Search

Journal of cosmology and astroparticle physics 04(04), 010 (2022). doi:10.1088/1475-7516/2022/04/010, We revisit the computation of bubble wall friction during a cosmological first-order phase transition, using an extended fluid Ansatz to solve the linearized Boltzmann equation. A singularity is found in the fluctuations of background species as the wall approaches the speed of sound. Using hydrodynamics, we argue that a discontinuity across the speed of sound is expected on general grounds, which manifests itself as the singularity in the solution of the linearized system. We discuss this result in comparison with alternative approaches proposed recently, which find a regular behaviour of the friction for all velocities., Published by IOP, London

Seminar, Hamburg, Germany; Journal of cosmology and astroparticle physics 02, 014 (2022). doi:10.1088/1475-7516/2022/02/014, Stochastic gravitational wave (GW) backgrounds from first-order phase transitions are an exciting target for future GW observatories and may enable us to study dark sectors with very weak couplings to the Standard Model. In this work we show that such signals may be significantly enhanced for hot dark sectors with a temperature larger than the one of the SM thermal bath. The need to transfer the entropy from the dark sector to the SM after the phase transition can however lead to a substantial dilution of the GW signal. We study this dilution in detail, including the effect of number-changing processes in the dark sector (so-called cannibalism), and show that in large regions of parameter space a net enhancement remains. We apply our findings to a specific example of a dark sector containing a dark Higgs boson and a dark photon and find excellent detection prospects for LISA and the Einstein telescope., Published by IOP, London

Axion-like particles (ALPs) decaying into photons are known to affect a wide range of astrophysical and cosmological observables. In this study we focus on ALPs with masses in the keV-MeV range and lifetimes between $10^4$ and $10^{13}$ seconds, corresponding to decays between the end of Big Bang Nucleosynthesis and the formation of the Cosmic Microwave Background (CMB). Using the CosmoBit module of the global fitting framework GAMBIT, we combine state-of-the-art calculations of the irreducible ALP freeze-in abundance, primordial element abundances (including photodisintegration through ALP decays), CMB spectral distortions and anisotropies, and constraints from supernovae and stellar cooling. This approach makes it possible for the first time to perform a global analysis of the ALP parameter space while varying the parameters of $\Lambda$CDM as well as several nuisance parameters. We find a lower bound on the ALP mass of around $m_a > 300\,\text{keV}$, which can only be evaded if ALPs are stable on cosmological timescales. Future observations of CMB spectral distortions with a PIXIE-like mission are expected to improve this bound by two orders of magnitude., Comment: 29+16 pages, 9 figures. V2 corresponds to the published version. Auxiliary material available on Zenodo at https://zenodo.org/record/6573347

A search for Beyond the Standard Model double-β decay modes of 76Ge has been performed with data collected during the Phase II of the GERmanium Detector Array (Gerda) experiment, located at the Laboratori Nazionali del Gran Sasso of INFN (Italy). Improved limits on the decays involving Majorons have been obtained, compared to previous experiments with 76Ge, with half-life values on the order of 1023 yr. For the first time with 76Ge, limits on Lorentz invariance violation effects in double-β decay have been obtained. The isotropic coefficient åof (3), which embeds Lorentz violation in double-β decay, has been constrained at the order of 10-6 GeV. We also set the first experimental limits on the search for light exotic fermions in double-β decay, including sterile neutrinos.

Journal of cosmology and astroparticle physics 05(5), 004 (2022). doi:10.1088/1475-7516/2022/05/004, The U$\mu \nu$SSM is a U(1)' extension of the U$\mu \nu$SSM supersymmetric model, where baryon-number-violating operators as well as explicit mass terms are forbidden, and the potential domain wall problem is avoided. The gauge anomaly-cancellation conditions impose the presence of exotic quark superfields in the spectrum of U$\mu \nu$SSM models, and allow the presence of several singlet superfields under the standard model gauge group, in addition to the right-handed neutrino superfields. The gauge structure implies an additional discrete Z $_{2}$ symmetry in the superpotential, ensuring the stability of a singlet which behaves as WIMP dark matter without invoking R-parity. We analyze this novel possibility in detail, using the fermionic component of the singlet as the dark matter candidate. In particular, we compute its amount of relic density via Z', Higgs-right sneutrino and dark matter mediated annihilations, and its potential signals in dark matter direct detection experiments. The constraints on the parameter space due to Z'; direct searches at the LHC are imposed in the analysis, as well as those from the hadronization inside the detector of the exotic quarks. Large regions of the parameter space turn out to be in the reach of the upcoming Darwin experiment., Published by IOP, London

