The South Pole Telescope (SPT), Atacama Cosmology Telescope (ACT), and Wilkinson Microwave Anisotropy Probe (WMAP) have each reported measurements of the cosmic microwave background's (CMB) angular power spectrum which favor the existence of roughly one additional neutrino species, in addition to the three contained in the standard model of particle physics. Neutrinos influence the CMB by contributing to the radiation density, which alters the expansion rate of the universe during the epoch leading up to recombination. In this paper, we consider an alternative possibility that the excess kinetic energy implied by these measurements was possessed by dark matter particles that were produced through a non-thermal mechanism, such as late-time decays. In particular, we find that if a small fraction (<1%) of the dark matter in the universe today were produced through the decays of a heavy and relatively long-lived state, the expansion history of the universe can be indistinguishable from that predicted in the standard cosmological model with an additional neutrino. Furthermore, if these decays take place after the completion of big bang nucleosynthesis, this scenario can avoid tension with the value of three neutrino species preferred by measurements of the light element abundances.
Mimetic gravity can be described as a formulation capable of mimicking different evolutionary scenarios regarding the universe dynamics. Notwithstanding its initial aim of producing a similar evolution to the one expected from the dark components of the standard cosmology, a recent association with loop quantum cosmology could also provide interesting results. In this work, we reinterpret the physics behind the curvature potential of mimetic gravity description of loop quantum cosmology. Furthermore, we also test the compatibility of our formulation for a Higgs-type field, proving that the mim…
We confront dark energy models which are currently similar to $Λ$CDM theory with observational data which include the SNe data, matter density perturbations and baryon acoustic oscillations data. DE cosmology under consideration may evolve to Big Rip, type II or type III future singularity, or to Little Rip or Pseudo-Rip universe. It is shown that matter perturbations data define more precisely the possible deviation from $Λ$CDM model than consideration of SNe data only. The combined data analysis proves that DE models under consideration are as consistent as $Λ$CDM model. We demonstrate that …
Heavy long-lived particles are abundant in BSM physics and will, under generic circumstances, get to dominate the energy density of the universe. The resulting matter dominated era has to end before the onset of Big Bang Nucleosynthesis through the decay of the heavy matter component of mass $M$ into a thermal bath of temperature $T$. The process of thermalization primarily involves near-collinear splittings of energetic particles into two particles with lower energy. The correct treatment of these processes requires the inclusion of coherence effects which suppress the splitting rate. We writ…
Cosmological measurements are affected by the energy density of both active and sterile massive neutrinos. We extend here a recent analysis of current cosmological data to non minimal cosmologies. Several possible scenarios are examined: a constant w \neq -1 dark energy equation of state, a non flat universe, a time varying dark energy component and coupled dark matter dark energy universes or modified gravity scenarios. When considering cosmological data only, (3+2) massive neutrino models with ~0.5 eV sterile species are allowed at 95% CL. This scenario has been shown to reconcile reactor, L…
Mimicking the large-scale structure of the Local Universe. Synthetic pre-labelled galaxies in large-scale structures
Universidad de Granada（格拉纳达大学）；Instituto Carlos I de Física Teórica y Computacional（卡洛斯一世理论物理与计算物理研究所）；Instituto de Astrofísica de Andalucía, CSIC（安达卢西亚天体物理研究所，西班牙高等科学研究委员会）；ATG Analytical（ATG分析公司）
The central smoothness of the functions defining a LTB solution plays a crucial role in their ability to mimick the effects of the cosmological constant. So far attention has been focused on $C^{1}$ models while in this paper we approach it a more general way, investigating the implications of higher order central smoothness conditions for LTB models reproducing the luminosity distance of a $ΛCDM$ Universe. Our analysis is based on a low red-shift expansion, and extends previous investigations by including also the constraint coming from the age of the Universe and re-expressing the equations …
The long standing anomaly in the positron flux as measured by the PAMELA and AMS-02 experiments could potentially be explained by dark matter (DM) annihilations. This scenario typically requires a large "boost factor" to be consistent with a thermal relic dark matter candidate produced via freeze-out. However, such an explanation is disfavored by constraints from CMB observations on energy deposition during the epoch of recombination. We discuss a scenario called late-decaying two-component dark matter (LD2DM), where the entire DM consists of two semi-degenerate species. Within this framework,…
