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Perspectives on fundamental cosmology from Low Earth Orbit and the Moon

Perspectives on fundamental cosmology from Low Earth Orbit and the Moon www.nature.com/npjmgrav PERSPECTIVE OPEN Perspectives on fundamental cosmology from Low Earth Orbit and the Moon 1✉ 2✉ 1✉ Gianfranco Bertone , Oliver L. Buchmueller and Philippa S. Cole The next generation of space-based experiments will go hunting for answers to cosmology’s key open questions which revolve around inflation, dark matter and dark energy. Low earth orbit and lunar missions within the European Space Agency’s Human and Robotic Exploration programme can push our knowledge forward in all of these three fields. A radio interferometer on the Moon, a cold atom interferometer in low earth orbit and a gravitational wave interferometer on the Moon are highlighted as the most fruitful missions to plan and execute in the mid-term. npj Microgravity (2023) 9:10 ; https://doi.org/10.1038/s41526-022-00243-2 INTRODUCTION as a specific model for how one or more scalar fields drove the expansion. The standard cosmological model provides a simple framework to −3 −1 On large scales, k ~10 − 0.1 Mpc , observations of the CMB explain a variety of observations, ranging from sub-galactic scales temperature anisotropies by Planck have confirmed to incredible to the size of the observable universe. Yet many open questions precision that density perturbations were small (fluctuations of remain: the model relies on an unknown mechanism for the −5 order 10 ) and almost scale-invariant. The simplest single-field, production of perturbations in the early universe, on an unknown slow-roll models of inflation are able to describe this spectrum of matter component, generically referred to as dark matter, and on the density perturbations. However, deviations from scale- an unknown mechanism that leads to an accelerated expansion of invariance on small scales could indicate a more complicated the universe, generically referred to as dark energy. model that exhibits a feature in the inflationary potential. Such The next generation of space-based experiments are our best models could have interesting observational signatures, such as chance of unveiling these mysteries. A united front of low earth 7,8 9 ultra-compact mini-haloes or primordial black holes . Further- orbit and lunar missions, as outlined in the European Space more, primordial non-Gaussianity has been constrained to be Agency’s (ESA) Human and Robotic Exploration (HRE) , will break small, f = − 0.9 ± 5.1, on large scales . This constraint has unprecedented ground on all of these fronts. Alongside the Laser NL,local limited the viability of many models of inflation that predicted Interferometer Space Antenna , a radio interferometer on the larger values of primordial non-Gaussianity, for example DBI Moon, a cold atom interferometer in low earth orbit and a 11,12 inflation and EFT inflation . However, reaching the f <1 gravitational wave interferometer on the Moon would provide a NL,local threshold will provide strong evidence that observations are not full-coverage approach to unravelling the key open questions in consistent with multi-field models of inflation . The final piece of cosmology today. the puzzle can be provided by the tensor-to-scalar ratio, which is In section “Key knowledge gaps” the key knowledge gaps in currently constrained to be less than 0.1 , a measurement of cosmology are highlighted, in section “Priorities for the space which would indicate the energy scale at which inflation programme” specific suggestions for experiments that should be happened. the priorities for ESA’s space programme and which questions they will answer are laid out, before concluding and discussing the future outlook in section “Future outlook and summary”. Dark matter Similarly, the existence of dark matter is supported by a wide array of independent observations, but we still know very little about KEY KNOWLEDGE GAPS the fundamental nature of this elusive component of the universe. Inflation In the past four decades, a strong effort went into the search for a The theory of inflation is arguably the most promising model of particular class of candidates: weakly interacting massive parti- 3 14 the physics of the early universe . The paradigm postulates that cles . However, no experiment has yet found evidence for these quantum fluctuations went on to seed the cosmological particles, and attention has turned to different classes of dark perturbations that we see imprinted on the Cosmic Microwave matter candidates in regions of parameter space where they Background (CMB) and were the beginnings of all of the structure would have evaded strong constraints from direct detection 15–17 in the universe today. And yet, much remains to be understood before now, for example axion-like-particles (ALPs) or about the properties of the quantum field that supposedly led to primordial black holes (PBHs) . the initial period of exponential expansion of the universe. Whilst Axion-like-particles are in particular a popular dark matter 4–6 15–17 the paradigm is fully consistent with cosmological data , we still candidate . The QCD (quantum chromodynamics) axion was currently lack direct smoking-gun evidence supporting it, as well