Classical pulsating stars such as Cepheid and RR Lyrae variables exhibit well-defined Period–Luminosity relations at near-infrared wavelengths. Despite their extensive use as stellar standard candles, the effects of metallicity on Period–Luminosity relations for these pulsating variables, and in turn, on possible biases in distance determinations, are not well understood. We present ongoing efforts in determining accurate and precise metallicity coefficients of Period–Luminosity-Metallicity relations for classical pulsators at near-infrared wavelengths. For Cepheids, it is crucial to obtain a homogeneous sample of photometric light curves and high-resolution spectra for a wide range of metallicities to empirically determine metallicity coefficient and reconcile differences with the predictions of the theoretical models. For RR Lyrae variables, using their host globular clusters covering a wide range of metallicities, we determined the most precise metallicity coefficient at near-infrared wavelengths, which is in excellent agreement with the predictions of the horizontal branch evolution and stellar pulsation models.

We employed data from the VISTA near-infrared YJKS survey of the Magellanic System to analyse the light curves of Type II Cepheids (T2Cs) in the Large and Small Magellanic Clouds (LMC and SMC, respectively). Using the T2Cs identified by the OGLE IV survey and Gaia mission, we built up a sample of about 330 pulsators belonging to both galaxies. For all these objects we obtained accurate intensity-averaged magnitudes in the YJKS bands by means of a template-fitting technique. We complemented our near-infrared data with optical photometry from the literature to calculate period-luminosity and period-Wesenheit relations for a variety of different bands and colour combinations and separately for the different T2C subclasses (BL Herculis, W Virginis, peculiar W Virginis, RV Tauri). These relations, calibrated with the LMC distance modulus, were tested using T2Cs belonging to Galactic globular clusters. We thus calculated the distances of 22 clusters and compared them with the literature values, mainly based on RR Lyrae stars, finding good agreement within 1 σ and dispersion of the order of 0.3 – 0.5 kpc, depending on the adopted period-luminosity/period-Wesenheit relation.

Pulsating stars play a crucial role in the calibration of the cosmic distance scale as well as in tracing the properties of the associated stellar populations. In the era of large observational surveys and precise astrometric missions, it is crucial to rely on accurate stellar pulsation models able to predict the observed behaviors for different physical assumptions. Indeed, the relations currently used in the literature to derive individual and mean distances of mainly radially pulsating stars such as Cepheids and RR Lyrae are well physically understood, but are also known to depend on a number of often unknown parameters. Recent extensive sets of stellar pulsation models developed by various authors show how variations in the physical assumptions can affect the theoretical prediction of the instability strip boundaries, the morphology and amplitude of light and radial velocity curves, and the consequent Period-Luminosity, Period-Luminosity-Color and Period-Wesenheit relations. These aspects are discussed in the framework of current open problems in the field of classical pulsating stars.

The main sequence offers a method for the systematization of quasar spectral properties. Extreme FeII emitters (or extreme Population A, xA) are believed to be sources accreting matter at very high rates. They are easily identifiable along the quasar main sequence, in large spectroscopic surveys over a broad redshift range. The very high accretion rate makes it possible that massive black holes hosted in xA quasars radiate at a stable, extreme luminosity-to-mass ratio. After reviewing the basic interpretation of the main sequence, we report on the possibility of identifying virial broadening estimators from low-ionization line widths, and provide evidence of the conceptual validity of redshift-independent luminosities based on virial broadening for a known luminosity-to-mass ratio.

The Megamaser Cosmology Project (MCP) measures the Hubble Constant by determining geometric distances to circumnuclear 22 GHz H2O megamasers in galaxies at low redshift (z < 0.05) but well into the Hubble flow. In combination with the recent, exquisite observations of the Cosmic Microwave Background by WMAP and Planck, these measurements provide a direct test of the standard cosmological model and constrain the equation of state of dark energy. The MCP is a multi-year project that has recently completed observations and is currently working on final analysis. Based on distance measurements to the first four published megamasers in the sample, the MCP currently determines H0 = 69.3 ± 4.2 km s−1 Mpc−1. The project is finalizing analysis for five additional galaxies. When complete, we expect to achieve a ~4% measurement. Given the tension between the Planck prediction of H0 in the context of the standard cosmological model and astrophysical measurements based on standard candles, the MCP provides a critical and independent geometric measurement that does not rely on external calibrations or a distance ladder.

