Source: https://www.sdss.org/science/cosmology-results-from-eboss/

Sidebar
Demonstration of the advances made in cosmology in the last decade. Stage-II experiments represent the experimental status in 2010, including WMAP, JLA Supernovae, and low redshift measurements of the baryon acoustic oscillations. Stage-III experiments represent the current status of cosmology experiments, as described below. Central values and 68% contours for each of the parameters describing expansion history and growth of structure in a cosmological model that allows for free curvature, neutrino mass, and constant equation of state for dark energy.

The SDSS Baryon Acoustic Oscillation (BAO) and Redshift-Space Distortion (RSD) measurements reveal an uninterrupted view of the cosmos over the last 11 billion years. This composite sample is the most constraining of its kind and allows a comprehensive assessment of the cosmological model. These final measurements are broadly described in the final eBOSS press release.

Contemporaneously with the BOSS and eBOSS surveys, which have fostered the development of the BAO and RSD techniques over the last 10 years, maps of the Cosmic Microwave Background (CMB) produced by the Planck satellite have given insight into the state of the Universe as it was during the recombination era. Large weak lensing surveys such as the Dark Energy Survey (DES) have measured cosmic shear to constrain the local matter density and amplitude of fluctuations. Type Ia supernovae (SNe Ia) measurements remain the most effective way to constrain expansion history at redshifts below $z<0.3$, with some of the latest results coming from the Pantheon sample of SNe Ia.

In the final eBOSS cosmology analysis (2020) , we present the cosmological model and its observational signatures. We use the BAO and RSD data from SDSS, the Planck CMB data, SNe Ia from the Pantheon sample, and weak lensing and clustering data from DES to provide the tightest available constraints on the parameters within the standard ΛCDM model and its extensions. In the brief summary of these results presented on this web page, we denote the Planck CMB data as 'CMB T&P' when no lensing is used, 'CMB lens' when only the lensing is used, and 'Planck' when all data are used. We refer to the DES weak lensing data as 'WL' and we refer to the full DES weak lensing, galaxy-galaxy lensing, and clustering data as 'DES'.

We begin with a discussion of BAO measurements in the context of the cosmic expansion history. We demonstrate that BAO are able to constrain single-parameter extensions to a ΛCDM cosmology that can not be constrained by CMB alone, and that BAO data are unique in their ability to provide robust, consistent measurements of the current expansion rate, $H_0$. We then discuss the insight offered by RSD measurements, showing that the RSD, CMB, and weak lensing measurements present a history of structure growth that is best described by a standard ΛCDM cosmology and a GR model for gravity. Finally, we present the cosmological model that best describes the available data and how constraints on that model have advanced in the last ten years.

More details about these analyses can be found in the final eBOSS cosmology analysis (2020) , with an emphasis on the SDSS, BOSS, and eBOSS cosmology programs.

BAO measurements from SDSS, normalized by the Planck ΛCDM prediction. Data are presented as the isotropic signal for measurements below redshift z<2. The data are presented as a combination of radial and transverse clustering measurements for the combined auto- and quasar cross-correlation function measurements at z>2 for Lyman-alpha.

RSD measurements from SDSS, normalized by the Planck ΛCDM prediction. The insets demonstrate the two-dimensional correlation function that captures the anisotropic clustering signal.

BAO and Expansion History

We use the final BAO constraints of background expansion history to measure curvature, dark energy, neutrino mass, and the local Hubble expansion rate. These BAO measurements are shown in the figure of Hubble Diagram residuals above, covering 11 Gyr of the history of the Universe.

(1) Detecting dark energy with BAO: Constraints on the matter and dark energy components of the Universe while allowing for free curvature allow us to assess the impact of the SDSS BAO measurements. BAO measurements alone lead to a constraint on the dark energy density with an 8 sigma confidence detection.

(2) Low-z and high-z BAO: SDSS offer a unique combination of galaxy and quasar BAO at z<=1.5 along with the Lyman-alpha forest BAO at z=2.33. With complementary degeneracy directions, low and high redshift measurements, when combined, allow precise constraints on both the matter density and the dark energy density.