We reassess the viability of a cosmological model including a fourth additional sterile neutrino species that self-interacts through a new pseudoscalar degree of freedom. We perform a series of extensive analyses fitting various combinations of cosmic microwave background (CMB) data from Planck, the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT), both alone and in combination with Baryon Acoustic Oscillation (BAO) and Supernova Ia (SnIa) observations. We show that the scenario under study, although capable to resolve the Hubble tension without worsening the so-called $S_8$ tension about the growth of cosmic structures, is severely constrained by high-multipole polarization data from both Planck and SPT. Intriguingly, when trading Planck TE-EE data for those from ACT, we find a $\gtrsim 3 \sigma$ preference for a non-zero sterile neutrino mass, $m_s=3.6^{+1.1}_{-0.6}$ eV (68 % C.L.), compatible with the range suggested by longstanding short-baseline (SBL) anomalies in neutrino oscillation experiments. The pseudoscalar model provides indeed a better fit to ACT data compared to $\Lambda$CDM ($\Delta\chi^2 \simeq -5$, $\Delta \rm{AIC}=-1.3$), although in a combined analysis with Planck the $\Lambda$CDM model is still favoured, as the preference for a non-zero sterile neutrino mass is mostly driven by ACT favouring a higher value for the primordial spectral index $n_s$ with respect to Planck. We show that the mild tension between Planck and ACT is due to the different pattern in the TE and EE power spectra on multipoles between $350 \lesssim \ell \lesssim 1000$. We also check the impact of marginalizing over the gravitational lensing information in Planck data, showing that the model does not solve the CMB lensing anomaly. Future work including higher precision data from current and upcoming CMB ground-based experiments will be crucial to test these results., Comment: 34 pages, 12 figures, 9 tables. Comments are welcome. v3: Version published in JCAP

Low-energy effective field theories containing a light scalar field are used extensively in cosmology, but often there is a tension between embedding such theories in a healthy UV completion and achieving a phenomenologically viable screening mechanism in the IR. Here, we identify the range of interaction couplings which allow for a smooth resummation of classical non-linearities (necessary for kinetic/Vainshtein-type screening), and compare this with the range allowed by unitarity, causality and locality in the underlying UV theory. The latter region is identified using positivity bounds on the $2\to2$ scattering amplitude, and in particular by considering scattering about a non-trivial background for the scalar we are able to place constraints on interactions at all orders in the field (beyond quartic order). We identify two classes of theories can both exhibit screening and satisfy existing positivity bounds, namely scalar-tensor theories of $P(X)$ or quartic Horndeski type in which the leading interaction contains an odd power of $X$. Finally, for the quartic DBI Galileon (equivalent to a disformally coupled scalar in the Einstein frame), the analogous resummation can be performed near two-body systems and imposing positivity constraints introduces a non-perturbative ambiguity in the screened scalar profile. These results will guide future searches for UV complete models which exhibit screening of fifth forces in the IR., 34+12 pages, 6 figures

A dark QCD sector is a relatively minimal extension of the Standard Model (SM) that admits Dark Matter (DM) candidates but requires no portal to the visible sector beyond gravitational interactions: A "nightmare scenario" for DM detection. We consider a secluded dark sector containing a single flavor of light, vector-like dark quark gauged under $SU(N)$. In the large-$N$ limit, this single-flavor theory becomes highly predictive, generating two DM candidates whose masses and dynamics are described by few parameters: A light quark-antiquark bound state, the dark analog of the $\eta'$ meson, and a heavy bound state of $N$ quarks, the dark analog of the $\Delta^{++}$ baryon. We show that the latter may freeze-in with an abundance independent of the confinement scale, forming DM-like relics for $N \lesssim 10$, while the former may generate DM via cannibalization and freeze-out. We study the interplay of this two-component DM system and determine the characteristic ranges of the confinement scale, dark-visible sector temperature ratio, and $N$ that admit non-excluded DM, once the effects of self-interaction constraints and bounds on effective degrees of freedom at the BBN and CMB epochs are included., Comment: 28 pages, 6 figures