Classical variables like RR Lyrae, classical and Type-II Cepheids and Mira variables all follow period-luminosity relations that make them interesting as distance indicators. Especially the RR Lyrae and δ Cepheids are crucial in establishing the distance scale in the Universe, and all classes of variables can be used as tracers of galactic structure. I will present an overview of recent period-luminosity relations and review the work that has been done using the Gaia DR1 data so far, and discuss possibilities for the future.

Classical Cepheids (hereafter Cepheids) are important standard candle as they obey the famous period-luminosity (PL) relation. Parallax measurements from Gaia offer a unique opportunity to derive or calibrate the PL relations for Galactic Cepheids, as traditionally their distances were measured via different methods. In this work, we attempted to derive the Gaia G-band PL relation based on the Gaia Data Release 1 (DR1) measurements. We adopted the inferred distances provided by Astraatmadja & Bailer-Jones (2016), calculated using two priors in a Bayesian analysis, and cross-matched to known Galactic Cepheids. The resulting G-band PL relation, however, exhibits a much larger scatter than expected. Hence the inferred distances based on the Gaia DR1 parallaxes are not suitable for calibrating the Galactic PL relation, and future Data Releases with improved parallax measurements are desirable.

Highly accreting quasars are possible cosmological probes, as their Eddington ratio is expected to saturate toward values of order unity. We present preliminary estimates of redshift- independent source luminosities and the Hubble diagram for quasars in the redshift range 0.1 ≲ z ≲ 2.6.

We recently showed that rotation significantly affects most observable Cepheid quantities, and that rotation, in combination with the evolutionary status of the star, can resolve the long-standing Cepheid mass discrepancy problem. We therefore provide a brief overview of our results regarding the problem of Cepheid masses. We also briefly mention the impact of rotation on the Cepheid period-luminosity(-color) relation, which is crucial for determining extragalactic distances, and thus for calibrating the Hubble constant.

I report on the recent discovery of modulation in the radial velocity curves in four classical Cepheids. This discovery may enable significant improvements in the accuracy of Baade-Wesselink distances by revealing a not previously considered systematic source of uncertainty.

Mock galaxy catalogues are essential to the error analysis of cosmological measurements from big galaxy surveys covering thousands of square degrees in the sky, like BOSS, WiggleZ, DES, or Euclid. The PTHalos mock galaxy catalogues were used in the BOSS survey to analyse the BAO measurement from the CMASS (z∼ 0.57) and LOWZ (z∼ 0.32) galaxy samples, which provided the best estimate to date of the cosmic distance scale from galaxy surveys at these redshifts. We review the PTHalos mocks galaxy catalogues and their key contributions to these analyses.

Cepheids and RR Lyrae stars are important pulsating variable stars in distance scale work because they serve as standard candles. Cepheids follow well-defined period-luminosity (PL) relations defined for bands extending from optical to mid-infrared (MIR). On the other hand, RR Lyrae stars also exhibit PL relations in the near-infrared and MIR wavelengths. In this article, we review some of the recent developments and calibrations of PL relations for Cepheids and RR Lyrae stars. For Cepheids, we discuss the calibration of PL relations via the Galactic and the Large Magellanic Cloud routes. For RR Lyrae stars, we summarize some recent work in developing the MIR PL relations.

Classical Cepheids form one of the foundations of modern cosmology and the extragalactic distance scale; however, cosmic microwave background observations measure cosmological parameters and indirectly the Hubble Constant, H0, to unparalleled precision. The coming decade will provide opportunities to measure H0 to 2% uncertainty thanks to the Gaia satellite, JWST, ELTs and other telescopes using Cepheids and other standard candles. In this work, we discuss the upcoming role for variable stars and asteroseismology in calibrating the distance scale and measuring H0 and what problems exist in understanding these stars that will feed back on these measurements.

Variable stars have a unique part to play in Galactic astronomy. Among the most important of these variables are the Cepheids (types I and II), the RR Lyraes and the Miras (O- and C-rich). The current status of the basic calibration of these stars in their roles as distance, structure and population indicators is outlined and some examples of recent applications of these stars to Galactic and extragalactic problems are reviewed. The expected impact of Gaia on this type of work is discussed and the need for complementary ground based observations, particularly large scale near-infrared photometry, is stressed.

The physical background of scaling laws of disk galaxies is reviewed. The match between analytically derived and observed scaling laws is briefly discussed. Accurate modeling of the fraction of baryons that end up populating a disk, and the conversion efficiency of those into stars, remains a challenging task for numerical simulations. The measurement of rotational velocity tends to be made with criteria of convenience rather than through rigorous definition. And yet, the Tully–Fisher and the disk size versus rotational velocity relations exhibit surprisingly small scatter. Practical recipes (and costs) to optimize the quality of template relations are considered.

