Dark strings have recently been suggested to exist in new models of dark matter that explain the excessive electronic production in the galaxy. We study the interaction of these dark strings with semilocal strings which are solutions of the bosonic sector of the Standard Model in the limit $\sin^2θ_{\rm w}=1$, where $θ_{\rm w}$ is the Weinberg angle. While embedded Abelian-Higgs strings exist for generic values of the coupling constants, we show that semilocal solutions with non-vanishing condensate inside the string core exist only above a critical value of the Higgs to gauge boson mass ratio when interacting with dark strings. Above this critical value, which is greater than unity, the energy per unit length of the semilocal-dark string solutions is always smaller than that of the embedded Abelian-Higgs-dark string solutions and we show that Abelian-Higgs-dark strings become unstable above this critical value. Different from the non-interacting case, we would thus expect semilocal strings to be stable for values of the Higgs to gauge boson mass ratio larger than unity. Moreover, the one-parameter family of solutions present in the non-interacting case ceases to exist when semilocal strings interact with dark strings.
Semilocal and electroweak strings are well-known to be unstable against unwinding by the condensation of the second Higgs component in their cores. A large class of current models of dark matter contains dark scalar fields coupled to the Higgs sector of the Standard Model (Higgs portal) and/or dark U(1) gauge fields. It is shown, that Higgs-portal-type couplings and a gauge kinetic mixing term of the dark U(1) gauge field have a significant stabilising effect on semilocal strings in the "visible" sector.
It has been pointed out that cosmic string solutions can exist in gauge field theories with broken symmetry even when $π_1(G/H)$ is trivial. The stability of such semilocal defects is not guaranteed by topology and depends on dynamical considerations. In the literature it has been tacitly assumed that if stable, such strings would form in the Early Universe in a manner analogous to the formation of a network of more robust topologically-stable strings. In this paper we find that except for unnaturally small values of the correlation length, a network of semilocal strings does not form. Instead…
In this work we calibrate two different analytic models of semilocal strings by constraining the values of their free parameters. In order to do so, we use data obtained from the largest and most accurate field theory simulations of semilocal strings to date, and compare several key properties with the predictions of the models. As this is still work in progress, we present some preliminary results together with descriptions of the methodology we are using in the characterisation of semilocal string networks.
We report on a detailed numerical study of the evolution of semilocal string networks, based on the largest and most accurate field theory simulations of these objects to date. We focus on the large-scale network properties, confirming earlier indications (coming from smaller simulations) that linear scaling is the attractor solution for the entire parameter space of initial conditions that we are able to probe. We also provide a brief comparison of our numerical results with the predictions of a previously developed one-scale model for the overall evolution of these networks. Two subsequent p…
Semilocal strings are vortices in the extended Abelian-Higgs model with two complex Higgs scalar fields among which a global $SU(2)$ symmetry acts. They are known to be stable (unstable against expansion) in type-I (II) superconductors, in which gauge field is heavier (lighter) than the Higgs scalar field. In this paper, we find that vortices can be stabilized in the whole parameter region including the type-II region by adding a potential term breaking the $SU(2)$ symmetry. We construct numerical solutions in various parameters and determine the vortex phase diagram consisting of six phases. …
We revisit previously developed analytic models for defect evolution and adapt them appropriately for the study of semilocal string networks. We thus confirm the expectation (based on numerical simulations) that linear scaling evolution is the attractor solution for a broad range of model parameters. We discuss in detail the evolution of individual semilocal segments, focusing on the phenomenology of segment growth, and also provide a preliminary comparison with existing numerical simulations.