(3) The curvature of space from BAO: When combined with Planck temperature and polarization data, SDSS BAO measurements allow an order of magnitude improvement on curvature constraints compared to Planck data alone. The BAO data provide strong evidence for a nearly flat geometry and constraints on curvature that are now roughly one order of magnitude within the fundamental limits.

(4) Local expansion history estimates: The BAO data allow robust, consistent measurements of $H0$ that are insensitive to the strict cosmological priors in CMB-only estimates. BAO estimates are insensitive to the use of CMB anisotropies altogether under the assumption of a ΛCDM cosmology, and including the Big Bang Nucleosynthesis constraints from primordial deuterium abundance. Under all assumptions, the $H0$ values from BAO are roughly 10% smaller than those from the Cepheid distance ladder and strong-lensing time delays, and geometric distance to MASERs. The consistency of the BAO results highlights that the '$H_0$ tension' can not be restricted to systematic errors in Planck or to the strict assumptions of the ΛCDM model.

We use the final RSD constraints from the SDSS Main Galaxy Sample (MGS), BOSS, and eBOSS programs to explore the impact of structure growth measurements on the cosmological model. These RSD measurements are shown above in the Hubble Diagram residual plot, covering the last eight billion years in the history of the Universe.

(5) Dark Energy constraints from growth: growth measurements provide 2-3x improvements on the precision in extended ΛCDM models when compared to CMB temperature and polarization data alone. Weak lensing data instill a preference for a flat geometry while RSD instill a preference for a cosmological constant.

(6) Consistency of General Relativity (GR) in predicting the rate of structure formation: RSD and weak lensing allow us to estimate the current amplitude of matter fluctuations. We find a picture of structure growth that is consistent with extrapolations of the amplitude of the measured CMB power spectrum under a GR model for gravity and a ΛCDM model for cosmic expansion.

(7) Testing GR predictions for matter and light: RSD measurements probe the gravitational response of matter while weak lensing measurements probe that of photons. These combined growth measurements provide evidence in support of the GR assumption that matter and photons follow the same interactions with a gravitational potential.

Global Cosmology Constraints

We combine the Planck (including lensing), Pantheon SNe Ia, SDSS, and DES data to determine the best fitting cosmological model. The SDSS data consist of the BAO+RSD measurements, while the DES data consist of the cosmic shear, galaxy clustering, and galaxy-galaxy lensing data (i.e., 3×2pt).

(8) Bounds on neutrino mass: The combined analysis allows very tight constraints on the summed mass of the three neutrino species, with an uncertainty that is almost equal to the lower bound of 60 meV allowed by neutrino oscillation experiments. Using the Planck data as a baseline, the largest improvement in precision comes from the addition of the SDSS BAO measurements, while the RSD improve the precision by another 23%.

(9) Role of SDSS in advancing cosmology over the last decade: We use a model with free curvature, neutrino mass, and constant equation of state for dark energy to assess the impact of the current, Stage-III generation of dark energy experiments relative to the Stage-II dark energy constraints that were possible when BOSS was achieving first light one decade ago. We define Stage-II experiments in a manner similar to the Dark Energy Task Force, specifically including WMAP, JLA Supernovae, and low redshift measurements of the baryon acoustic oscillations. The posterior volume spanned by w, curvature ($Ω_k$), $H_0$, fluctuation amplitude ($σ_8$), and neutrino mass decreases by a factor of 40 when adding the SDSS BAO and RSD data to Stage-II experiments. The biggest impact from SDSS is in improved constraints on $Ω_k$, $H_0$, and neutrino mass. The volume decreases by another factor of 25 when adding Planck, Pantheon SNe Ia, and DES data, for a total improvement of three orders of magnitude in the precision in this five-dimensional parameter space.

