The Cosmological Spacetime

Abstract

We present here the transformations required to recast the Robertson-Walker metric and Friedmann-Robertson-Walker equations in terms of observer-dependent coordinates for several commonly assumed cosmologies. The overriding motivation is the derivation of explicit expressions for the radius R h of our cosmic horizon in terms of measurable quantities for each of the cases we consider. We show that the cosmological time dt diverges for any finite interval ds associated with a process at R → R h , which therefore represents a physical limit to our observations. This is a key component required for a complete interpretation of the data, particularly as they pertain to the nature of dark energy. With these results, we affirm the conclusion drawn in our earlier work that the identification of dark energy as a cosmological constant does not appear to be consistent with the data.

Angular correlation of the cosmic microwave background in theRh=ctUniverse

“…Simply stated, Weyl's postulate says that any proper distance R(t) must be the product of a universal expansion factor a(t) and an unchanging co-moving radius r, such that R(t) = a(t)r. The conventional way of writing an FRW metric adopts this coordinate definition, along with the cosmic time t, which is actually the observer's proper time at his/her location. But what is often overlooked is the fact that the gravitational radius, R h , which has the same definition as the Schwarzschild radius, and actually coincides with the better known Hubble radius, is in fact itself a proper distance too (see also Melia & Abdelqader 2009). And when one forces this radius to comply with Weyl's postulate, there is only one possible choice for a(t), i.e., a(t) = (t/t 0 ), where t 0 is the current age of the Universe.…”

TheRh =ctuniverse without inflation

“…where H 0 is the current value of the Hubble constant (Melia & Abdelqader 2009). With this expansion factor, Eq.…”

A two-point diagnostic for the H ii galaxy Hubble diagram

“…More recently, Plionis et al (2011) and Terlevich et al (2015) demonstrated that the L(Hβ) − σ correlation is a viable high-z tracer, and used a compilation of 156 combined sources, including 24 GEHRs, 107 local HIIGx, and 25 high-z HIIGx, to constrain the parameters in ΛCDM, producing results consistent with Type Ia SNe. Most recently, we (Wei et al 2017) extended this very promising work even further by demonstrating that GEHRs and HIIGx may be utilized, not only to refine and confirm the parameters in the standard model but-perhaps more importantly-to compare and test the predictions of competing cosmologies, such as ΛCDM and the R h = ct universe (Melia 2003(Melia , 2007(Melia , 2013a(Melia , 2016(Melia , 2017aMelia & Abdelqader 2009;Melia & Shevchuk 2012).…”