High spatial-resolution measurements of surface brightness fluctuations (SBFs) with the Hubble Space Telescope (HST) provide the most precise distances available to early-type galaxies beyond the Local Group. The observable SBF magnitude in a given bandpass is a basic property of any stellar system, corresponding to a ratio of the first and second moments of the stellar luminosity function. Calibration of the method has presented challenges, but we now have an excellent empirical determination of how the SBF observable varies with galaxy color in broad bandpasses at the red end of the optical spectrum, and we are working towards a similar calibration for HST's Wide-Field Camera 3 in the near-infrared wavelength range, where the SBF magnitudes are considerably brighter. From HST Advanced Camera for Surveys data, we have determined the relative distances of the Virgo and Fornax clusters to within a precision of 2%, and resolved their internal structures. More recent measurements allow us to tie the Coma cluster, the standard of comparison for distant cluster studies, to the same precise distance scale. The SBF method can be calibrated in an absolute sense either empirically using Cepheids or theoretically based on stellar population models. The agreement between model and empirical zero points provides an independent confirmation of the Cepheid distance scale.

Eclipsing binaries are powerful tools for determining the fundamental parameters of stars and, therefore, for measuring accurate, independent distances to nearby galaxies. I present distance measurements that are in progress based on early-type eclipsing binary systems in several Local Group galaxies at a range of metallicities, and discuss the strengths of the method, the limitations and possible sources of systematic error. The goal is to establish several local stepping stones along the extragalactic distance ladder, which will help calibrate the Cepheid period–luminosity relation and thus resolve the ongoing controversy about the distance scale, with its ramifications for cosmology and stellar ages.

We present new and independent estimates of the distances to the Magellanic Clouds (MCs) using near-infrared (NIR) and optical–NIR period–Wesenheit (PW) relations. The slopes of the PW relations are, within the dispersion, linear over the entire period range and independent of metal content. The absolute zero points were fixed using Galactic Cepheids with distances based on the infrared surface-brightness method. The true distance modulus we found for the Large Magellanic Cloud—(m − M)0 = 18.48 ± 0.01 ± 0.10 mag—and the Small Magellanic Cloud—(m − M)0 = 18.94 ± 0.01 ± 0.10 mag—agree quite well with similar distance determinations based on robust distance indicators. We also briefly discuss the evolutionary and pulsation properties of MC Cepheids.

Aiming at comparing different morphological models of galaxy clusters, we use two new methods to construct a cosmological-model-independent test of the distance-duality (DD) relation. The luminosity distances come from the Union2 compilation of Type Ia supernovae. The angular-diameter distances are given by the two cluster models of De Filippis et al. and Bonamente et al. The advantage of our new methods is that they can lead to reduced statistical errors. The morphologies of the cluster models are mainly focused on a comparison between the elliptical and spherical β models. The spherical β model is divided into two groups, in terms of different reduction methods of angular-diameter distances, i.e. the conservative and corrected spherical β models. Our results show that the DD relation is consistent with the elliptical β model at the 1σ confidence level (CL) for both methods, whereas for almost all spherical β-model parameterizations the DD relation can only be accommodated at the 3σ CL, particularly for the conservative spherical β model. To minimize systematic uncertainties, we also apply the test to the overlap sample, i.e. to the same set of clusters modeled by both De Filippis et al. and Bonamente et al. The DD relation is compatible with the elliptically modeled overlap sample at the 1σ CL; however, for most parameterizations the DD relation cannot be accommodated even at the 3σ CL by any of the two spherical β models. Therefore, it is reasonable that the marked triaxial ellipsoidal model is a better geometric hypothesis describing the structure of galaxy clusters than the spherical β model if the DD relation is valid for cosmological observations.

The Pleiades is the best-studied open cluster in the sky. It is one of the primary open clusters used to define the ‘zero-age main sequence,' and hence it serves as a cornerstone for programs which use main-sequence fitting to derive distances. This role is called into question by the ‘Pleiades distance controversy:' the distance to the Pleiades from Hipparcos of approximately 120 pc is significantly different from the distance of 133 pc derived using other techniques. To resolve this issue, we plan to use Very Long Baseline Interferometry to derive a new, independent trigonometric parallax distance to the Pleiades. In these proceedings we present our observational program and report some preliminary results.