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------------------ 2607 - HUBBLE CONSTANT - leads to the age of the Universe?
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- The Hubble Constant method not only works, but it remains the best way we have to calculate the Universe's age even today. However, there are many simplifying assumptions you can make that will give you an easy answer that isn't necessarily correct. Here's how to figure out the age of the Universe.
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- Standard candles and standard rulers are two different techniques astronomers use to measure the expansion of space at various times/distances in the past. Based on how quantities like luminosity or angular size change with distance, we can infer the expansion history of the Universe.
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- Using the candle method is part of the distance ladder, yielding 73 km/s/Mpc.
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- Using the ruler is part of the early signal method, yielding 67 km/s/Mpc.
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- To put this rate of expansion in more familiar terms: 73 km/s/Mpc is equal to 49,300 miles per hour for every distance of 1,000,000 lightyears.
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- This expansion rate is called the Hubble constant rate of expansion.
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- On the largest scales, the galaxies we find in the Universe obey a very simple relation between the two observable quantities of distance and redshift, where the farther away an object is from us, the greater its measured redshift will be.
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- Define redshift refers to the expanding space stretching the wavelength of light . As the wavelength gets wider the frequency of light decreases and the wavelength stretches towards the red end of the light spectrum. Thus “redshift“.
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- The recession speed that you would infer from a galaxy's redshift equals the distance to that galaxy multiplied by the Hubble constant.
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- That Hubble constant has the same value for pretty much every galaxy we measure, particularly for galaxies within a few billion light-years of us. Even though there are additional cosmic motions inherent to each galaxy induced by gravitational effects, this law remains true when you average over all the galaxies you can find.
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- What we measure the Hubble constant to be depends on how you measure it:
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- If we measure it by using signals that were imprinted all the way back in the earliest stages of the Big Bang, we get a value for the Hubble constant of 67 km/s/Mpc, with an uncertainty of 1-2%,
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- If we measure it by measuring individual light sources that don't arrive until the Universe is already billions of years old, we obtain a value for the Hubble constant of 73 km/s/Mpc, with an uncertainty of just 2-3%.
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- Why these two values don't match, and why they give such different, mutually inconsistent answers, is one of the major conundrums of modern cosmology.
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- The Hubble constant itself comes in units that are a speed (km/s) per unit distance (Mpc, where 1 megaparsec is about 3.26 million light-years). If you look at a galaxy that's 100 Mpc away, you'd expect it to recede away ten times faster than one only 10 Mpc away, but only one-tenth as fast as a galaxy 1,000 Mpc away. That's the simple power of the redshift-distance relationship.
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- There are approximately 3.1 × 10^19 kilometers in one megaparsec, which means that if you turn the Hubble constant into an inverse time, you find some fascinating things.
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- The "time" that a value of 67 km/s/Mpc corresponds to is equivalent to 14.6 billion years.
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- The "time" that a value of 73 km/s/Mpc corresponds to is equivalent to 13.4 billion years.
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- These are both almost equal to the accepted age of the Universe, but not quite. In addition, they're both almost equal to one another, but differ by approximately the same amount that the two estimates for the Hubble constant differ by 9%.
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- However, we cannot simply change the age of the Universe by changing the Hubble constant, and there's a subtle but vital reason why this is so.
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- The first Friedmann equation details the Hubble expansion rate squared on the left hand side, which governs the evolution of spacetime. The right side includes all the different forms of matter and energy, along with spatial curvature (in the final term), which determines how the Universe evolves in the future.
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- GOOGLE ‘Friedmann equation” to see what it looks like. But I will not attempt to explain it. It has been called the most important equation in all of cosmology, and was derived by Friedmann back in 1922.
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- The value of the Hubble constant today isn't simply the inverse of the value of the age of the Universe, even though the units work out to give you a measure of time. Instead, the expansion rate that you measure, the Hubble constant today, must balance the sum total of every form of energy that contributes to the Universe's composition, including:
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----------------------------------- normal matter,
----------------------------------- dark matter,
----------------------------------- neutrinos,
----------------------------------- radiation,
----------------------------------- dark energy,
----------------------------------- spatial curvature,
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- If the Universe is exclusively made up of radiation, you find that the Hubble constant multiplied by the age of the Universe since the Big Bang equals ½, exactly.
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- If the Universe is exclusively made up of normal and/or dark matter, you find that the Hubble constant multiplied by the age of the Universe equals ⅔, exactly.