Dark energy models with various scenarios of evolution are considered from the viewpoint of the formalism for the equation of state. It is shown that these models are compatible with current astronomical data. Some of the models presented here evolve arbitrarily close to $Λ$CDM up to the present, but diverge in the future into a number of different possible asymptotic states, including asymptotic de-Sitter (pseudo-rip) evolution, little rips with disintegration of bound structures, and various forms of finite-time future singularities. Therefore it is impossible from observational data to dete…
Light sterile neutrinos mixing with the active ones have been recently proposed to solve different anomalies observed in short-baseline oscillation experiments. These neutrinos can also be produced by oscillations of the active neutrinos in the early universe, leaving possible traces on different cosmological observables. Here we perform an updated study of the neutrino kinetic equations in (3+1) and (2+1) oscillation schemes, dynamically evolving primordial asymmetries of active neutrinos and taking into account for the first time CP-violation effects. In the absence of neutrino asymmetries, …
It has been suggested that both recent cosmological data and the results of flavor oscillation experiments (MiniBooNE and LSND) lend support to the existence of low-mass sterile neutrinos. The cosmological data appear to weakly favor additional forms of radiation in the Universe, beyond photons and three standard neutrino families. We reconsider the cosmological evidence by making the resulting confidence intervals on the additional effective neutrino species as prior-independent as possible. We find that, once the prior-dependence is removed, the latest cosmological data show no evidence for …
By making use of a class of steep exponential type of potentials, which has been recently used to describe quintessential inflation, we show how a unified picture for both inflation, dark energy and dark matter can emerge entirely through dissipative effects. Dissipation provides a way for extending the applicability of a larger class of these potentials in the sense of leading to a consistent early Universe inflationary picture and producing observables in agreement with the Planck legacy data. Likewise, dissipative effects lead to dark matter production with consistent abundances and, toward…
It is proposed that an ultra-light fermionic species, dubbed cosmic magnino has condensed into a ferromagnetic state in the Universe. The extended structure of domain walls associated with this ferromagnetism accounts for the observed Dark Energy. In modification of the situation with an electron gas, it is proposed that the Stoner criterion is satisfied due to magnetic dipolar repulsion. The cosmological requirements then yeild a lower bound on the magnetic moment of the cosmic magnino. The proposed magnetism is supposed to be associated with a new non-standard electromagnetism. If the magnin…
Within the context of hot big-bang cosmology, a cosmic background of presently low energy neutrinos is predicted to exist in concert with the photons of the cosmic background radiation. The number density of the cosmological neutrinos is of the same order as that of the photons of the cosmic background radiation. That makes neutrinos the second most abundant particle species in the universe. In the early universe, when these neutrinos were highly relativistic, their effects in determining the ultimate structure and evolution of the universe were significant.
It is generally expected that adding light sterile species would increase the effective number of neutrinos, $N_{eff}$. In this paper we discuss a scenario that $N_{eff}$ can actually decrease due to the neutrino oscillation effect if sterile neutrinos have self-interactions. We specifically focus on the eV mass range, as suggested by the neutrino anomalies. With large self-interactions, sterile neutrinos are not fully thermalized in the early Universe because of the suppressed effective mixing angle or matter effect. As the Universe cools down, flavor equilibrium between active and sterile sp…
The interacting dark matter (IDM) scenario allows for the acceleration of the Universe without Dark Energy. We constrain the IDM model by using the newly revised observational data including $H(z)$ data and Union2 SNe Ia via the Markov chain Monte Carlo method. When mimicking the $Λ$CDM model, we obtain a more stringent upper limit to the effective annihilation term at $κC_1\approx 10^{-3.4}\rm{Gyr}^{-1}$, and a tighter lower limit to the relevant mass of Dark Matter particles at $M_x\approx 10^{-8.6}\rm{Gev}$. When mimicking the $w$CDM model, we find that the effective equation of state of ID…
Precision measurements of the number of effective relativistic neutrino species and the primordial element abundances require accurate theoretical predictions for early Universe observables in the Standard Model and beyond. Given the complexity of accurately modelling the thermal history of the early Universe, in this work, we extend a previous method presented by the author to obtain simple, fast and accurate early Universe thermodynamics. The method is based upon the approximation that all relevant species can be described by thermal equilibrium distribution functions characterized by a temp…