We derive lower bounds for the Higgs-curvature coupling from vacuum stability during inflation in three inflationary models: quadratic and quartic chaotic inflation, and Starobinsky-like power-law inflation. In contrast to most previous studies we take the time-dependence of the Hubble rate into account both in the geometry of our past light-cone and in the Higgs effective potential, which is approximated with three-loop renormalisation group improvement supplemented with one-loop curvature corrections. We find that in all three models, the lower bound is $\xi\gtrsim 0.051\ldots 0.066$ depending on the top quark mass. We also demonstrate that vacuum decay is most likely to happen a few $e$-foldings before the end of inflation., Comment: 22 pages, 5 figures, v3: Accepted for publication on JCAP, minor typos fixed

We analyse the dynamics of the relativistic bubble expansion during the first order phase transition focusing on the ultra relativistic velocities $\gamma\gg 1$. We show that fields much heavier than the scale of the phase transition can significantly contribute to the friction and modify the motion of the bubble wall leading to interesting phenomenological consequences. NLO effects on the friction due to the soft vector field emission are reviewed as well., Comment: Non-vanishing width of the bubble wall effects are taken into account

Journal of cosmology and astroparticle physics 12(12), 006 (1-28) (2021). doi:10.1088/1475-7516/2021/12/006, A metastable cosmic-string network is a generic consequence of many grand unified theories (GUTs) when combined with cosmic inflation. Metastable cosmic strings are not topologically stable, but decay on cosmic time scales due to pair production of GUT monopoles. This leads to a network consisting of metastable long strings on superhorizon scales as well as of string loops and segments on subhorizon scales. We compute for the first time the complete stochastic gravitational-wave background (SGWB) arising from all these network constituents, including several technical improvements to both the derivation of the loop and segment contributions. We find that the gravitational waves emitted by string loops provide the main contribution to the gravitational-wave spectrum in the relevant parameter space. The resulting spectrum is consistent with the tentative signal observed by the NANOGrav and Parkes pulsar timing collaborations for a string tension of G $_{��}$ ��� 10$^{-11���-7}$ and has ample discovery space for ground- and space-based detectors. For GUT-scale string tensions, G $_{��}$ ��� 10$^{-8���-7}$, metastable strings predict a SGWB in the LIGO-Virgo-KAGRA band that could be discovered in the near future., Published by IOP, London

The U$\mu\nu$SSM is a $U(1)'$ extension of the $\mu\nu$SSM supersymmetric model, where baryon-number-violating operators as well as explicit mass terms are forbidden, and the potential domain wall problem is avoided. The gauge anomaly-cancellation conditions impose the presence of exotic quark superfields in the spectrum of U$\mu\nu$SSM models, and allow the presence of several singlet superfields under the standard model gauge group, in addition to the right-handed neutrino superfields. The gauge structure implies an additional discrete $Z_2$ symmetry in the superpotential, ensuring the stability of a singlet which behaves as WIMP dark matter without invoking $R$-parity. We analyze this novel possibility in detail, using the fermionic component of the singlet as the dark matter candidate. In particular, we compute its amount of relic density via $Z'$, Higgs-right sneutrino and dark matter mediated annihilations, and its potential signals in dark matter direct detection experiments. The constraints on the parameter space due to $Z'$ direct searches at the LHC are imposed in the analysis, as well as those from the hadronization inside the detector of the exotic quarks. Large regions of the parameter space turn out to be in the reach of the upcoming Darwin experiment.

The relic gravitational wave background due to tensor linear perturbations generated during Higgs inflation is computed. Both the Standard Model and a well-motivated phenomenological completion (that accounts for all the experimentally confirmed evidence of new physics) are considered. We focus on critical Higgs inflation, which improves on the non-critical version and features an amplification of the tensor fluctuations. The latter property allows us to establish that future space-borne interferometers, such as DECIGO, BBO and ALIA, may detect the corresponding primordial gravitational waves., Comment: v2: 20 pages, 2 figures, published version