first postulated in the 70s to solve the strong CP problem . Gravitation Astroparticle Physics Amsterdam (GRAPPA), Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands. Imperial College London, Exhibition Rd, South Kensington, London SW7 2BX, United Kingdom. email: g.bertone@uva.nl; o.buchmueller@imperial.ac.uk; p.s.cole@uva.nl Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; G. Bertone et al. However, ALPs more generally, often motivated by string theories A diversified experimental approach involving astronomical in which ultra-light particles are ubiquitous, display the qualities surveys and gravitational waves searches are arguably our best required to explain all or part of the dark matter. Whilst searches hope to make progress in the search for smoking-gun evidence of for the standard axion with a mass of order of a few hundred keV inflation, identification of dark matter, and understanding of dark have yielded no detections, "invisible” axions with very small energy. We will highlight possibilities for future space-based masses are still viable candidates. Search strategies vary depend- experiments that can break new ground on these frontiers. ing on the mass of the axion, which can’t be theoretically predicted, but the most common approach is to probe their PRIORITIES FOR THE SPACE PROGRAMME interactions with electromagnetic fields and constrain the axion- photon coupling . Astrophysical observations are able to look for Space experiments may soon provide important clues on the signatures of axion to photon conversion in the presence of nature of inflation, dark matter and dark energy. As an overview of electromagnetic fields, for example, by looking for such processes the current context, we list in Table 1 some experiments that 21–23 in the vicinity of the magnetosphere of neutron stars , or their might in particular enable gravitational wave searches for production in the solar core, triggered by X-rays scattering off signatures of dark matter and primordial gravitational waves with electrons and protons in the presence of the Sun’s strong space-borne interferometers as well as indirect detection of dark magnetic fields . matter and probing primordial fluctuations with Moon-based For masses less than 1eV, axions are a sub-set of the broader radio telescopes. We choose to focus on three key probes as most class of ultra-light dark matter models, with masses down to relevant in the framework of ESA’s Human and Robotic Explora- −24 (theoretically) 10 eV, although Lyman-alpha forest constraints tion Directorate to address the knowledge gaps discussed above: −20 25 26 have ruled out axion masses less than 2 × 10 eV , see for a A. a radio interferometer on the Moon (RIM) review. Ultra-light dark matter models postulate a new ultra-light B. a space gravitational wave detector using cold atoms boson, which displays wave-like properties on galactic scales, but (AEDGE) behaves like cold dark matter on larger scales where the cold dark C. a gravitational waves interferometer on the Moon (GWIM) matter (CDM) paradigm has strong support from observations. The behaviour on galactic scales, due to the Bose-Einstein condensate which forms, can have interesting signatures that Radio interferometer on the Moon 27,28 could explain small-scale problems with CDM and would have The most relevant experiment for ESA’s Directorate of Human and distinctive features for distinguishing between models such as 38–41 Robotic Exploration is the radio interferometer on the Moon . fuzzy dark matter, self-interacting fuzzy dark matter and superfluid The rationale for this experiment is that placing a radio telescope 29,30 dark matter . on the far side of the Moon would give it access to wavelengths Another promising candidate that received a lot of renewed shorter than 30 MHz. Radiation at these frequencies is distorted or attention after the LIGO/Virgo observations of order 10 solar mass completely absorbed by the Earth’s ionosphere. An interferometer 31–33 binary black hole mergers is primordial black holes . They are on the Moon will bypass this limitation, as well as shield the the only proposed explanation of dark matter that requires no instruments from the background generated by terrestrial radio new physics beyond the standard model, which makes them an sources. Furthermore, the size of the array, which determines the attractive candidate. However, strong constraints have now been resolution of the detector, is less restricted than an Earth-based placed across the parameter space via microlensing, gravitational detector like the Hydrogen Epoch of Reionization Array (HERA) , waves and CMB observations which have essentially ruled them the Low Frequency Array (LoFAR) or the Square Kilometre Array out as making up the entirety of the dark matter budget in all but (SKA) . one window around an asteroid mass. See e.g., Ref. for a review A radio telescope on the Moon would allow us to peer into the of current constraints. There is also the possibility of two- so-called dark ages of the universe , i.e., the epoch between the component dark matter models that include primordial black emission of the CMB and the reionization of the universe, holes and another particle, with interesting signatures of triggered by the formation of the first stars. By studying