In the primordial Universe, neutrino decoupling occurs only slightly before electron-positron annihilations. This leads notably to an increased neutrino energy density compared to the standard instantaneous decoupling approximation, parametrized by the effective number of neutrino species $N_{\rm eff}$. A precise calculation of neutrino evolution is needed to assess its consequences during the later cosmological stages, and requires to take into account multiple effects such as neutrino oscillations, which represents a genuine numerical challenge. Recently, several key improvements have allowe…
The coherent oscillation of axionic fields naturally drives copious production of dark photon particles in the early universe, due to resonance and tachyonic enhancement. During the process, energy is abruptly transferred from the former to the latter, sourcing gravitational wave generation. The resulting gravitational waves are eventually to be observed as stochastic background today. We report analytical results of this production and connect them to the recent pulsar-timing results by the NANOGrav collaboration. We show an available parameter space, around the mass $m_ϕ\sim 10^{-13} \, {\rm…
We consider a modification to the standard cosmological history consisting of introducing a new species $ϕ$ whose energy density red-shifts with the scale factor $a$ like $ρ_ϕ\propto a^{-(4+n)}$. For $n>0$, such a red-shift is faster than radiation, hence the new species dominates the energy budget of the universe at early times while it is completely negligible at late times. If equality with the radiation energy density is achieved at low enough temperatures, dark matter can be produced as a thermal relic during the new cosmological phase. Dark matter freeze-out then occurs at higher tempera…
We consider the effects of new light species on the Cosmic Microwave Background. In the massless limit, these effects can be parameterized in terms of a single number, the relativistic degrees of freedom. We perform a thorough survey of natural, minimal models containing new light species and numerically calculate the precise contribution of each of these models to this number in the framework of effective field theory. After reviewing the relevant details of early universe thermodynamics, we provide a map between the parameters of any particular theory and the predicted effective number of de…
There are indications that the neutrino oscillation data from reactor experiments and the LSND and MiniBooNE experiments show a preference for two sterile neutrino species, both with masses in the eV region. We show that this result has a significant impact on some important cosmological parameters. Specifically, we use a combination of CMB, LSS and SN1A data and show that the existence of two light, sterile neutrinos would rule out the cosmological constant as dark energy at 95% confidence level, and lower the expansion age of the universe to 12.58 \pm 0.26 Gyr.
In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann-Lemaitre universes is a special case of generalized Lotka-Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka-Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann-Lemaitre cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserve the structure of the dynamical equations. Using the standard tools of Lotka-Volterra dynamics, we obtain t…
We present fully nonlinear consistency relations for the squeezed bispectrum of Large Scale Structure. These relations hold when the matter component of the Universe is composed of one or more species, and generalize those obtained in Peloso, Pietroni '13 and Kehagias, Riotto '13 in the single species case. The multi-species relations apply to the standard dark matter + baryons scenario, as well as to the case in which some of the fields are auxiliary quantities describing a particular population, such as dark matter halos or a specific galaxy class. If a large scale velocity bias exists betwe…
We derive a new model for neutrino-plasma interactions in an expanding universe that incorporates the collective effects of the neutrinos on the plasma constituents. We start from the kinetic description of a multi-species plasma in the flat Friedmann-Robertson-Walker metric, where the particles are coupled to neutrinos through the charged- and neutral-current forms of the weak interaction. We then derive the fluid equations and specialize our model to (a) the lepton epoch, where we consider a pair electron-positron plasma interacting with electron (anti-)neutrinos, and (b) after the electron-…
The thermal decoupling description of dark matter (DM) and co-annihilating partners is reconsidered. If DM is realized at around the TeV-mass region or above, even the heaviest electroweak force carriers could act as long-range forces, leading to the existence of meta-stable DM bound states. The formation and subsequent decay of the latter further deplete the relic density during the freeze-out process on top of the Sommerfeld enhancement, allowing for larger DM masses. While so far the bound-state formation was described via the emission of an on-shell mediator ($W^{\pm}$, $Z$, $H$, $g$, phot…