Primordial electromagnetic fields can strongly affect the cosmic evolution of axions, and vice versa. We show that if helical electromagnetic fields are coherently produced in the early universe, their remnants source a field velocity to the coupled axions and enhance the relic abundance of axion dark matter. We discuss the implications for the QCD axion and axion-like particles that are coupled to the SM or hidden gauge groups. For a QCD axion coupled to hidden photons, we find that the conventional window for the axion decay constant $10^{8}\, \mathrm{GeV} \lesssim f \lesssim 10^{12}\, \mathrm{GeV}$ can be completely closed due to overproduction of axion dark matter by helical electromagnetic fields as little as $\alpha \, \Delta N_{\mathrm{eff}} \gtrsim 10^{-12}$, where $\alpha$ is the gauge coupling and $\Delta N_{\mathrm{eff}}$ is the effective extra relativistic degrees of freedom of the hidden photons., Comment: 24 pages, 3 figures, v2: published in JCAP

(2022). doi:10.1088/1475-7516/2022/04/010, We revisit the computation of bubble wall friction during a cosmological first-order phase transition, using an extended fluid Ansatz to solve the linearized Boltzmann equation. A singularity is found in the fluctuations of background species as the wall approaches the speed of sound. Using hydrodynamics, we argue that a discontinuity across the speed of sound is expected on general grounds, which manifests itself as the singularity in the solution of the linearized system. We discuss this result in comparison with alternative approaches proposed recently, which find a regular behaviour of the friction for all velocities.

We construct families, and concrete examples, of simple extensions of the Standard Model that can yield ultralight {real or} complex vectors or scalars with potential astrophysical relevance. Specifically, the mass range for these putative fundamental bosons ($\sim 10^{-10}-10^{-20}$ eV) would lead dynamically to both new non-black hole compact objects (bosonic stars) and new non-Kerr black holes, with masses of $\sim M_\odot$ to $\sim 10^{10} M_\odot$, corresponding to the mass range of astrophysical black hole candidates (from stellar mass to supermassive). For each model, we study the properties of the mass spectrum and interactions after spontaneous symmetry breaking, discuss its theoretical viability and caveats, as well as some of its potential and most relevant phenomenological implications {linking them to the} physics of compact objects., Comment: 27 pages, 2 figures

In the Starobinsky model of inflation, the observed dark matter abundance can be produced from the direct decay of the inflaton field only in a very narrow spectrum of close-to-conformal scalar fields and spinors of mass $\sim 10^7$ GeV. This spectrum can be, however, significantly broadened in the presence of effective non-renormalizable interactions between the dark and the visible sectors. In particular, we show that UV freeze-in can efficiently generate the right dark matter abundance for a large range of masses spanning from the keV to the PeV scale and arbitrary spin, without significantly altering the heating dynamics. We also consider the contribution of effective interactions to the inflaton decay into dark matter., 24 pages, 6 figures, new section, typos corrected, references added, matches the published version

We provide a general framework for self-interacting warm dark matter (WDM) in cosmological perturbations, by deriving from first principles a Boltzmann hierarchy which retains certain independence from a particular interaction Lagrangian. We consider elastic interactions among the massive particles, and obtain a hierarchy which is more general than the ones usually obtained for non-relativistic (as for cold DM) or for ultra-relativistic (as for neutrinos) approximations. The more general momentum-dependent kernel integrals in the Boltzmann collision terms, are explicitly calculated for different field-mediator models, including examples of a scalar field (either massive or massless) or a massive vector field. As an application, we study the evolution of the interaction rate per particle under the relaxation time approximation, and assess when a given self-interaction is relevant in comparison with the Hubble expansion rate. Our framework aims to be a useful starting point to evaluate DM self-interaction effects in the linear power spectrum, necessary to then study its evolution all the way to non-linear stages of structure formation, where certain DM interactions were proven to be relevant., Comment: Published in Journal of Cosmology and Astroparticle Physics, 57 pages, 3 figures and 4 appendices

We revisit a cosmological constraint on dark matter decaying into dark radiation at late times. In Enqvist et al. (2015), we mainly focused on the effects of decaying dark matter (DDM) on the cosmic microwave background (CMB) and nonlinear matter power spectrum. Extending our previous analysis, here we use N-body simulation to investigate how DDM affects the halo mass function. This allows us to incorporate the cluster counts observed by the Sunyaev-Zel'dovich effect to study a bound on the lifetime of DDM. We also update the data of CMB and cosmic shear power spectrum with the Planck 2015 results and KiDS450 observations, respectively. From these cosmological observations, we obtain an lower bound on the lifetime $\Gamma^{-1}\ge 175\,$Gyr from the Planck2015 results (CMB+SZ cluster count) combined with the KiDS450 and the recent measurements of the baryon acoustic scale., Comment: 12 pages, 5 figures, 1 table