We report on a large scale numerical study of networks of semilocal cosmic strings in flat space in the parameter regime in which they are perturbatively stable. We find a population of segments with an exponential length distribution and indications of a scaling network without significant loop formation. Very deep in the stability regime strings of superhorizon size grow rapidly and ``percolate'' through the box. We believe these should lead at late times to a population of infinite strings similar to topologically stable strings. However, the strings are very light; scalar gradients dominat…
We study the intercommuting of semilocal strings and Skyrmions, for a wide range of internal parameters, velocities and intersection angles by numerically evolving the equations of motion. We find that the collisions of strings and strings, strings and Skyrmions, and Skyrmions and Skyrmions, all lead to intercommuting for a wide range of parameters. Even the collisions of unstable Skyrmions and strings leads to intercommuting, demonstrating that the phenomenon of intercommuting is very robust, extending to dissimilar field configurations that are not stationary solutions. Even more remarkably,…
We discuss the properties of semilocal strings minimally coupled to gravity. Semilocal strings are solutions of the bosonic sector of the Standard Model in the limit $\sin^2θ_W=1$ (where $θ_W$ is the Weinberg angle) and correspond to embedded Abelian-Higgs strings for a particular choice of the scalar doublet. We focus on the limit where the gauge boson mass is equal to the Higgs boson mass such that the solutions fulfill the Bogomolnyi-Prasad-Sommerfield (BPS) bound.
We study the stability properties of the twisted vortex solutions in the semilocal Abelian Higgs model with a global $\mathbf{SU}(2)$ invariance. This model can be viewed as the Weinberg-Salam theory in the limit where the non-Abelian gauge field decouples, or as a two component Ginzburg-Landau theory. The twisted vortices are characterized by a constant global current ${\cal I}$, and for ${\cal I}\to 0$ they reduce to the semilocal strings, that is to the Abrikosov-Nielsen-Olesen vortices embedded into the semilocal model. Solutions with ${\cal I}\neq 0$ are more complex and, in particular, t…
We review a class of non-topological defects in the standard electroweak model, and their implications. Starting with the semilocal string, which provides a counterexample to many well known properties of topological vortices, we discuss electroweak strings and their stability with and without external influences such as magnetic fields. Other known properties of electroweak strings and monopoles are described in some detail and their potential relevance to future particle accelerator experiments and to baryon number violating processes is considered. We also review recent progress on the cosm…
Among the inflationary models based on string theory, the D3/D7 model has the advantage that the flatness of the inflaton potential can be protected even with moduli stabilization. However, the Abrikosov-Nielsen-Olesen BPS cosmic strings produced at the end of original D3/D7 inflation lead to an additional contribution to the CMB anisotropy. To make this contribution consistent with the WMAP results one needs an extremely small gauge coupling in the effective D-term inflation model. Such couplings may be difficult to justify in string theory. Here we develop a generalized version of the D3/D7 …
We present the first ever calculation of cosmic microwave background CMB anisotropy power spectra from semilocal cosmic strings, obtained via simulations of a classical field theory. Semilocal strings are a type of non-topological defect arising in some models of inflation motivated by fundamental physics, and are thought to relax the constraints on the symmetry breaking scale as compared to models with (topological) cosmic strings. We derive constraints on the model parameters, including the string tension parameter mu, from fits to cosmological data, and find that in this regard BPS semiloca…
A variation on the abelian Higgs model, with global SU(2) x local U(1) symmetry broken to global U(1) was recently shown by Vachaspati and Achucarro to admit stable, finite energy cosmic string solutions even though the manifold of minima of the potential energy does not have non-contractible loops. Here the most general solutions, both in the single and multi-vortex cases, are described in the Bogomol'nyi limit. The gravitational field of the vortices considered as cosmic strings is obtained and monopole-like solutions surrounded by an event horizon are found.