We explore the effective degrees of freedom in the early universe, from before the electroweak scale at a few femtoseconds after the Big Bang, until the last positrons disappeared a few minutes later. We first look at the established concepts of effective degrees of freedom for energy density, pressure and entropy density, and introduce effective degrees of freedom for number density as well. We discuss what happens with particle species as their temperature cools down from relativistic to semi- and non-relativistic temperatures, and then annihilates completely. This will affect the pressure a…
The early universe may have contained internally thermalized dark sectors that were decoupled from the Standard Model. In such scenarios, the relic dark thermal bath, composed of the lightest particle in the dark sector, can give rise to an epoch of early matter domination prior to Big Bang Nucleosynthesis, which has a potentially observable impact on the smallest dark matter structures. This lightest dark particle can easily and generically have number-changing self-interactions that give rise to "cannibal" behavior. We consider cosmologies where an initially sub-dominant cannibal species com…
The constraints on non-minimal dark sectors involving ensembles of unstable dark-matter species are well established and quite stringent in cases in which these species decay to visible-sector particles. However, in cases in which these ensembles decay exclusively to other, lighter dark-sector states, the corresponding constraints are less well established. In this paper, we investigate how information about the expansion rate of the universe at low redshifts gleaned from observations of Type Ia supernovae can be used to constrain ensembles of unstable particles which decay primarily into dark…
The recent observation that the Cosmic Microwave Background (CMB) may prefer a neutrino excess has triggered a number of works studying this possibility. The effect obtained by the non-interacting massless neutrino excess could be mimicked by some extra radiation component in the early universe, such as a cosmological gravitational wave background. Prompted by the fact that a possible candidate to source those gravitational waves would be cosmic strings, we perform a parameter fitting study with models which considers both cosmic strings and the effective number of neutrinos as free parameters…
If the dark matter is produced in the early universe prior to Big Bang nucleosynthesis, a modified cosmological history can drastically affect the abundance of relic dark matter particles. Here, we assume that an additional species to radiation dominates at early times, causing the expansion rate at a given temperature to be larger than in the standard radiation-dominated case. We demonstrate that, if this is the case, dark matter production via freeze-in (a scenario when dark matter interacts very weakly, and is dumped in the early universe out of equilibrium by decay or scattering processes …
We consider a dark matter (DM) model offering a very natural explanation of the observed relation, $Ω_{\rm dark} \sim Ω_{\rm visible}$. This generic consequence of the model is a result of the common origin of both types of matter (DM and visible) which are formed during the same QCD transition. The masses of both types of matter in this framework are proportional to one and the same dimensional parameter of the system, $Λ_{\rm QCD}$. The focus of the present work is the detail study of the dynamics of the $\cal{CP}$-odd coherent axion field $a(x)$ just before the QCD transition. We argue that…
We consider relatively heavy neutrinos $ν_H$, mostly contributing to a sterile state $ν_s$, with mass in the range 10 MeV $\lesssim m_s \lesssim m_π \sim 135$ MeV, which are thermally produced in the early universe in collisional processes involving active neutrinos, and freezing out after the QCD phase transition. If these neutrinos decay after the active neutrino decoupling, they generate extra neutrino radiation, but also contribute to entropy production. Thus, they alter the value of the effective number of neutrino species $N_{\rm eff}$ as for instance measured by the cosmic microwave bac…
Recent cosmological data favour additional relativistic degrees of freedom beyond the three active neutrinos and photons, often referred to as 'dark' radiation. Light sterile neutrinos is one of the prime candidates for such additional radiation. However, constraints on sterile neutrinos based on the current cosmological data have been derived using simplified assumptions about thermalisation of the sterile neutrino at the Big Bang Nucleosynthesis (BBN) epoch. These assumptions are not necessarily justified and here we solve the full quantum kinetic equations in the (1 active + 1 sterile) scen…
In the framework of a 3+1 scheme with an additional inert state, we consider the thermalisation of sterile neutrinos in the early Universe taking into account the full $4\times4$ mixing matrix. The evolution of the neutrino energy distributions is found solving the momentum-dependent kinetic equations with full diagonal collision terms, as in previous analyses of flavour neutrino decoupling in the standard case. The degree of thermalisation of the sterile state is shown in terms of the effective number of neutrinos, $N_{\rm eff}$, and its dependence on the three additional mixing angles ($θ_{1…