We investigate how sterile neutrinos with a range of masses influence cosmology in MeV-scale reheating temperature scenarios. By computing the production of sterile neutrinos through the combination of mixing and scattering in the early Universe, we find that light sterile neutrinos, with masses and mixings as inferred from short-baseline neutrino oscillation experiments, are consistent with big-bang nucleosynthesis (BBN) and cosmic microwave background (CMB) radiation for the reheating temperature of ${\cal O}(1)$ MeV if the parent particle responsible for reheating decays into electromagnetic components (radiative decay). In contrast, if the parent particle mainly decays into hadrons (hadronic decay), the bound from BBN becomes more stringent. In this case, the existence of the light sterile neutrinos can be cosmologically excluded, depending on the mass and the hadronic branching ratio of the parent particle., 33 pages, 10 figures, to appear in JCAP

Photons traveling cosmological distances through the inhomogeneous Universe experience a great variation in their in-medium induced effective mass. Using the EAGLE suite of hydrodynamical simulations, we infer the free electron distribution and thereby the effective photon mass after reionization. We use this data to study the inter-conversion of kinetically mixed photons and dark photons, which may occur at a great number of resonance redshifts, and obtain the "optical depth" against conversion along random lines-of-sight. Using COBE/FIRAS, Planck, and SPT measurements, we constrain the dark photon parameter space from the depletion of CMB photons into dark photons that causes both spectral distortions and additional anisotropies in the CMB. Finally, we also consider the conversion of sub-eV dark radiation into ordinary photons. We make the line-of-sight distributions of both, free electrons and dark matter, publicly available., 29 pages, 17 figures

Dark matter (DM) from freeze-in or superWIMP production is well known to imprint non-cold DM signatures on cosmological observables. We derive constraints from Lyman-$\alpha$ forest observations for both cases, basing ourselves on a reinterpretation of the existing Lyman-$\alpha$ limits on thermal warm DM. We exclude DM masses below 15 keV for freeze-in, in good agreement with previous literature, and provide a generic lower mass bound for superWIMPs that depends on the mother particle decay width. Special emphasis is placed on the mixed scenario, where contributions from both freeze-in and superWIMP are similarly important. In this case, the imprint on cosmological observables can deviate significantly from thermal warm DM. Furthermore, we provide a modified version of the Boltzmann code CLASS, analytic expressions for the DM distributions, and fits to the DM transfer functions that account for both mechanisms of production. Moreover, we also derive generic constraints from $\Delta N_\mathrm{eff}$ measurements and show that they cannot compete with those arising from Lyman-$\alpha$ observations. For illustration, we apply the above generic limits to a coloured $t$-channel mediator DM model, in which case contributions from both freeze-in through scatterings and decays, as well as superWIMP production can be important. We map out the entire cosmologically viable parameter space, cornered by bounds from Lyman-$\alpha$ observations, the LHC, and Big Bang Nucleosynthesis., Comment: 31 pages + references, 5 figures, v2: Legend of Fig. 2 corrected, Appendix A expanded, references added

We study the origin of fifth forces in scalar-tensor theories of gravity in the so-called Jordan frame, where the modifications to the gravitational sector are manifest. We focus on theories of Brans-Dicke type in which an additional scalar field is coupled directly to the Ricci scalar of General Relativity. We describe how the necessary diffeomorphism invariance of the modified gravitational sector leads to a modification of the usual gauge fixing term (for the harmonic gauge), as compared to Einstein gravity. This allows us to perform a consistent linearization of the gravitational sector in the weak-field limit, which gives rise to a kinetic mixing between the non-minimally coupled scalar field and the graviton. It is through this mixing that a fifth force can arise between matter fields. We are then able to compute the matrix elements for fifth-force exchanges directly in the Jordan frame, without the need to perform a conformal transformation to the so-called Einstein frame, where the gravitational sector is of Einstein-Hilbert form. We obtain results that are in agreement with the equivalent Einstein-frame calculations and illustrate, still in the Jordan frame, the pivotal role that sources of explicit scale symmetry breaking in the matter sector play in admitting fifth-force couplings., Comment: revtext format, 36 pages, 3 figures