the 35,36 interaction between the two . redshifted 21-cm line absorption feature, we can obtain unprece- dented information on the history of reionization, and search for Dark energy the signatures of dark matter annihilation or decay by looking for 46,47 Dark energy is a generic term for the mechanism responsible for specific forms of the absorption feature . the observed accelerated expansion of the universe. One of the Furthermore, a radio interferometer on the Moon could in key questions that may bring us closer to the identification of dark principle have baselines as long as 300km, which would enable 48–50 energy is whether its energy density has remained constant unprecedented access to information about very small scales . throughout the history of the universe, as would be the case if it Measuring the 21cm power spectrum would provide a tracer for arises from the so-called vacuum energy, or whether it evolves the underlying dark matter power spectrum. This could unlock with time, as appropriate for an evolving quantum field. See e.g., information about dark matter sub-structures, the existence of Ref. for a review. primordial black holes, and the validity of slow-roll inflationary Table 1. Recommendations for addressing key questions in fundamental cosmology with the ESA HRE programme in the short, middle and long term. Open fundamental scientific Focus of ESA HRE platform : LEO, Context of related recent and future space Short, middle or long term question Moon, Mars, BLEO experiments Origin of primordial fluctuations Moon LISA, AEDGE, RIM Middle term Nature of dark matter LEO LISA, AEDGE, AEDGE pathfinder, RIM, GWIM Middle term Phase transitions LEO LISA, AEDGE Middle term Existence of primordial Moon LISA, AEDGE, GWIM Middle term black holes npj Microgravity (2023) 10 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; G. Bertone et al. models. Tomographic analysis will also enable information to be of post-Newtonian parameters would offer powerful probes of the gathered at a range of redshifts, providing new insight into the predictions of general relativity and searches for deviations due to, evolution of our Universe between the time of the CMB and today. for example, a graviton mass . Comparing measurements in Finally, a lunar radio telescope would allow us also to efficiently different frequency ranges will also make possible sensitive probe the so-called primordial non-gaussianity via the 21cm probes of Lorentz invariance . 51–53 bispectrum , which would provide a powerful test of the An opportunity to learn about the nature of dark matter from theory of inflation. 21cm observations will complement upcoming gravitational wave signals can also be realised by observations of large-scale structure surveys which will help us to understand how coalescing black holes in the deci-Hz band. Intermediate mass 3 5 structures are evolving, allowing for even more information to be black holes (10 − 10 M ) and primordial black holes (of any 70,71 extracted from the as yet un-probed region both in terms of mass) may be surrounded by dense dark matter spikes .If redshift and access to small scales. 21cm observations from the these black holes form binaries with a much lighter companion, −2.5 Moon therefore add to the line of inquiry on all three fronts: i.e., intermediate and extreme mass ratios (q = m /m <10 ), 2 1 inflation, dark matter and dark energy. then the dark matter may imprint a dephasing on the gravitational Arguably the largest challenge to overcome will be how to deal waveform of the inspiralling binary. The amount of dephasing with extremely large foregrounds. They are expected to be 6 or 7 could teach us something about the nature of the dark matter orders of magnitude larger than the signal being sought, and surrounding the black holes, for example whether it’s cold and therefore systematics will need to be incredibly well understood. collisionless, or whether it’s an ultra-light scalar field. LISA will have 54,55 Extremely careful subtraction of galactic foregrounds will need 72–74 sensitivity to such effects for larger mass systems , future to be performed so that any signal found in the data can be ground-based gravitational wave observatories will have sensitiv- 56–58 confidently interpreted . ity to low-mass systems, and an experiment such as AEDGE could bridge the gap to cover the entire frequency range and promote Cold atom interferometer multi-band searches for the same signal. The gravitational wave The direct detection of gravitational waves (GW) with LIGO/Virgo, signal could also be accompanied by an electromagnetic counter- that led to the Nobel prize for Physics in 2017, has opened new part that might provide information about an environment opportunities for cosmology. The space interferometer LISA has involving dark matter if the particle is able to convert to radiation been selected to be ESA’s third large-class mission, and it is or interact with it in some way like it does in the case of, for scheduled to be launched in 2034. Experience with the electro- example, axions. magnetic spectrum shows the importance of measurements over Possible non-black hole binary cosmological targets for the a range of frequencies, and we note that there is a gap between deci-Hz band include GWs from first-order