We discuss Preheating after an inflationary stage driven by the Standard Model (SM) Higgs field non-minimally coupled to gravity. We find that Preheating is driven by a complex process in which perturbative and non-perturbative effects occur simultaneously. The Higgs field, initially an oscillating coherent condensate, produces non-perturbatively W and Z gauge fields. These decay very rapidly into fermions, thus preventing gauge bosons to accumulate and, consequently, blocking the usual parametric resonance. The energy transferred into the fermionic species is, nevertheless, not enough to rehe…
We study the formation and destruction of molecules in the ejecta of Population III supernovae (SNe) using a chemical kinetic approach to follow the evolution of molecular abundances from day 100 to day 1000 after explosion. The chemical species included range from simple di-atomic molecules to more complex dust precursor species. All relevant chemical processes that are unique to the SN environment are considered. Our work focuses on zero-metallicity progenitors with masses of 20, 170, and 270 Msun, and we study the effect of different levels of heavy element mixing and the inward diffusion o…
We study the growth of perturbations in an expanding Newtonian universe with Bose-Einstein condensate dark matter. We first ignore special relativistic effects and derive a differential equation governing the evolution of the density contrast in the linear regime taking into account quantum pressure and self-interaction. This equation can be solved analytically in several cases. We argue that an attractive self-interaction can enhance the Jeans instability and fasten the formation of structures. Then, we take into account pressure effects (coming from special relativity) in the evolution of th…
We explore the potential of measurements of cosmological effects, such as neutrino spectral distortions from the neutrino decoupling and neutrino clustering in our Galaxy, via cosmic neutrino capture on tritium. We compute the precise capture rates of each neutrino species including such cosmological effects to probe them. These precise estimates of capture rates are also important in that the would-be deviation of the estimated capture rate could suggest new neutrino physics and/or a non-standard evolution of the universe. In addition, we discuss the precise differences between the capture ra…
We employ state-of-the art cosmological observables including supernova surveys and BAO information to provide constraints on the mass and mixing angle of a non-resonantly produced sterile neutrino species, showing that cosmology can effectively rule out sterile neutrinos which decay between BBN and the present day. The decoupling of an additional heavy neutrino species can modify the time dependence of the Universe's expansion between BBN and recombination and, in extreme cases, lead to an additional matter-dominated period; while this could naively lead to a younger Universe with a larger Hu…
How can effective barotropic matter emerge from the interaction of cosmological fluids in an isotropic and homogeneous cosmological model ? The dynamics of homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker universes is a natural special case of generalized Lotka-Volterra systems where each of the universe's fluid components can be seen as a competitive species in a predator-prey model. (Jungle universe : arXiv:1306.1037) In addition to numerical simulations illustrating this behaviour among the barotropic fluids filling the universe, we analytically pinpoint that effective time-dep…
Revisiting the spectrum of a scalar field in an anisotropic universe
School of Liberal Arts and Sciences, Korea National University of Transportation（韩国国立交通大学生命科学与艺术学院）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
Neutrino physics in the early Universe is key to our understanding of later cosmological stages, such as primordial nucleosynthesis (BBN) or the formation of large-scale structures. The coming decade promises new experimental results to explore and constrain cosmological models even more precisely - which requires robust theoretical predictions. This PhD thesis presents a study of the evolution of neutrinos in the first seconds after the Big Bang, more precisely when the temperature of the Universe is of the order of one mega-electronvolt. This evolution is obtained numerically by solving kine…
Non-thermal photons deriving from radiative transitions among the internal ladder of atoms and molecules are an important source of photons in addition to thermal and stellar sources in many astrophysical environments. In the present work the calculation of reaction rates for the direct photodissociation of some molecules relevant in early Universe chemistry is presented; in particular, the calculations include non-thermal photons deriving from the recombination of primordial hydrogen and helium atoms for the cases of H2, HD and HeH+. New effects on the fractional abundances of chemical specie…
