]. These constraints, however, are typically only appli- 0 −14 0 Published by the American Physical Society under the terms of cable for m 0 ≥ ω¯ ∼ 10 eV, ω¯ being the background the Creative Commons Attribution 4.0 International license. A p p Further distribution of this work must maintain attribution to plasma frequency today. More recently, limits on very light the author(s) and the published article’s title, journal citation, dark photons were obtained using the observation that and DOI. Funded by SCOAP3. the kinetic mixing allows for an off-shell (nonresonant) 2470-0010=2020=101(6)=063030(14) 063030-1 Published by the American Physical Society SAMUEL D. MCDERMOTT and SAMUEL J. WITTE PHYS. REV. D 101, 063030 (2020) absorption of dark photons, subsequently heating baryonic Y 2ζð3Þ n ¼ X ðzÞ 1 − p η T3ð1 þ zÞ3: ð Þ matter; if this heating is sufficiently large, it may destroy the e e 2 π2 0 1 thermal equilibrium of the Milky Way’s interstellar medium [29], that of ultrafaint dwarf galaxies such as Leo T [30],or In Eq. (1), XeðzÞ is the free electron fraction, Yp is the cold gas clouds in the Galactic Center [31]. This idea has primordial helium abundance, η is the baryon to photon also been used to project the sensitivity that could be ratio, and T0 is the temperature of the CMB today. The obtained from future 21 cm experiments which observe function XeðzÞ can be obtained using the open-source absorption spectra during the cosmic dark ages [32]. code class [34], and we fix Yp ¼ 0.245 [35,36] and T0 ¼ In this work, we put forth a simple cosmological picture 2.7255 K [37]. of dark photon dark matter, requiring only that (i) dark In general, dark photons and SM photons will convert matter is not overly depleted after recombination and (ii) the with equal probability. An asymmetry in energy flow is energy deposited into the SM plasma does not produce therefore possible only due to initial conditions: at the time unwanted signatures in BBN, the CMB, or the Ly-α forest. of the formation of the CMB the SM photons are described We identify (and describe in a unified manner) the resonant to good precision by a blackbody at a temperature ð1 þ Þ and nonresonant contributions to both of these classes of T0 zCMB , while dark photons that constitute the cold observables. We find that these simple and robust require- dark matter must be a collection of nonthermal particles ments lead to extremely stringent constraints for light with a number density far larger than nγ and an energy photon dark matter, covering dark photon masses all the spectrum peaked very close to m 0 (for the sake of −22 A way down to ∼10 eV. Our constraints are stronger completeness, we will also address the possible existence than existing bounds across a wide range of masses (in of dark photons with a very small initial number density). some cases by more than 5 orders of magnitude), and The total energy taken from the reservoir of cold dark 1 are robust against astrophysical uncertainties. photons and introduced to the SM photon bath is This work is organized as follows. We begin by outlining Z the relevant on- and off-shell conversion processes that alter Δρ 0 ¼ 0 ð Þ ρ 0 ð Þ ð Þ the energy and number densities of the dark sector and SM A →γ dzPA →γ z × A z ; 2 plasma. We then discuss various cosmological implications for the existence of light dark photon dark matter, including where PA0→γðzÞ is the redshift-dependent probability of 0 modifications to the evolution of the energy density after conversion from an A to a SM photon and ρA0 ðzÞ is the neutrino decoupling, spectral distortions produced in the redshift-dependent energy density of dark photons. Later, CMB, dark matter evaporation, and modifications to the we will consider the energy injected normalized to the Ly-α forest from the heating of the IGM. We conclude by number density of baryons, which is given by Eq. (2) with discussing more speculative ways in which sensitivity can the simplifying substitution ρA0 ðzÞ → ρA0 ðzÞ=nbðzÞ. If the be extended to the low mass regime. conversion probability is small, one can approximate 3 0 0 ρ 0 ð Þ ∼ ð1 þ Þ ρ ρ A z z A0 , with A0 being the mean dark matter II. PLASMA MASS AND (DARK) PHOTON density today; however, in some cases, the probability is CONVERSION sufficiently large that dark matter density prior to con- version is significantly greater than the dark matter density Dark photons and SM photons can interconvert through after, in which case the aforementioned approximation is cosmic time. Accurately treating this conversion requires not valid. accounting for plasma effects: the SM photon has a Similarly to Eq. (2), we may write the energy extracted modified dispersion relation in a charged plasma, given 2 2 from the SM photon bath as [6,9] by ω ¼ ReΠðω;k;neÞþk . The dimensionful scale 4 Z 3 4 that governs the SM photon dispersion relationP is the T0 x ð1 þ zÞ Δρ 0 ð Þ¼ 0 ð Þ ð Þ Πðω Þ∝ω2 ð Þ¼4πα ð Þ γ→A E 2 dzdx Pγ→A x; z ; 3 plasma mass Re ;k;ne p z EM ni z =EF;i; π ex − 1 here, nqi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiis the number density of species i and 2 2 2 3 where x ≡ E=T, and we have explicitly included the energy E ¼ m þð2π n Þ = is the charged particle Fermi F;i i i dependence in the conversion probability since the CMB energy.