phase transitions in the the frequencies covered by LIGO/Virgo, as well as proposed early Universe, e.g., during electroweak symmetry breaking in detectors Einstein Telescope and Cosmic Explorer on Earth, and modifications of the Standard Model with additional interactions, LISA in space, in the deci-Hz band. or during the breaking of higher gauge symmetries . The deci-Hz A promising candidate to explore this frequency band is the frequency range could also probe different parameter ranges for AEDGE mission concept , which is based on novel quantum such transitions, and combining measurements with those by technology utilising Cold Atom (CA) techniques. Gravitational other experiments like LISA or LIGO/Virgo could help unravel waves alter the distance between the cold atom clouds as they different contributions, e.g., from bubble collisions, sound waves pass through the interferometer. 76,77 and turbulence . Another cosmological target for the deci-Hz AEDGE will be able to probe the gravitational waves due to 78 band is the possible GW spectrum produced by cosmic strings . coalescing intermediate mass black holes with masses In standard cosmology this spectrum would be almost scale- 100 − 10 M . This could shed light on the existence of invariant, but there could be modifications due to a non-standard intermediate black holes, and their potential role as seeds for evolution of the early Universe. A detection or constraint on such the growth of supermassive black holes . Additionally, black observables could additionally provide clues as to the nature of holes in the pair-instability mass gap will enter the deci-Hz range. dark matter, especially in the case of ultra-light dark matter If this gap is populated then it will motivate a deeper under- particles which are expected to be produced alongside GWs from standing of supernova collapse, or the need to invoke alternative phase transitions in the early Universe and topological defects mechanisms for producing such large black holes such as such as cosmic strings. 61–63 hierarchical mergers . Improved constraints on order 100M As outlined in the Cold Atom in Space Community Roadmap , primordial black holes should also be possible, which would 64 AEDGE, its pathfinder experiments, and other cold-atom experi- complement constraints from the CMB on this mass range . ments in space would also be able to make sensitive measure- AEDGE can also probe a wide array of dark matter candidates. ments relevant to several other aspects of fundamental physics, Scalar field dark matter, for instance, causes quantities such as the including the gravitational redshift, the equivalence principle, electron mass and the fine structure constant to oscillate with 80,81 possible long-range fifth forces , variations in fundamental frequency and amplitude determined by the dark matter mass constants and popular models of dark energy . and local density. This leads to variation in the atomic transition With the AION experiment in the UK , the MAGIS experiment in frequencies, which imprint on the relative phase difference 84 85 the US , the MIGA experiment in France , the ZAIGA experiment between cold atom clouds that atom interferometers measure. 86 87 in China , as well as the proposed European ELGAR project , Proposed AEDGE sensitivities will enable the coupling between there is already a large programme of terrestrial cold atom scalar dark matter and electrons, photons or via the Higgs-portal experiments in place. These experiments serve as terrestrial to be probed with up to 10 orders of magnitude improvement, pathfinders for a large-scale mission like AEDGE, and it would be with respect to current constraints from MICROSCOPE , on mass −18 −12 important to complement those with a dedicated technology ranges between 10 and 10 eV. Other couplings can also be development programme to pave the way for space-based cold probed, for example the axion-nucleon coupling for axion-like DM −14 atom pathfinder experiments. First, dedicated pathfinders could lighter than 10 eV, or the coupling between a dark vector boson 66,67 be hosted at the International Space Station, building the and the difference between baryon and lepton number . Furthermore, AEDGE offers a new channel for probing strong foundation of a medium-class mission. This could then lead in gravity regimes, where any deviations from general relativity are the long-term to a large-class mission such as AEDGE to explore most likely to be noticeable. For example, precise measurements the ultimate physics potential of the deci-Hz band. Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2023) 10 G. Bertone et al. A gravitational waves interferometer on the Moon 18. Bertone, G. & Tait, T. 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Correspondence and requests for materials should be addressed to Gianfranco 71. Eda, K., Itoh, Y., Kuroyanagi, S. & Silk, J. Gravitational waves as a probe of dark Bertone, Oliver L. Buchmueller or Philippa S. Cole. matter minispikes. Phys. Rev. D 91, 044045 (2015). 72. Kavanagh, B. J., Nichols, D. A., Bertone, G. & Gaggero, D. Detecting dark matter Reprints and permission information is available at http://www.nature.com/ around black holes with gravitational waves: effects of dark-matter dynamics on reprints the gravitational waveform. Phys. Rev. D 102, 083006 (2020). 