Title: Implications for Hubble Voltage from the Ages of the Earliest Astrophysical Objects

Authors: Sunny Vagnozzi et al.

Institution of the first author:

Kavli Institute for Cosmology (KICC) and Institute of Astronomy, University of Cambridge

Status: Preprint available on ArXiv

One of the most important concepts that have shaped our current understanding of astronomy is the expansion of the universe. Einstein showed through his theory of General relativity that space is “expandable” and that the basic state of the large-scale universe is one of expansion, contraction, or perfect equilibrium. Then, with the help of previous work by Henrietta Leavitt, Edwin Hubble measured the distances of 46 relatively local galaxies and combined these observations with the speed (redshift) from the literature, as in Figure 1 below. Not only did this work demonstrate the existence of galaxies outside of the Milky Way for the first time, but it also showed that these galaxies were moving away from us, and ultimately, that the universe itself was expanding.

It turns out that the rate of expansion of the universe, also known as the Hubble constant (H0), has enormous consequences for the physics underlying the cosmos, thus refining the value of H0 was a primary endeavor in observational astronomy. Today, there are two main competing methods for measuring H0: one that uses local objects, in an effort similar to that of Hubble, and another that uses remote metrics and information encoded in the Cosmic microwave background. Over the past few years, their disagreement has grown stronger and stronger, leading to what is now called ‘Hubble Tension’. Why are these two measures at odds? Is there still a new underlying physics to be discovered? Or are there systematic issues that have not yet been fully understood by either method?Let’s take a step back and take our bearings. When tackling large questions, it is always helpful to overcome small logical consistency checks first. Could there be an easy way to set at least one upper bound on the Hubble constant? One of the two main measures of H0 particularly problematic? Answering these questions is the goal of the article covered by Today’s Astrobite.

Figure 1: Here is an example of a ‘Hubble diagram’, which plots the distances to different galaxies and their corresponding recession speeds. Galaxies at greater distances are moving away from us faster as the entire universe expands. The different colored lines indicate different values ​​of the Hubble constant in units of km / s / Mpc. Credit: NASA, ESA, STScI.

What can ancient objects in the Universe tell us about the Hubble constant?

An interesting feature of our current understanding of the cosmos is that at each instant the rate of expansion of the universe is inversely proportional to the age of the universe at that time (let’s not go into math to find out why this is the case, unless you really want!). Additionally, it is assumed that every object we find in the universe must be younger than the universe itself because no object formed exactly at the time of the Big Bang. This means that every object we find places a lower limit on the age of the universe (the universe must be at least as old as the object). By combining these two pieces of information, the authors believe that it is possible to set an upper limit on the value of H0 via the lower limit of the age of the universe. For the strongest constraints, a sample of ancient objects covering several billion years of cosmic history is then needed.

To obtain a sample of the oldest objects in the universe covering a wide range of cosmic time, the authors consult a series of surveys (SDSS, CANDELS, PanSTARRS, among others) which targeted both galaxies and quasars. After applying a series of quality cuts, the authors group these objects into redshift slices and select only the oldest in each redshift slice. The result is a catalog of the object ages and their associated redshifts (Figure 2 below), which can be used to derive an upper bound on H0 using the inverse proportionality of the age of the universe and the rate of expansion.

Figure 2: Ages on the y-axis and redshifts on the x-axis are shown for the objects used in this study. Each data point is colored by the survey or by the work of the literature from which it comes. The different curves indicate the predicted age-redshift relationship for different values ​​of the Hubble constant. Fig. 1 in the original work.

How to set an upper limit on H0 with old objects

With the sample of the oldest galaxies and quasars found in their sample (along with their ages and redshifts), the authors are in place to derive an upper limit on H0. To do this, the authors build a very simple 3-parameter model that includes the Hubble constant, the density of matter in the universe (Ωm, a cosmological parameter necessary to calculate the Hubble constant), and what the authors called the “incubation time” or τin (the difference between the age of the universe at a given time and the age of the oldest objects at a given time). The authors randomly draw different values ​​for these parameters and combine the density of matter and the Hubble constant to predict an age of the universe at a given redshift. The difference between the age of the universe, the age of the oldest objects in the universe, and the incubation time, should be zero for a perfect match. By sampling thousands of different combinations of values, authors can map the most likely values ​​(this process is generically called Markov Monte Carlo chain). Their results are given below in a “wedge graph”, which is a compact representation of the 1 and 2-dimensional likelihood distributions of the various parameters.

Figure 3: “Corner plot” for the likelihood distributions of the 3 parameters (Hubble constant, density of matter and incubation time) in their model. Blue lines indicate one-dimensional likelihood distributions for each individual parameter, while outlines indicate joint two-dimensional likelihood distributions. From this result, the authors derive a 95% confidence limit on the value of the Hubble constant

At the 95% confidence level, the authors find that H0 is limited to 4σ, the authors’ result here is only a 2σ voltage with local measurements and is perfectly consistent with the CMB measurement. In general, a deviation of 2σ (2 standard deviations of disagreement) is usually not a problem, and for most physicists would not even be considered “proof” of new physics. Both measurements (more or less) pass this test!

The authors emphasize here that their analysis relies heavily on the validity of ages in their sample of ancient astrophysical objects and on the validity of the cosmological concordance model (also known as Λ-cold dark matter, or ΛCDM). If either of these fails, their results are no longer valid. Given the strength of ΛCDM (it’s called the concordance model for a reason, after all!), Then the crucial factor here is the age of the astrophysical objects. Constraining the age of galaxies and quasars is no easy task. This work can be greatly enhanced by improving our methods of estimating the ages of distant objects and finding ancient objects at ever increasing redshifts. There is no doubt that these two goals are within reach: Astronomers will continue to build samples of well-studied objects throughout the universe, and will point ever more sophisticated and sensitive telescopes into the night sky. As the authors conclude, measuring the age of objects in the universe offers an interesting avenue for understanding the fundamental laws of the cosmos.

Edited by: Haley Wahl

About Lukas Zalesky

I’m a PhD student at the University of Hawaii Institute of Astronomy. I am interested in understanding how galaxies form and evolve over billions of years, as well as the gravitational lens through galaxy clusters. Outside of research, I spend my time with animals, exercising, practicing Zen, and exploring the beautiful island of Oahu.

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