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- If the Universe is entirely made of dark energy, you will find that there is no exact answer; the value of the Hubble constant multiplied by the age of the Universe always continues to increase towards infinity as time goes on.
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- This means that if we want to accurately calculate the age of the Universe, we can do it, but the Hubble constant alone isn't enough. In addition, we also need to know what the Universe is made out of.
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- Two imagined Universes with the same expansion rate today but made out of different forms of energy will have different expansion histories and, therefore, different ages from one another.
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- Measuring back in time and distance can inform how the Universe will evolve and accelerate/decelerate far into the future. We can learn that acceleration turned on about 7.8 billion years ago with the current data, but also learn that the models of the Universe without dark energy have either Hubble constants that are too low or ages that are too young to match with observations.
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- If dark energy evolves with time, either strengthening or weakening, we will have to revise our present picture. This relationship enables us to determine what's in the Universe by measuring its expansion history.
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- To find out how old the Universe actually is since the onset of the hot Big Bang, all we have to do is determine the expansion rate of the Universe and what the Universe is made out of.
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- There are a variety of methods that we can use to make this determination, but there's one vital thing we have to remember: many of the ways we have of measuring one parameter like the expansion rate are dependent on our assumptions about what the Universe is made out of.
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- We cannot assume that the Universe is made out of a certain amount of matter, a certain amount of radiation, and a certain amount of dark energy in a way that's independent of the expansion rate itself. Perhaps the most powerful way to illustrate this is to look at the leftover glow from the Big Bang itself: the Cosmic Microwave Background.
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- The leftover glow from the Big Bang, the CMB, isn't uniform, but has tiny imperfections and temperature fluctuations on the scale of a few hundred microkelvin. While this plays a big role at late times, after gravitational growth, it's important to remember that the early Universe, and the large-scale Universe today, is only non-uniform at a level that's less than 0.01%.
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- Planck satellite has detected and measured these fluctuations to better precision than ever before, and can use the fluctuation patterns that arise to place constraints on the Universe's expansion rate and composition.
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- Every direction in the Universe displays the same average temperature as every other direction: approximately 2.725 K. When you subtract that mean value out, you get the pattern fluctuations, or departures from the average temperature.
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- These temperature fluctuations exhibit particular patterns in their magnitude on a variety of angular scales, with the fluctuations rising in magnitude down to some particular angular scale of about 1 degree, then decreasing and increasing in an oscillatory fashion. Those oscillations tell us some vital statistics about the Universe.
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- Four different cosmologies lead to the same fluctuation patterns in the CMB, but an independent cross-check can accurately measure one of these parameters independently, breaking the degeneracy.
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- By measuring a single parameter independently we can better constrain what the Universe we live in has for its fundamental compositional properties. However, even with some significant wiggle-room remaining, the age of the Universe isn't in doubt.
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- Four different cosmologies lead to the same fluctuation patterns in the CMB, but an independent. What's most important to realize is that there are many possible combinations of values that can fit any particular graph. For example, given the fluctuations we see, we can have a Universe with:
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----- 4% normal matter, 21% dark matter, 75% dark energy and a Hubble constant of 72
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----- 5% normal matter, 30% dark matter, 65% dark energy and a Hubble constant of 65
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----- 8% normal matter, 47% dark matter, 49% dark energy, -4% curvature and a Hubble constant of 51.
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- A pattern emerges having a larger Hubble constant if you have less matter and more dark energy, or a smaller Hubble constant if you have more matter and less dark energy. What's remarkable about these combinations, however, is that they all lead to almost exactly the same age for the Universe since the Big Bang.
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- There are many possible ways to fit the data that tells us what the Universe is made of and how quickly it's expanding, but these combinations all have one thing in common: they all lead to a Universe that's the same age, as a faster-expanding Universe must have more dark energy and less matter, while a slower-expanding Universe requires less dark energy and greater amounts of matter.
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- The reason that we can claim the Universe is 13.8 billion years old to such enormous precision is driven by the full suite of data that we have.
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- A Universe that expands more quickly needs to have less matter and more dark energy, and its Hubble constant multiplied by the age of the Universe will have a larger value.
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- A slower-expanding Universe requires more matter and less dark energy, and its Hubble constant multiplied by the age of the Universe gets a smaller value.
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- However, in order to be consistent with what we observe, the Universe can be no younger than 13.6 billion years and no older than 14.0 billion years, to more than 95% confidence.
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- There are many properties of the Universe that are indeed in doubt, but its age isn't one of them.
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- February 6, 2020 2607
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--------------------- Thursday, February 6, 2020 --------------------
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