We continue a comprehensive numerical study of semilocal string networks and their cosmological evolution. These can be thought of as hybrid networks comprised of (non-topological) string segments, whose core structure is similar to that of Abelian Higgs vortices, and whose ends have long--range interactions and behaviour similar to that of global monopoles. Our study provides further evidence of a linear scaling regime, already reported in previous studies, for the typical length scale and velocity of the network. We introduce a new algorithm to identify the position of the segment cores. Thi…
We demonstrate that the stability of the semilocal vortex can be significantly improved by the presence of a dilatonic coupling of the form e^\frac{q | Φ|^2}{η^2} F_{μν}F^{μν} with q>0 where ηis the scale of symmetry breaking that gives rise to the vortex. For q=0 we obtain the usual embedded (semilocal) Nielsen-Olesen vortex. We find the stability region of the parameter β= (\frac{m_Φ}{m_A})^2 (m_Φand m_A are the masses of the scalar and gauge fields respectively). We show that the stability region of βis 0<β<β_{max}(q) where β_{max}(q=0)=1 (as expected) and β_{max}(q) is an increasing functi…
We consider non-Abelian semilocal strings (vortices, or vortex-strings) arising in N=2 supersymmetric U(N) gauge theory with Nf=N+Ñ matter hypermultiplets in the fundamental representation (quarks), and a Fayet-Iliopoulos term ξ. We present, for the first time ever, a systematic field-theoretic derivation of the world-sheet theory for such strings, describing dynamics of both, orientational and size zero modes. Our derivation is complete in the limit, ln(L)\rightarrow \infty, where L is an infrared (IR) regulator in the transverse plane. In this limit the world-sheet theory is obtained exactly…
We study non-Abelian vortex strings in ${\mathcal N}=2$ supersymmetric QCD with the gauge group U$(N)$ deformed by the mass $μ$ of the adjoint matter. This deformation breaks ${\mathcal N}=2$ supersymmetry down to ${\mathcal N}=1$ and in the limit of large $μ$ the theory flows to ${\mathcal N}=1$ QCD. Non-Abelian strings in addition to translational zero modes have orientation moduli. In the ${\mathcal N}=2$ limit of small $μ$ the dynamics of orientational moduli is described by the two dimensional $CP(N-1)$ model for QCD with $N_f=N$ flavors of quark hypermultiplets. For the case of $N_f>N$ t…
The standard electroweak model is extended by means of a second Brout-Englert-Higgs-doublet. The symmetry breaking potential is chosen is such a way that (i) the Lagrangian possesses a custodial symmetry, (ii) a stationary, axially symmetric ansatz of the bosonic fields consistently reduces the Euler-Lagrange equations to a set of differential equations. The potential involves, in particular, a direct interaction between the two doublets. Stationary, axially-symmetric solutions of the classical equations are constructed. Some of them can be assimilated to embedded Nielsen-Olesen strings. From …
We study BPS non-abelian semilocal vortices in U(Nc) gauge theory with Nf flavors, Nf > Nc, in the Higgs phase. The moduli space for arbitrary winding number is described using the moduli matrix formalism. We find a relation between the moduli spaces of the semilocal vortices in a Seiberg-like dual pairs of theories, U(Nc) and U(Nf-Nc). They are two alternative regularizations of a "parent" non-Hausdorff space, which tend to the same moduli space of sigma-model lumps in the infinite gauge coupling limits. We examine the normalizability of the zero-modes and find the somewhat surprising phenome…
Recently a low-energy effective theory on non-Abelian semilocal vortices in SQCD with the U(N) gauge group and N + \tilde{N} quark flavors was obtained in field theory arXiv:1104.2077. The result is exact in a certain limit of large infrared cut-off. The resulting model was called the zn model. We study quantum dynamics of the zn model in some detail. First we solve it at large N in the leading order. Then we compare our results with those of Hanany and Tong hep-th/0403158 (the HT model) who based their derivation on a certain type-IIA formalism, rather than on a field-theory construction. In …
We embed the semilocal Chern-Simons-Higgs theory into an N=2 supersymmetric system. We construct the corresponding conserved supercharges and derive the Bogomol'nyi equations of the model from supersymmetry considerations. We show that these equations hold provided certain conditions on the coupling constants as well as on the Higgs potential of the system, which are a consequence of the huge symmetry of the theory, are satisfied. They admit string-like solutions which break one half of the supersymmetries --BPS Chern-Simons semilocal cosmic strings-- whose magnetic flux is concentrated at the…
We consider a benchmark bulk theory in four-dimensions: N=2 supersymmetric QCD with the gauge group U(N) and N_f flavors of fundamental matter hypermultiplets (quarks). The nature of the BPS strings in this benchmark theory crucially depends on N_f. If N_f\geq N and all quark masses are equal, it supports non-Abelian BPS strings which have internal (orientational) moduli. If N_f>N these strings become semilocal, developing additional moduli ρrelated to (unlimited) variations of their transverse size. Using the U(2) gauge group with N_f=3,4 as an example, we derive an effective low-energy theor…