(10) Summary cosmological model: The tightest constraints on the cosmological model are found when combining current measurements of the expansion history, CMB, and growth of structure. This combination reveals a dark energy density measured to 0.7% precision under an assumed ΛCDM model. We find ∼1% precision estimates on the dark energy density ($Ω_Λ$), $H_0$, and $σ_8$ regardless of cosmological model, with a preference for a cosmological constant and a flat Universe under all models explored. The complementarity of BAO and SNe Ia data allow tight constraints of curvature and the dark energy equation of state, resulting in a Dark Energy Task Force Figure of Merit of 92. The full suite of cosmology constraints presented in the final eBOSS cosmology analysis (2020) are presented in the table below.

Marginalized values and 68% confidence limits for cosmological models using Planck, Pantheon SNe, SDSS BAO, SDSS RSD, and DES data (weak lensing, galaxy-galaxy lensing, and clustering).

After recombination, without the pressure of the photons, the baryons simply fall into the Newtonian potential wells with the cold dark matter, an event usually referred to as the end of the Compton drag epoch. [source]

Prior to the recombination of baryons and electrons, the large density of free electrons couples the baryons to the photons through Coulomb and Compton interactions so that the three species move together as a single fluid. This continues until, in the process of recombination, the rate of Compton scattering between photons and electrons becomes too low, freeing the baryons from the photons. We thus define the drag epoch z_d as the time at which the baryons are released from the Compton drag of the photons in terms of a weighted integral over the Thomson scattering rate. [source, pg4]

The time when the baryons are “released” from the drag of the photons is known as the drag epoch, z_d. From then on photons expand freely while the acoustic waves “freeze in” the baryons in a scale given by the size of the horizon at the drag epoch. Four species: Dark matter, Baryons, Photons & Neutrinos. Initial perturbations adiabatic: all species perturbed approximately same fractional amount. Neutrinos do not interact and move too fast to be stopped by gravity, so they stream away Dark matter responds to gravity and falls onto the perturbation overdensity Perturbation dominated by photons and baryons as they are coupled. Perturbation is overdensity and overpressure. Overpressure tries to equalize with surrounding resulting in an expanding sound wave moving at the speed of sound which is approximately 2/3 the speed of light The perturbation in photons & baryons is carried outward As the expanding universe cools down, it reaches a point when the electrons and protons begin to combine Photons do not scatter as efficiently and start to decouple The sound speed drops and the pressure wave slows down Sound horizon at the drag epoch is the comoving distance a wave can travel prior to z_d The baryon acoustic oscillations provide a characteristic scale that is “frozen” in the galaxy distribution providing a standard ruler that can be measured as a function of redshift in either the galaxy correlation function or the galaxy power spectrum The BAO determination of the universe geometry is quite robust against systematics [source]

To be useful for cosmology, we need a standard ruler: an object of a known size at a single redshift, z, or a population of objects at different redshifts whose size changes in a well-known way (or is actually constant) with redshift. Ideally the standard ruler falls into both classes, which, as we will argue below, is the case for the BAO, to good approximation. [source]

Results from 6 lensed systems [1907.04869] H0LiCOW XIII. A 2.4% measurement of $H_{0}$ from lensed quasars: $5.3σ$ tension between early and late-Universe probes “Gravitational lensing offers an independent method of determining H0. When a background object (the “source”) is gravitationally lensed into multiple images by an intervening mass (the “lens”), light rays emitted from the source will take different paths through space-time at the different image positions. Because these paths have different lengths and pass through different gravitational potentials, light rays emitted from the source at the same time will arrive at the observer at different times depending on which image it arrives at. If the source is variable, this “time delay” between multiple images can be measured by monitoring the lens and looking for flux variations corresponding to the same source event. The time delay is related to a quantity referred to as the “time-delay distance”, D∆t, and depends on the mass distribution in the lensing object, the mass distribution along the line of sight (LOS), and cosmological parameters. D∆t is primarily sensitive to H0, although there is a weak dependence on other parameters (e.g., Coe & Moustakas 2009; Linder 2011; Treu & Marshall 2016). This one-step method is completely independent of and complementary to the CMB and the distance ladder. The distances probed by time-delay cosmography are also larger than those from the distance ladder, making this method immune to a monopole in the bulk velocity field of the local Universe (i.e., a 'Hubble bubble')” (excerpt from pg2)

Bonvin et al. (2017) noted that the first three H0LiCOW systems showed a trend of lower lens redshift systems having a larger inferred value of H0, but could not conclude anything due to the small sample size. With a sample of six lenses, we see that this general trend still remains, as well as a trend of decreasing H0 with increasing D∆t. Even with six lenses, these correlations are not significant enough to conclude whether this is a real effect arising from some unknown systematic, a real physical effect related to cosmology, or just a statistical fluke (see Appendix A).