73. Coogan, A., Bertone, G., Gaggero, D., Kavanagh, B. J. & Nichols, D. A. Measuring Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims the dark matter environments of black hole binaries with gravitational waves. in published maps and institutional affiliations. Phys. Rev. D. 105, 043009 (2022). 74. Ng, K. K., Isi, M., Haster, C.-J. & Vitale, S. Multiband gravitational-wave searches for ultralight bosons. Phys. Rev. D 102, 083020 (2020). 75. Zhou, R., Bian, L., Guo, H.-K. & Wu, Y. Gravitational wave and collider searches for Open Access This article is licensed under a Creative Commons electroweak symmetry breaking patterns. Phys. Rev. D 101, 035011 (2020). Attribution 4.0 International License, which permits use, sharing, 76. Jinno, R. & Takimoto, M. Gravitational waves from bubble collisions: an analytic adaptation, distribution and reproduction in any medium or format, as long as you give derivation. Phys. Rev. D 95, 024009 (2017). appropriate credit to the original author(s) and the source, provide a link to the Creative 77. Galtier, S. & Nazarenko, S. V. Direct evidence of a dual cascade in gravitational Commons license, and indicate if changes were made. The images or other third party wave turbulence. Phys. Rev. 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D 94, 044051 (2016). © The Author(s) 2023 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2023) 10 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png npj Microgravity Springer Journals

Perspectives on fundamental cosmology from Low Earth Orbit and the Moon

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www.nature.com/npjmgrav PERSPECTIVE OPEN Perspectives on fundamental cosmology from Low Earth Orbit and the Moon 1✉ 2✉ 1✉ Gianfranco Bertone , Oliver L. Buchmueller and Philippa S. Cole The next generation of space-based experiments will go hunting for answers to cosmology’s key open questions which revolve around inflation, dark matter and dark energy. Low earth orbit and lunar missions within the European Space Agency’s Human and Robotic Exploration programme can push our knowledge forward in all of these three fields. A radio interferometer on the Moon, a cold atom interferometer in low earth orbit and a gravitational wave interferometer on the Moon are highlighted as the most fruitful missions to plan and execute in the mid-term. npj Microgravity (2023) 9:10 ; https://doi.org/10.1038/s41526-022-00243-2 INTRODUCTION as a specific model for how one or more scalar fields drove the expansion. The standard cosmological model provides a simple framework to −3 −1 On large scales, k ~10 − 0.1 Mpc , observations of the CMB explain a variety of observations, ranging from sub-galactic scales temperature anisotropies by Planck have confirmed to incredible to the size of the observable universe. Yet many open questions precision that density perturbations were small (fluctuations of remain: the model relies on an unknown mechanism for the −5 order 10 ) and almost scale-invariant. The simplest single-field, production of perturbations in the early universe, on an unknown slow-roll models of inflation are able to describe this spectrum of matter component, generically referred to as dark matter, and on the density perturbations. However, deviations from scale- an unknown mechanism that leads to an accelerated expansion of invariance on small scales could indicate a more complicated the universe, generically referred to as dark energy. model that exhibits a feature in the inflationary potential. Such The next generation of space-based experiments are our best models could have interesting observational signatures, such as chance of unveiling these mysteries. A united front of low earth 7,8 9 ultra-compact mini-haloes or primordial black holes . Further- orbit and lunar missions, as outlined in the European Space more, primordial non-Gaussianity has been constrained to be Agency’s (ESA) Human and Robotic Exploration (HRE) , will break small, f = − 0.9 ± 5.1, on large scales . This constraint has unprecedented ground on all of these fronts. Alongside the Laser NL,local limited the viability of many models of inflation that predicted Interferometer Space Antenna , a radio interferometer on the larger values of primordial non-Gaussianity, for example DBI Moon, a cold atom interferometer in low earth orbit and a 11,12 inflation and EFT inflation . However, reaching the f <1 gravitational wave interferometer on the Moon would provide a NL,local threshold will provide strong evidence that observations are not full-coverage approach to unravelling the key open questions in consistent with multi-field models of inflation . The final piece of cosmology today. the puzzle can be provided by the tensor-to-scalar ratio, which is In section “Key knowledge gaps” the key knowledge gaps in currently constrained to be less than 0.1 , a measurement of cosmology are highlighted, in section “Priorities for the space which would indicate the energy scale at which inflation programme” specific suggestions for experiments that should be happened. the priorities for ESA’s space programme and which questions they will answer are laid out, before concluding and discussing the future outlook in section “Future outlook and summary”. Dark matter