A new class of twisted, current carrying, stationary, straight string solutions having finite energy per unit length is constructed numerically in an extended Abelian Higgs model with global SU(2) symmetry. The new solutions correspond to deformations of the embedded Abrikosov-Nielsen-Olesen (ANO) vortices by a twist -- a relative coordinate dependent phase between the two Higgs fields. The twist induces a global current flowing through the string, and the deformed solutions bifurcate with the ANO vortices in the limit of vanishing current. For each value of the winding number $n=1,2...$ (dete…
A new two dimensional $\mathcal{N}=(0,2)$ Supersymmetric Non-Linear Sigma Model describes the dynamics of internal moduli of the BPS semi-local vortex string supported in four dimensional $\mathcal{N}=2$ SQED. While the core of these strings is very similar to Abrikosov-Nielsen-Olesen vortices, they are defined with a characteristic size modulus, much like the instanton lump size. This entails that the constituting fields of the vortex do not decay exponentially, as one goes far away from the core of the string, but as a rational function. The appearance of an extra scale in the problem also a…
A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory -- an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry -- is carried out. Here the twist refers to a relative phase between the two complex scalars (with linear dependence on, say, the $z$ coordinate), and importantly it leads to a global current flowing along the the string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO) solution embedded in the semilocal theory. Our numerical investigations of the small fluctuation spectrum confirm previous results t…
Non-Abelian strings for an Einstein-Yang-Mills-Higgs theory are explicitly constructed. We consider N_f Higgs fields in the fundamental representation of the U(1)xSU(N_c) gauge group in order to have a color-flavor SU(N_c) group remaining unbroken. Choosing a suitable ansatz for the metric, Bogomol'nyi-like first order equations are found and rotationally symmetric solutions are proposed. In the N_f = N_c case, solutions are local strings and are shown to be truly non-Abelian by parameterizing them in terms of orientational collective coordinates. When N_f > N_c, the solutions correspond to se…
We show that local/semilocal strings in Abelian/non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.
We investigate the implications of the nontrivial vacuum structure of little Higgs models. In particular, focusing on the littlest Higgs model, we demonstrate the existence of three types of topological defects. One is a global cosmic string that is truly topological. The second is more subtle; a semilocal cosmic string, which may be stable due to dynamical effects. The final defect is a $Z_2$ monopole solution with an unusual structure. We briefly discuss the possible cosmological consequences of such nonperturbative structures, although we note that these depend crucially on the fermionic co…
Motivated by astrophysical observations of excess electronic production in the galaxy, new theoretical models of the dark matter sector have been proposed in which the Standard model couples to the dark matter sector through an attractive interaction. The coupling of the Standard model to "dark strings", which are solutions of the low energy dark sector has been investigated recently. Here, we discuss the interaction between dark strings and standard cosmic strings and show that they can form bound states. In the presence of the interaction term, a Bogomolny-Prasad-Sommerfield (BPS) bound exis…
In a class of non-Abelian solitonic vortex strings supported in certain N=2 super-Yang-Mills theories we search for the vortex which can behave as a critical fundamental string. We use the Polchinski-Strominger criterion of the ultraviolet completeness. We identify an appropriate four-dimensional bulk theory: it has the U(2) gauge group, the Fayet-Iliopoulos term and four flavor hypermultiplets. It supports semilocal vortices with the world-sheet theory for orientational (size) moduli described by the weighted CP(2,2) model. The latter is superconformal. Its target space is six-dimensional. Th…
We study the production of dark matter and dark radiation after reheating in string inflation models where the Calabi-Yau has a fibred structure and the visible sector lives on D3 branes. We show how the interplay between different physical constraints from inflation, reheating, supersymmetry breaking and dark radiation, leads to distinct predictions for the nature of dark matter.
We point out that the Kalb-Ramond field can couple to the Ramond and Neveu-Schwarz fields of superstring theory in a way that can generate a coupling of the Kalb-Ramond field to dark matter dipole moments. Electroweak dipole dark matter could then arise from the Ramond sector of superstrings with a low string scale up to 120 TeV.