Bonvin 2017 pg12: “Intriguingly, we note that the H0 values yielded by each system individually get larger for lower lens redshifts. So far, we cannot state if this comes from a simple statistical fluke, an unknown systematic error or hints towards an unaccounted physical property. The addition of two more lenses from the H0LiCOW sample will certainly help us in that regard.”

[1907.02533] A SHARP view of H0LiCOW: $H_{0}$ from three time-delay gravitational lens systems with adaptive optics imaging

The Hubble constant determined through an inverse distance ladder including quasar time delays and Type Ia supernovae; Astronomy & Astrophysics (A&A)

Collaborations: H0LiCOW¹ | SHARP² | STRIDES³ | COSMOGRAIL⁴ |

“The blind analysis of a seventh lens system using methods very similar to those adopted by H0LiCOW has recently been published by the STRIDES collaboration (Shajib et al. 2019, an independent analysis adopting a different modeling software is currently under way), finding 74.2+2.7−3.0km s−1Mpc−1, in agreement with the H0LiCOW result. This most recent system is particularly interesting since it has two sets of multiple images at different redshifts, which help break some of the degeneracies, and results in the most precise individual measurement so far. In order to make further progress in this important arena, members of the COSMOGRAIL, H0LiCOW, SHARP and STRIDES collaborations interested in time-delay cosmography of lensed quasars have decided to join forces with other scientists and form a new “umbrella” collaboration named TDCOSMO (Time-Delay COSMOgraphy).” [source, pg 2]

[1912.08027] TDCOSMO. I. An exploration of systematic uncertainties in the inference of $H_0$ from time-delay cosmography

Lensing software

[1506.07524] COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses XV. Assessing the achievability and precision of time-delay measurements [1607.00017] H0LiCOW I. $H_0$ Lenses in COSMOGRAIL's Wellspring: Program Overview [1904.07237] Next generation cosmography with strong lensing and stellar dynamics

Other Articles: H0ly Cow! A New Measurement of the Hubble Constant | astrobites Cosmologists Debate How Fast the Universe Is Expanding, Quanta Magazine, by Natalie Wolchover Cosmic Magnifying Glasses Yield Independent Measure of Universe's Expansion Astronomically Rare 'Double Lens' Yields Best Single System Measurement Of Cosmic Expansion A Crisis in Cosmology – W. M. Keck Observatory

Researchers: Sherry Suyu, (MPA, De) Simon Birrer, (Stanford) | github projects | Chris Fassnacht, (UCD) | UC Davis articles | Tomasso Treu (UCLA): presentation at July 2019 KITP conference Lucas Macri, (TAMU) Anowar Shajib, (UCLA) Geoff Chih-Fan Chen, (UCD)

Terms: ¹ H0LiCOW: H0 lenses in COSMOGRAIL’s Wellspring ² SHARP: Strong lensing at High Angular Resolution Program ³ STRIDES: STRong-lensing Insights into Dark Energy Survey ⁴ COSMOGRAIL: COSmological MOnitoring of GRAvItational Lenses

Above plot is from [1807.06209] Planck 2018 results. VI. Cosmological parameters, page 26.

Excellent reddit explanatory post

Other plots: Kowalski et al | Ned's article | Google Images query |

Other refs: [0904.0024] Approaches to Understanding Cosmic Acceleration, by Silvestri and Trodden The Standard Model of Cosmology and the Dark Universe, p158, large PDF Supernova Cosmology Project

NRAO article on Radio astronomy and Black Holes. Contains a great infographic.