Primordial black holes may have been produced in the early stages of the thermal history of the Universe after cosmic inflation. If so, dark matter in the form of elementary particles can be subsequently accreted around these objects, in particular when it gets non-relativistic and further streams freely in the primordial plasma. A dark matter mini-spike builds up gradually around each black hole, with density orders of magnitude larger than the cosmological one. We improve upon previous work by carefully inspecting the computation of the mini-spike radial profile as a function of black hole mass, dark matter particle mass and temperature of kinetic decoupling. We identify a phase-space contribution that has been overlooked and that leads to changes in the final results. We also derive complementary analytical formulae using convenient asymptotic regimes, which allows us to bring out peculiar power-law behaviors for which we provide tentative physical explanations., Comment: 54 pages, 11 figures. v2: minor corrections, references added. Matches the published version

We explore the dark matter phenomenology of a weak-scale right-handed neutrino in the context of a Two Higgs Doublet Model. The expected signal at direct detection experiments is different from the usual spin-independent and spin-dependent classification since the scattering with quarks depends on the dark matter spin. The dark matter relic density is set by thermal freeze-out and in the presence of non-standard cosmology, where an Abelian gauge symmetry is key for the dark matter production mechanism. We show that such symmetry allows us to simultaneously address neutrino masses and the flavor problem present in general Two Higgs Doublet Model constructions. Lastly, we outline the region of parameter space that obeys collider, perturbative unitarity and direct detection constraints., Comment: 27 pages, 3 figures. Matches the version accepted for publication in JCAP

In the context of gauge theories, observable quantities, if properly defined and computed, do not depend on the gauge-fixing procedure. In this paper, we develop a formalism that implements this (apparent) tautology in the case of inflation. As a simple application, we discuss Coleman-Weinberg "hilltop" inflation.

We investigate first order phase transitions arising from hidden sectors which are in thermal equilibrium with the Standard Model bath in the Early Universe. Focusing on two simplified scenarios, an higgsed U(1) and a two scalar singlet model, we show the impact of friction effects acting on the bubble walls on the gravitational wave spectra and on the consequences for present and future interferometer experiments. We further comment on the possibility of disentangling the properties of the underlying theory featuring the first order phase transition should a stochastic gravitational wave signal be discovered., 31 pages, 8 figures, matches version published in JCAP; typos in v2 are fixed

Multi-peaked spectra of the primordial gravitational waves are considered as a phenomenologically relevant source of information about the dynamics of sequential phase transitions in the early Universe. In particular, such signatures trace back to specific patterns of the first-order electroweak phase transition in the early Universe occurring in multiple steps. Such phenomena appear to be rather generic in multi-scalar extensions of the Standard Model. In a particularly simple extension of the Higgs sector, we have identified and studied the emergence of sequential long- and short-lasting transitions as well as their fundamental role in generation of multi-peaked structures in the primordial gravitational-wave spectrum. We discuss the potential detectability of these signatures by the proposed gravitational-wave interferometers., Comment: 33 pages, 7 figures; references added; discussion of the results updated; published version

We provide a complete classification of Poincar\'e-invariant scalar field theories with an enlarged set of classical symmetries to leading order in derivatives, namely for the so-called $P(X,\phi)$ theories, in two or more spacetime dimensions. We find only three possibilities: Dirac-Born-Infeld, Cuscuton and Scaling theories. The latter two classes of actions involve an arbitrary function of the scalar field. As an application, we use the scaling symmetry to derive an infinite set of constraints on the Wilsonian coefficients of the low-energy Effective Field Theory. Furthermore, we study the extension of these results to cosmological (FLRW) and (Anti-)de Sitter spacetimes. We find in particular that the Cuscuton action has a generic set of symmetries around any background spacetime that possesses Killing vector fields, while the DBI actions have well-known analogues that we summarize explicitly., Comment: 26 pages

We show that for a relatively light majoron ($\ll 100 $ eV) non-thermal production from topological defects is an efficient production mechanism. Taking the type I seesaw as benchmark scheme, we estimate the primordial majoron abundance and determine the required parameter choices where it can account for the observed cosmological dark matter. The latter is consistent with the scale of unification. Possible direct detection of light majorons with future experiments such as PTOLEMY and the formation of boson stars from the majoron dark matter are also discussed., 27 pages, 3 figures; v2: references added, matches published version