We show that in a wide class of string derived models of particle physics, heavy string modes with masses around the GUT scale can serve as a viable dark matter candidate. These heavy string modes wind around specific cycles in the extra-dimensional space, closely related to the fundamental group $π_1$. As a consequence of a non-trivial $π_1$, there is an exact discrete symmetry that stabilizes such winding strings. The dark matter candidate couples to the Standard Model via gravity and via the exchange of heavy string states. We find that, for reasonable values of the string coupling, our dar…
In N=2 supersymmetric QCD with the U(N) gauge group and N_f>N we study the crossover transition from the weak coupling regime at large ξto strong coupling at small ξwhere ξis the Fayet--Iliopoulos parameter. We find that at strong coupling a dual non-Abelian weakly coupled N=2 theory exists which describes low-energy physics at small ξ. The dual gauge group is U(N_f-N) and the dual theory has N_f flavors of light dyons, to be compared with N_f quarks in the original U(N) theory. Both, the original and dual theories are Higgsed and share the same global symmetry SU(N) x SU(N_f-N) x U(1), albeit…
The non-topological $Z^\prime$ string in the 331 model and its classical stability
School of Physics, Nankai University（南开大学物理学院）；Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University（华中师范大学粒子物理研究所及夸克与轻子物理教育部重点实验室）
A brief review is given of dark matter in SUGRA, strings and branes. For SUGRA models the implications of Yukawa coupling unification on dark matter are discussed in the light of $g-2$ and $b\to sγ$ constraints. A brief discussion is given of the dark matter in orbifold string compactifications under constraints of modular invariance and radiative breaking of the electroweak symmetry. Finally a new candidate for dark matter - an extra-weakly interacting massive particle or an XWIMP- is discussed. Such dark matter can arise in a wide class of models, including the Stueckelberg extensions of MSS…
We study cosmological constraints on dark pure Yang-Mills sectors. Dark glueballs are overproduced for large regions of ultraviolet parameter space. The problem may be alleviated in two ways: via a large preferential reheating into the visible sector, motivating certain inflation or modulus decay models, or via decays into axions or moduli, which are strongly constrained by nucleosynthesis and $ΔN_{\text{eff}}$ bounds. String models frequently have multiple hidden Yang-Mills sectors, which are subject to even stronger constraints due to the existence of multiple dark glueballs.
The stability of "visible" electroweak-type cosmic strings is investigated in an extension of the Standard Model (SM) by a minimal dark sector, consisting of a U(1) gauge field, broken spontaneously by a scalar. The "visible" and dark sectors are coupled through a Higgs-portal and a gauge-kinetic mixing term. It is found that strings whose core is "filled" with a dark scalar condensate exhibit better stability properties than their analogues in the SM, when the electroweak mixing angle is close to $θ_{\rm W}=π/2$. They become unstable as one lets $θ_{\rm W}$ approach its physical value. The in…
The supersymmetric particle spectrum is calculated in type I string theories formulated as orientifold compactifications of type IIB string theory. A string scale at an intermediate value of $10^{11}-10^{12}$ GeV is assumed and extra vector-like matter states are introduced to allow unification of gauge coupling constants to occur at this scale. The qualitative features of the spectrum are compared with Calabi-Yau compactification of the weakly coupled heterotic string and with the eleven dimensional supergravity limit of $M$-theory. Some striking differences are observed. Assuming that the li…
We examine the milli-charged dark matter scenario from a string theory perspective. In this scenario, kinetic and mass mixings of the photon with extra U(1) bosons are claimed to give rise to small electric charges, carried by dark matter particles, whose values are determined by continuous parameters of the theory. This seems to contradict folk theorems of quantum gravity that forbid the existence of irrational charges in theories with a single massless gauge field. By considering the underlying structure of the U(1) mass matrix that appears in type II string compactifications, we show that m…
The mixing of graviphotons and dark brane photons to the Standard Model hypercharge is analyzed in full generality, in weakly-coupled string theory. Both the direct mixing as well as effective terms that provide mixing after inclusion of SM corrections are estimated to lowest order. The results are compared with Effective Field Theory (EFT) couplings, originating in a hidden large-N theory coupled to the SM. The string theory mixing terms are typically subleading compared with the generic EFT couplings. The case where the hidden theory is a holographic theory is also analyzed, providing also s…