Wikipedia VLBI article

First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

#cosmology #astrophysics

Physics Physics Quantum Mechanics Linear Algebra Classical Mechanics Electrodynamics Math Methods in Physics Special Relativity General Relativity LaTeX

Math How to learn our Math! Basic Algebra Precalculus Methods of Proof Single Variable Calculus Multivariable Calculus Linear Algebra Differential Equations | What are Differential Equations and how do they work? skdh | Set Theory Real Analysis Partial Differential Equations Variational Calculus Topology Differential Geometry Discrete Mathematics Complex Analysis Tensor Calculus

Graduate Mathematics Functional Analysis Stochastic Calculus

Works In Progress Engineering Dynamics Linear Circuit Analysis Engineering Thermodynamics

#physics #math #quantum

http://arxiv.org/abs/1902.03196 Baryon acoustic oscillation, Hubble parameter, and angular size measurement constraints on the Hubble constant, dark energy dynamics, and spatial curvature. Authors: Joseph Ryan, Yun Chen, Bharat Ratra http://arxiv.org/abs/1805.06408 Constraints on dark energy dynamics and spatial curvature from Hubble parameter and baryon acoustic oscillation data. Authors: Joseph Ryan, Sanket Doshi, Bharat Ratra [1811.02376] First Cosmological Results using Type Ia Supernovae from the Dark Energy Survey: Measurement of the Hubble Constant

search_arxiv.php: ti:carnegie+AND+(ti:hubble+OR+abs:hubble) (Carnegie-Chicago Hubble Program) all:symposi*+AND+cat:astro-ph.CO cat:astro-ph.CO+AND+(all:workshop+OR+all:conference)

inspirehep queries: All inspirehep search terms Conference series papers on the history of physics relevant to HEP Papers with accompanying YouTube videos Citations of your institution's papers Articles discussed in Quanta Magazine

#cosmology #physics #astrophysics

Tip of the Red Giant Branch as a Distance Indicator

[1907.05922] The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch

Video of a presentation by Mark Reid at the KITP-UCSB conference Tensions between the Early and the Late Universe on July 16, 2019: H0: NGC 4258 and the Megamaser Cosmology Project | KITP_h0tTakes tweets |

TGRB method – another method useful in measuring the Hubble constant H0, in addition to the cosmic distance ladder, inverse distance ladder, megamasers, H0liCOW time-delay gravitational lensing, gravitational waves, CMB, etc.

Wikipedia: Tip of the Red Giant Branch

The Carnegie Supernova Project: Absolute Calibration and the Hubble Constant https://arxiv.org/abs/1809.06381

The Carnegie-Chicago Hubble Program. I. An Independent Approach to the Extragalactic Distance Scale Using only Population II Distance Indicators https://arxiv.org/abs/1604.01788

A promising alternative to Cepheids is the Tip of the Red Giant Branch (TRGB) method (Madore et al. 2009; Jang et al. 2017). A significant advantage with TRGB is that the older stellar populations being considered are found in both early- and late-type galaxies, allowing for potentially more nearby calibrating SN Ia hosts. The method is also typically carried out in the outskirts of the hosts, reducing the crowding significantly. The Carnegie-Chicago Hubble Program (CCHP; Beaton et al 2016; Freedman 2018) aims to measure H0 using population II distance indicators and the CSP-I and CSP-II samples will be a significant component of their work. For the purposes of this paper, we will forgo using the existing TRGB sample as it is rather sparse and lacks SNe Ia that were observed in the NIR. We therefore use the Cepheid sample of Riess et al. (2016) to calibrate our Hubble diagram as it is the most comprehensive dataset under a single photometric system. In the following sections, we present the general method, then consider different data subsamples and their effects on the derived value of H0. excerpt from The Carnegie Supernova Project: Absolute Calibration and the Hubble Constant [1809.06381]

