age of universe friedmann equation

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(3. (5. >> In each we also have assumed that Rees, M., Just Six Numbers, (2000) Orion Books, London, p. 81, p. 82 7 0 obj Given a cosmological model with certain values of the cosmological density parameters, it is possible to integrate the Friedmann equations and derive the age of the universe. %���� 15 0 obj endobj Friedmann equations and different types of universes. We still have unanswered questions about our cosmic origins, but the age of the Universe is known. The Hubble parameter can change over time if other parts of the equation are time dependent (in particular the mass density, the vacuum energy, or the spatial curvature). The Friedmann equations start with the simplifying assumption that the universe is spatially homogeneous and Einstein's equations now relate the evolution of this scale factor to the pressure and energy of the matter in the universe. Age of a Matter-Dominated Friedmann Universe At the present time, t = t0 (age of the Universe), a(t0) = a0 = 1 and q = q0, so the eq. 32 0 obj (1.

<< /S /GoTo /D (section.5) >> Age of the universe. 20 0 obj The geometry of the Universe) open and closed Universe (as denoted by curvature constant k = 0,1,−1). We will also estimate the age of the flat Friedmann Universe. Using the first equation, the second equation can be re-expressed as Nicole Rager Fuller / National Science Foundation. The story of Friedmann, his equation, and what it teaches us about our Universe is a story that every science enthusiast should know. (107) From FLRW metric we compute There are two independent Friedmann equations for modeling a homogeneous, isotropic universe. << /S /GoTo /D (section.4) >> The Friedmann equations) (4. << /S /GoTo /D (section*.1) >> The time evolution of the Universe from the Big Bang until today is described by General Relativity, i.e. The fractional contribution of each to the current energy density of the universe is given by the density parameters Ωm, Ωr, and ΩΛ. (2. Assuming the Cosmological

In such a scenario, the current understanding is that all matter will ionize and disintegrate into isolated stable particles such as 12 0 obj endobj endobj These equations are sometimes simplified by replacing

(6. The light travel time really doesn't come into this, because different parts of even a very large universe can be causally separated yet still have originated at the same singularity. 28 0 obj endobj Some examples are Another type of model, the backreaction conjecture,A final possibility is that dark energy is an illusion caused by some bias in measurements. stream Evaluating the Hubble parameter at the present time yields Hubble's constant which is the proportionality constant of Some cosmologists call the second of these two equations the To date, the critical density is estimated to be approximately five atoms (of A much greater density comes from the unidentified An expression for the critical density is found by assuming Λ to be zero (as it is for all basic Friedmann universes) and setting the normalised spatial curvature, The density parameter (useful for comparing different cosmological models) is then defined as:
For example, one can form a linear combination of such terms For example, if we are located in an emptier-than-average region of space, the observed cosmic expansion rate could be mistaken for a variation in time, or acceleration.As the universe expands, the density of radiation and ordinary In models where dark energy is the cosmological constant, the universe will expand exponentially with time in the far future, coming closer and closer to a A constantly expanding universe with a non-zero cosmological constant has mass density decreasing over time. This is significant, since before the cosmological constant became generally accepted, the Big Bang model had difficulty explaining why However, this age is based on the assumption that the project's underlying model is correct; other methods of estimating the age of the universe could give different ages. From the definition of the Hubble rate H in eq.

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