Similarly, the existence of dark matter is supported by a wide array of independent observations, but we still know very little about KEY KNOWLEDGE GAPS the fundamental nature of this elusive component of the universe. Inflation In the past four decades, a strong effort went into the search for a The theory of inflation is arguably the most promising model of particular class of candidates: weakly interacting massive parti- 3 14 the physics of the early universe . The paradigm postulates that cles . However, no experiment has yet found evidence for these quantum fluctuations went on to seed the cosmological particles, and attention has turned to different classes of dark perturbations that we see imprinted on the Cosmic Microwave matter candidates in regions of parameter space where they Background (CMB) and were the beginnings of all of the structure would have evaded strong constraints from direct detection 15–17 in the universe today. And yet, much remains to be understood before now, for example axion-like-particles (ALPs) or about the properties of the quantum field that supposedly led to primordial black holes (PBHs) . the initial period of exponential expansion of the universe. Whilst Axion-like-particles are in particular a popular dark matter 4–6 15–17 the paradigm is fully consistent with cosmological data , we still candidate . The QCD (quantum chromodynamics) axion was currently lack direct smoking-gun evidence supporting it, as well first postulated in the 70s to solve the strong CP problem . Gravitation Astroparticle Physics Amsterdam (GRAPPA), Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands. Imperial College London, Exhibition Rd, South Kensington, London SW7 2BX, United Kingdom. email: g.bertone@uva.nl; o.buchmueller@imperial.ac.uk; p.s.cole@uva.nl Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; G. Bertone et al. However, ALPs more generally, often motivated by string theories A diversified experimental approach involving astronomical in which ultra-light particles are ubiquitous, display the qualities surveys and gravitational waves searches are arguably our best required to explain all or part of the dark matter. Whilst searches hope to make progress in the search for smoking-gun evidence of for the standard axion with a mass of order of a few hundred keV inflation, identification of dark matter, and understanding of dark have yielded no detections, "invisible” axions with very small energy. We will highlight possibilities for future space-based masses are still viable candidates. Search strategies vary depend- experiments that can break new ground on these frontiers. ing on the mass of the axion, which can’t be theoretically predicted, but the most common approach is to probe their PRIORITIES FOR THE SPACE PROGRAMME interactions with electromagnetic fields and constrain the axion- photon coupling . Astrophysical observations are able to look for Space experiments may soon provide important clues on the signatures of axion to photon conversion in the presence of nature of inflation, dark matter and dark energy. As an overview of electromagnetic fields, for example, by looking for such processes the current context, we list in Table 1 some experiments that 21–23 in the vicinity of the magnetosphere of neutron stars , or their might in particular enable gravitational wave searches for production in the solar core, triggered by X-rays scattering off signatures of dark matter and primordial gravitational waves with electrons and protons in the presence of the Sun’s strong space-borne interferometers as well as indirect detection of dark magnetic fields . matter and probing primordial fluctuations with Moon-based For masses less than 1eV, axions are a sub-set of the broader radio telescopes. We choose to focus on three key probes as most class of ultra-light dark matter models, with masses down to relevant in the framework of ESA’s Human and Robotic Explora- −24 (theoretically) 10 eV, although Lyman-alpha forest constraints tion Directorate to address the knowledge gaps discussed above: −20 25 26 have ruled out axion masses less than 2 × 10 eV , see for a A. a radio interferometer on the Moon (RIM) review. Ultra-light dark matter models postulate a new ultra-light B. a space gravitational wave detector using cold atoms boson, which displays wave-like properties on galactic scales, but (AEDGE) behaves like cold dark matter on larger scales where the cold dark C. a gravitational waves interferometer on the Moon (GWIM) matter (CDM) paradigm has strong support from observations. The behaviour on galactic scales, due to the Bose-Einstein condensate which forms, can have interesting signatures that Radio interferometer on the Moon 27,28 could explain small-scale problems with CDM and would have The most relevant experiment for ESA’s Directorate of Human and distinctive features for distinguishing between models such as 38–41 Robotic Exploration is the radio interferometer on the Moon . fuzzy dark matter, self-interacting fuzzy dark matter and superfluid The rationale for this experiment is that placing a radio telescope 29,30 dark matter . on the far side of the Moon would give it access to wavelengths Another promising candidate that received a lot of renewed shorter than 30 MHz. Radiation at these frequencies is distorted