# Week 2: Unveiling the Cosmos - Dark Energy, Universal Expansion, and the Legacy of Hubble

March 8, 2024

Hello, everyone! Welcome back to our cosmic journey! Last week, we covered some alternative methods of finding cosmological distances, such as using Cepheid variables or the Tully-Fisher relation. Let’s quickly revisit each concept. Methods such as the Tully-Fisher relation, cosmic redshift, and Cepheid variables play significant roles in measuring cosmic distances, each with its own set of challenges like metallicity effects, photometric contamination, and galactic extinction. Cepheid variables, which vary in brightness with well-defined periods, offer a direct way to measure distances by using the relationship between their pulsation period and luminosity.

This week, we embark on an enlightening exploration of the importance of distance measurements. Our study will center around two topics: dark energy and the Hubble Constant. We’ll also reflect on the significance of Type Ia supernovae in measuring cosmic distances and how this relates to Hubble’s groundbreaking discovery.

The Mysterious Fabric of Dark Energy:

Dark energy is intrinsically related to the accelerating expansion of the universe. This mysterious energy, which permeates all of space, acts as a counterbalance to gravity, propelling the cosmos to expand at an ever-increasing rate. By reviewing the effects of dark energy and its intricate relationship with Hubble’s Law, we gain insight into one of the most puzzling phenomena in modern cosmology. While no one knows exactly what dark energy and dark matter are, some theories exist which postulate dark matter to be a superfluid.

Calculating the Expansion of the Universe:

What exactly is the Hubble constant? Put simply, it is a parameter which represents the rate of expansion of the universe. It describes the relationship between the distances of galaxies and their recessional velocities (the speed they are moving away from us).

I started a hands-on exercise to learn more about how Hubble actually found his constant. Analyzing distance measurements and recessional velocities to several galaxies (of which these values are known) results in all the information we need to calculate Hubble’s constant. I created a graph of the values, with distance (in megaparsecs) on the x-axis and velocity (in kilometers per second) on the y-axis. The slope of the line of best fit is the estimated value of the Hubble constant, in units of km/s/Mpc. Funnily enough, Hubble used Cepheid variables to find his distance measurements, while I’ll be using Type Ia supernovae.

Why is this important? Well, Hubble’s Law can be expressed as *v*=*H*0×*d,* where *v* is the recessional velocity of a galaxy, *H*0 is the Hubble constant, and *d* is the distance of the galaxy from an observer. So if we look at two galaxies who are some distance *d*, at some point in time, they were touching. This point in time is the moment of the Big Bang. Thus, the age of the universe is around the reciprocal of the Hubble constant, or around 13.4 billion years old. This is how some simple distance measurements using Cepheid variables lead to larger discoveries down the line.

Role of Redshifts:

When the light from faraway galaxies travels through expanding space, its wavelengths get stretched, which makes the light appear redder than it originally was. Astronomers convert the amount of observed redshift into a measure of the velocity at which a galaxy is moving away from us. This is yet another piece of evidence for the expansion of the universe.

To better understand how redshifts are implemented, I solved for the distance versus redshift relations, where I worked out the luminosity distance-redshift relation for a given scale factor a(t) of the universe.

Journeying Forward:

The concepts of dark energy, the expanding universe, and the legacy of Hubble provide us with a richer understanding of the cosmos. Join us next week as we venture into the nitty-gritty of type Ia supernovae and what makes them so useful to astronomers.

Until next time.

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