https://arxiv.org/abs/1703.10616 The Carnegie-Chicago Hubble Program. III. The Distance to NGC 1365 via the Tip of the Red Giant Branch The aim of the Carnegie-Chicago Hubble Program (CCHP) is a direct route to H0 using Type Ia supernovae (SNe Ia) calibrated entirely via Population (Pop) II stars. The SNe Ia zero point is determined using a distance ladder built from RR Lyrae (RRL) and the Tip of the Red Giant Branch (TRGB) distances to Local Group galaxies. This zero point is then applied to the full sample of SNe Ia in the smooth Hubble flow to arrive at a local, direct estimate of H0. Eventually, the TRGB will be calibrated in the Galaxy based on Gaia trigonometric parallaxes for a three step route to the Hubble constant.Since this path is independent of the traditional Pop I Cepheid distance scale that currently sets the SNe Ia zero point, it has the potential to provide insight into the growing (now>3-σ) difference inthe value of H0 as determined by direct (the distance ladder; e.g.Freedman et al. 2012; Riess et al.2016) and indirect methods (via modeling of the Cosmic Microwave Background; e.g.Komatsu et al. 2011;Planck Collaboration et al. 2016)

Tip of the Red Giant Branch as a Distance Indicator The tip of the red giant branch (TRGB) method is a powerful, Pop II distance indicator. It uses the I-band luminosity of the brightest RGB stars. It turns out that in this wavelength, the magnitude of the TRGB stars is very insensitive to metallicity, and also to age.

RR Lyrae variable class of stars https://en.wikipedia.org/wiki/RR_Lyrae_variable

inverse distance ladder method; First Cosmological Results using Type Ia Supernovae from the Dark Energy Survey: Measurement of the Hubble Constant https://arxiv.org/abs/1811.02376 Our measurement makes minimal assumptions about the underlying cosmological model, and our analysis was blinded to reduce confirmation bias. We examine possible systematic uncertainties and all are presently below the statistical uncertainties. Our H0 value is consistent with estimates derived from the Cosmic Microwave Background assuming a LCDM universe (Planck Collaboration et al. 2018). traditional measurements of H0 with SNe Ia use a distance ladder of parallax and Cepheid variable stars, the inverse distance ladder relies on absolute distance measurements from the BAOs to calibrate the intrinsic magnitude of the SNe Ia. a new paper (https://arxiv.org/abs/1811.00537 ) @LloydEKnox, K. Aylor, M. Joy, @cosmic_mar, S. Raghunathan, and K. Wu, called “Sounds Discordant: Classical Distance Ladder and LCDM-based Determinations of the Cosmological Sound Horizon.” ___ Excerpts from Have We Mis-Measured the Universe: SciAm article by Corey S. Powell

everything we know about the origin of the sound horizon depends on a theoretical model of how the universe behaved during its unseen initial 380,000 years. If the models are wrong and the size of the sound horizon is different than what they predict, that adjustment would change all of the numbers derived from it, including the Hubble constant.

Researchers already invoke dark matter to explain galactic motion and dark energy to account for the universe’s accelerating expansion. The divergent measurements of the Hubble constant may be the first sign of the existence of a third dark component, Knox argues—a “dark turbo,” perhaps, that added to the energy of the early universe, hastening its expansion and changing the pitch of its sounds. A related possibility is dark energy has more than one form, or changes over time in complicated ways. A recent study of 1,598 distant quasars using NASA’s Chandra X-Ray Observatory offers intriguing, if preliminary, evidence for the latter interpretation.

New observations of the early universe by the South Pole Telescope in Antarctica and the Atacama Cosmology Telescope in Chile will further probe the sound horizon. Knox is also part of a proposed next-generation ground-based project called CMB-S4 that intends to map the polarization of the microwave sky with great sensitivity. Further, Freedman is nearly finished with her comprehensive data re-analysis. Studies of gravitational waves will provide a completely independent way to assess the true Hubble value as well.

she is developing a new type of distance measurement using red giant stars as reference points. At the same time, she is running a double-blind experiment to reanalyze all of her existing data for bias and mistakes. ___

#astrophysics #cosmology