or attention after the LIGO/Virgo observations of order 10 solar mass completely absorbed by the Earth’s ionosphere. An interferometer 31–33 binary black hole mergers is primordial black holes . They are on the Moon will bypass this limitation, as well as shield the the only proposed explanation of dark matter that requires no instruments from the background generated by terrestrial radio new physics beyond the standard model, which makes them an sources. Furthermore, the size of the array, which determines the attractive candidate. However, strong constraints have now been resolution of the detector, is less restricted than an Earth-based placed across the parameter space via microlensing, gravitational detector like the Hydrogen Epoch of Reionization Array (HERA) , waves and CMB observations which have essentially ruled them the Low Frequency Array (LoFAR) or the Square Kilometre Array out as making up the entirety of the dark matter budget in all but (SKA) . one window around an asteroid mass. See e.g., Ref. for a review A radio telescope on the Moon would allow us to peer into the of current constraints. There is also the possibility of two- so-called dark ages of the universe , i.e., the epoch between the component dark matter models that include primordial black emission of the CMB and the reionization of the universe, holes and another particle, with interesting signatures of triggered by the formation of the first stars. By studying the 35,36 interaction between the two . redshifted 21-cm line absorption feature, we can obtain unprece- dented information on the history of reionization, and search for Dark energy the signatures of dark matter annihilation or decay by looking for 46,47 Dark energy is a generic term for the mechanism responsible for specific forms of the absorption feature . the observed accelerated expansion of the universe. One of the Furthermore, a radio interferometer on the Moon could in key questions that may bring us closer to the identification of dark principle have baselines as long as 300km, which would enable 48–50 energy is whether its energy density has remained constant unprecedented access to information about very small scales . throughout the history of the universe, as would be the case if it Measuring the 21cm power spectrum would provide a tracer for arises from the so-called vacuum energy, or whether it evolves the underlying dark matter power spectrum. This could unlock with time, as appropriate for an evolving quantum field. See e.g., information about dark matter sub-structures, the existence of Ref. for a review. primordial black holes, and the validity of slow-roll inflationary Table 1. Recommendations for addressing key questions in fundamental cosmology with the ESA HRE programme in the short, middle and long term. Open fundamental scientific Focus of ESA HRE platform : LEO, Context of related recent and future space Short, middle or long term question Moon, Mars, BLEO experiments Origin of primordial fluctuations Moon LISA, AEDGE, RIM Middle term Nature of dark matter LEO LISA, AEDGE, AEDGE pathfinder, RIM, GWIM Middle term Phase transitions LEO LISA, AEDGE Middle term Existence of primordial Moon LISA, AEDGE, GWIM Middle term black holes npj Microgravity (2023) 10 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; G. Bertone et al. models. Tomographic analysis will also enable information to be of post-Newtonian parameters would offer powerful probes of the gathered at a range of redshifts, providing new insight into the predictions of general relativity and searches for deviations due to, evolution of our Universe between the time of the CMB and today. for example, a graviton mass . Comparing measurements in Finally, a lunar radio telescope would allow us also to efficiently different frequency ranges will also make possible sensitive probe the so-called primordial non-gaussianity via the 21cm probes of Lorentz invariance . 51–53 bispectrum , which would provide a powerful test of the An opportunity to learn about the nature of dark matter from theory of inflation. 21cm observations will complement upcoming gravitational wave signals can also be realised by observations of large-scale structure surveys which will help us to understand how coalescing black holes in the deci-Hz band. Intermediate mass 3 5 structures are evolving, allowing for even more information to be black holes (10 − 10 M ) and primordial black holes (of any 70,71 extracted from the as yet un-probed region both in terms of mass) may be surrounded by dense dark matter spikes .If redshift and access to small scales. 