If even a relatively small number of black holes were created in the early universe, they will constitute an increasingly large fraction of the total energy density as space expands. It is thus well-motivated to consider scenarios in which the early universe included an era in which primordial black holes dominated the total energy density. Within this context, we consider Hawking radiation as a mechanism to produce both dark radiation and dark matter. If the early universe included a black hole dominated era, we find that Hawking radiation will produce dark radiation at a level $ΔN_{\rm eff} …
We investigate whether an Early-Universe stochastic gravitational-wave background (SGWB) can account for the common spectrum process reported by NANOGrav, while also being consistent with current and projected CMB measurements of extra radiation. We compute the contribution of effective number of relativistic species, $ΔN_{eff}$, for a number of Early-Universe models proposed to explain the pulsar timing array (PTA) spectrum. We demonstrate that models predicting $ΔN_{eff}$ above the CMB limit would be firmly excluded, implying that the NANOGrav signal in tension with these bounds must instead…
We summarize three recent efforts to constrain the first few moments of cosmic creation before and during the epoch of inflation. We consider two means to explain a slight dip in the power spectrum of the cosmic microwave background for multipoles in the range of $\ell= 10-30$ from both the {\it Planck} and {\it WMAP} data. We show that such a dip could be the result of resonant creation of a massive particle that couples to the inflaton field. For best-fit models, the epoch of resonant particle creation reenters the horizon at wave numbers of $k_* \sim 0.00011 \pm 0.0004 $ ($h$ Mpc$^{-1}$). T…
The causal tail of stochastic gravitational waves can be used to probe the energy density in free streaming relativistic species as well as measure $g_\star(T)$ and beta functions $β(T)$ as a function of temperature. In the event of the discovery of loud stochastic gravitational waves, we demonstrate that LISA can measure the free streaming fraction of the universe down to the the $10^{-3}$ level, 100 times more sensitive than current constraints. Additionally, it would be sensitive to $\mathcal{O}(1)$ deviations of $g_\star$ and the QCD $β$ function from their Standard Model value at temperat…
We study the dissipative effects of baryon physics on cosmic statistics at small scales using a cosmological simulation of a (50 Mpc/h)^3 volume of the universe. The MareNostrum simulation was performed using the AMR code RAMSES, and includes most of the physical ingredients which are part of the current theory of galaxy formation, such as metal-dependent cooling and UV heating, subgrid modelling of the ISM, star formation and supernova feedback. We re-ran the same initial conditions for a dark matter only universe, as a reference point for baryon-free cosmic statistics. In this paper, we pres…
We revise the cosmological standard model presuming that matter, i.e. baryons and cold dark matter, exhibits a non-vanishing pressure mimicking the cosmological constant effects. In particular, we propose a scalar field Lagrangian $\mathcal L_1$ for matter with the introduction of a Lagrange multiplier as constraint. We also add a symmetry breaking effective potential accounting for the classical cosmological constant problem, by adding a second Lagrangian $\mathcal{L}_2$. Investigating the Noether current due to the shift symmetry on the scalar field, $φ\rightarrowφ+c^0$, we show that $\mathc…
The separate universe technique provides a means of establishing consistency relations between short wavelength observables and the long wavelength matter density fluctuations within which they evolve by absorbing the latter into the cosmological background. We extend it to cases where non-gravitational forces introduce a Jeans scale in other species like dynamical dark energy or massive neutrinos. The technique matches the synchronous gauge matter density fluctuations to the local expansion using the acceleration equation and accounts for the temporal nonlocality and scale dependence of the l…
In cosmology, phenomenologically motivated expressions for running vacuum are commonly parametrized as linear functions $Λ(H^2)$ or $Λ(R)$. Such kind of models assume an equation of state for vacuum given by $\,\overline P_Λ=-\,\overlineρ_Λ$, relating their background pressure $\,\overline P_Λ$ and mean energy density $\,\overlineρ_Λ\equivΛ/8πG$. This equation of state requires that the dynamic for vacuum is due to the energy exchange with the material species. Most of the approaches to background level consider only the energy exchange between vacuum and the transient dominant material compon…
Measuring distances to galaxies, determining their chemical composition, investigating the nature of their stellar populations and the absorbing properties of their interstellar medium are fundamental activities in modern extragalactic astronomy helping to understand the evolution of galaxies and the expanding universe. The optically brightest stars in the universe, blue supergiants of spectral A and B, are unique tools for these purposes. With absolute visual magnitudes up to M_V = -9.5 they are the ideal to obtain accurate quantitative information about galaxies through the powerful modern m…