We point out that string theory can solve the conundrum to explain the emergence of an electroweak dipole moment from electroweak singlets through induction of those dipole moments through a Kalb-Ramond dipole coupling. This can generate a U_Y(1) portal to dark matter and entails the possibility that the U_Y(1) gauge field is related to a fundamental vector field for open string interactions. The requirement to explain the observed dark matter abundance relates the coupling scale in the corresponding low-energy effective U_Y(1) portal to the dark matter mass. The corresponding electron recoil …
Four-dimensional compactifications of string theory provide a controlled set of possible gauge representations accounting for BSM particles and dark sector components. In this review, constraints from perturbative Type II string compactifications in the geometric regime are discussed in detail and then compared to results from heterotic string compactifications and non-perturbative/non-geometric corners. As a prominent example, an open string realization of the QCD axion is presented. The status of deriving the associated low-energy effective action in four dimensions is discussed and open ave…
We study well-motivated dark matter candidates arising from weakly-coupled hidden sectors in compactified string/$M$-theory. Imposing generic top-down constraints greatly restricts allowed candidates. By considering the possible mechanisms for achieving the correct dark matter relic density, we compile categories of viable dark matter candidates and annihilation mediators. We consider the case where supersymmetry breaking occurs via moduli stabilisation and is gravitationally mediated to the visible and other hidden sectors, without assuming sequestering of the sector in which supersymmetry is…
Recently a special vortex string was found [5] in a class of soliton vortices supported in four-dimensional Yang-Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang-Mills theory has the U(2) gauge group and the Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP(2,2) model. The full target space is R_4\times Y_6 where Y_6 is a non-compact Calabi-Yau space. We study the above vortex str…
The Large Volume Scenario for getting a non-supersymmetric vacuum in type IIB string theory leads, through the Weyl anomaly and renormalization group running, to an interesting phenomenology. However, for gravitino masses below 500 TeV there are cosmological problems and the resulting Higgs mass is well below 124 GeV. Here we discuss the phenomenology and cosmology for gravitino masses which are $\gtrsim$ 500 TeV. We find that not only is the cosmological modulus problem alleviated and the right value for dark matter density obtained, but also the Higgs mass is in the 122-125 GeV range. Howeve…
The dark matter issue is among the most perplexing in contemporary physics. The problem is more enigmatic due to the wide range of possible solutions, ranging from the ultra-light to the super-massive. String theory gives rise to plausible dark matter candidates due to the breaking of the non--Abelian Grand Unified Theory (GUT) symmetries by Wilson lines. The physical spectrum then contains states that do not satisfy the quantisation conditions of the unbroken GUT symmetry. Given that the Standard Model states are identified with broken GUT representations, and provided that any ensuing symmet…
We analyze different phenomenological aspects of D-brane constructions. First, we obtain that scenarios with the gauge group and particle content of the supersymmetric standard model lead naturally to intermediate values for the string scale, in order to reproduce the value of gauge couplings deduced from experiments. Second, the soft terms, which turn out to be generically non universal, and Yukawa couplings of these scenarios are studied in detail. Finally, using these soft terms and the string scale as the initial scale for their running, we compute the neutralino-nucleon cross section. In …
Recent astrophysical observations have motivated novel theoretical models of the dark matter sector. A class of such models predicts the existence of GeV scale cosmic strings that communicate with the standard model sector by Aharonov-Bohm interactions with electrically charged particles. We discuss the cosmology of these "dark strings" and investigate possible observational signatures. More elaborate dark sector models are argued to contain hybrid topological defects that may also have observational signatures.
We consider the conditions needed to unify the description of dark matter, dark energy and inflation in the context of the string landscape. We find that incomplete decay of the inflaton field gives the possibility that a single field is responsible for all three phenomena. By contrast, unifying dark matter and dark energy into a single field, separate from the inflaton, appears rather difficult.
Reheating in string compactifications is generically driven by the decay of the lightest modulus which produces Standard Model particles, dark matter and light hidden sector degrees of freedom that behave as dark radiation. This common origin allows us to find an interesting correlation between dark matter and dark radiation. By combining present upper bounds on the effective number of neutrino species N_eff with lower bounds on the reheating temperature as a function of the dark matter mass m_DM from Fermi data, we obtain strong constraints on the (N_eff,m_DM)-plane. Most of the allowed regio…