21cm observations from the these black holes form binaries with a much lighter companion, −2.5 Moon therefore add to the line of inquiry on all three fronts: i.e., intermediate and extreme mass ratios (q = m /m <10 ), 2 1 inflation, dark matter and dark energy. then the dark matter may imprint a dephasing on the gravitational Arguably the largest challenge to overcome will be how to deal waveform of the inspiralling binary. The amount of dephasing with extremely large foregrounds. They are expected to be 6 or 7 could teach us something about the nature of the dark matter orders of magnitude larger than the signal being sought, and surrounding the black holes, for example whether it’s cold and therefore systematics will need to be incredibly well understood. collisionless, or whether it’s an ultra-light scalar field. LISA will have 54,55 Extremely careful subtraction of galactic foregrounds will need 72–74 sensitivity to such effects for larger mass systems , future to be performed so that any signal found in the data can be ground-based gravitational wave observatories will have sensitiv- 56–58 confidently interpreted . ity to low-mass systems, and an experiment such as AEDGE could bridge the gap to cover the entire frequency range and promote Cold atom interferometer multi-band searches for the same signal. The gravitational wave The direct detection of gravitational waves (GW) with LIGO/Virgo, signal could also be accompanied by an electromagnetic counter- that led to the Nobel prize for Physics in 2017, has opened new part that might provide information about an environment opportunities for cosmology. The space interferometer LISA has involving dark matter if the particle is able to convert to radiation been selected to be ESA’s third large-class mission, and it is or interact with it in some way like it does in the case of, for scheduled to be launched in 2034. Experience with the electro- example, axions. magnetic spectrum shows the importance of measurements over Possible non-black hole binary cosmological targets for the a range of frequencies, and we note that there is a gap between deci-Hz band include GWs from first-order phase transitions in the the frequencies covered by LIGO/Virgo, as well as proposed early Universe, e.g., during electroweak symmetry breaking in detectors Einstein Telescope and Cosmic Explorer on Earth, and modifications of the Standard Model with additional interactions, LISA in space, in the deci-Hz band. or during the breaking of higher gauge symmetries . The deci-Hz A promising candidate to explore this frequency band is the frequency range could also probe different parameter ranges for AEDGE mission concept , which is based on novel quantum such transitions, and combining measurements with those by technology utilising Cold Atom (CA) techniques. Gravitational other experiments like LISA or LIGO/Virgo could help unravel waves alter the distance between the cold atom clouds as they different contributions, e.g., from bubble collisions, sound waves pass through the interferometer. 76,77 and turbulence . Another cosmological target for the deci-Hz AEDGE will be able to probe the gravitational waves due to 78 band is the possible GW spectrum produced by cosmic strings . coalescing intermediate mass black holes with masses In standard cosmology this spectrum would be almost scale- 100 − 10 M . This could shed light on the existence of invariant, but there could be modifications due to a non-standard intermediate black holes, and their potential role as seeds for evolution of the early Universe. A detection or constraint on such the growth of supermassive black holes . Additionally, black observables could additionally provide clues as to the nature of holes in the pair-instability mass gap will enter the deci-Hz range. dark matter, especially in the case of ultra-light dark matter If this gap is populated then it will motivate a deeper under- particles which are expected to be produced alongside GWs from standing of supernova collapse, or the need to invoke alternative phase transitions in the early Universe and topological defects mechanisms for producing such large black holes such as such as cosmic strings. 61–63 hierarchical mergers . Improved constraints on order 100M As outlined in the Cold Atom in Space Community Roadmap , primordial black holes should also be possible, which would 64 AEDGE, its pathfinder experiments, and other cold-atom experi- complement constraints from the CMB on this mass range . ments in space would also be able to make sensitive measure- AEDGE can also probe a wide array of dark matter candidates. ments relevant to several other aspects of fundamental physics, Scalar field dark matter, for instance, causes quantities such as the including the gravitational redshift, the equivalence principle, electron mass and the fine structure constant to oscillate with 80,81 possible long-range fifth forces , variations in fundamental frequency and amplitude determined by the dark matter mass constants and popular models of dark energy . and local density. This leads to variation in the atomic transition With the AION experiment in the UK , the MAGIS experiment in frequencies, which imprint on the relative phase difference 84 85 the US , the MIGA experiment in France , the ZAIGA experiment between cold atom clouds that atom interferometers measure. 86 87 in China , as well as the proposed European ELGAR project , Proposed AEDGE sensitivities will enable the coupling between there is already a large programme of terrestrial cold atom scalar dark matter and electrons, photons or via the Higgs-portal experiments in place. These experiments serve as terrestrial to be probed with up to 10 orders of magnitude improvement, pathfinders for a large-scale mission like AEDGE, and it would be with respect to current constraints from MICROSCOPE , on mass −18 −12 important to complement those with a dedicated technology ranges between 10 and 10 eV. 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