First, the two comoving observers may both be at rest with respect to the bulk of the universe but in an expanding universe, they’re not at rest with respect to each other! The “bulk” here is moving relative to the “bulk” there, the distance between the two locations increasing over time. This induces a velocity-related Doppler redshift. This Doppler redshift is the dominant redshift when the source of the light and its target are not too far apart (and by “not too far”, I mean less than about 8–9 billion light years, when the so-called redshift factor is less than 1.)
When the distance is really, really great, however, there is another thing to consider. That light ray is really old. It was emitted at a time when the universe was much, much more dense on average than today. Greater density means greater gravitational potential, and the gravitational potential implies time dilation. When it comes to light rays that come from beyond about 8–9 billion light years, this gravitational time dilation cannot be ignored anymore. Clocks really were ticking slower back then, so however many cycles that light ray had every second back then, it will show up with fewer cycles per second when that second is measured by a clock now.
So the above is the "standard model" that differentiates dark energy from gravitational potential energy as time at the origin of the Big Bang....the Timescape model says that gravitational potential time dilation as greater density (momentum) is the same as the dark energy accelerating matter apart.
Professor David Wiltshire, who led the study, said, "Our findings show that we do not need dark energy to explain why the universe appears to expand at an accelerating rate.
"Dark energy is a misidentification of variations in the kinetic energy of expansion, which is not uniform in a universe as lumpy as the one we actually live in."
https://phys.org/news/2024-12-dark-energy-doesnt-lumpy-universe.html
Solution to the cosmological constant problem by David L. Wiltshire
dynamical spatial curvature
arises as time-varying spatial gradients of the kinetic spatial curvature, and depends
directly on the void volume fraction.
the largest typical voids, which I heuristically call small voids
in the Timescape model, the void volume fraction, fv, is the only free function
The results are striking since the signature of large negative spatial curvature, common
to several backreaction scenarios with emerging spatial curvature, is evident in the
radial profile of the stacked voids (see Fig. 2)
Is the Observable Universe Consistent with the Cosmological Principle?
but non-fundamental symmetry assumption
In his 1979 book Theoretical Cosmology, Raychaudhuri [7] identifies four approaches to the CP: (i) philosophical; (ii) mathematical; (iii) deductive; and (iv) empirical.
The first, philosophical, is said to have emotional appeal. The second, mathematical, is said to have the appeal of mathematical beauty (symmetry). ....this form is fixed by the symmetries.
Later we will argue that this actually extends to orientations on the sky, so the Hubble tension may be a three-dimensional problem and not a one-dimensional (redshift) problem, as is routinely assumed.
inter-connected by filamentary structures, woven around three-dimensional underdense regions identified as cosmic voids. The complex network and arrangement of matter in the cosmic web is postulated to arise from quantum fluctuations in an otherwise homogeneous medium in the inflationary era. There is a treasure trove of information encoded in the structural patterns of the primordial field as well the subsequent large scale structure of the Universe that emerges from it.
void models providing a putative replacement for dark energy
cosmic time has been exploited as means to assess the viability of void models
https://arxiv.org/pdf/2408.00358
The conventional limit neglects an important coupling of the quasilocal energy and angular momentum defined by the regional time–averaged motion of matter sources. For rotating galaxies we set out a new, self-consistent quasilocal Newtonian limit of general relativity, which does not assume a Minkowskian spacetime background a priori. It introduces novel, first-order features that fundamentally modify galactic dynamics
spacetime itself carries its own energy and angular momentum [4–7]. Moreover, the highly
nonlinear nature of general relativity gives rise to a noncommutativity
https://academic.oup.com/mnrasl/article/537/1/L55/7926647
timescape is characterized by the void fraction, , which represents the fractional volume of the expanding regions of the universe made up by voids.
https://arxiv.org/pdf/2503.13391
this second horizon, analogous to a cosmological horizon, emerges due to the
de Sitter-like nature of the void at large distances. We found that as the absolute value of
the contrast parameter δc increases, the size of the black hole horizon increases, while that
of the cosmological horizon decreases. Furthermore, in all cases, the inner horizon remains
larger than the Schwarzschild radius, reinforcing the impact of the void on the gravitational
structure.
Thus, our analysis revealed that the cosmic void surrounding the black hole significantly
modifies its properties. Vice versa, our findings seem also to indicate that the black hole
contributes to the void stability, since there exists a region between the singularity and the
edge of the void whose spacetime resembles a de Sitter one, introducing a repulsive effect
that counteracts possible gravitational collapses and stabilizes the system.
the relevant frame is one in which time symmetries are removed.
the relevant frame is one in which time symmetries are removed....emoves the time symmetries...we cannot tell whether particles subject to such motion are at rest in an expanding space, or moving in a static space. The argument about whether particles are moving or space is expanding is an argument about something that is fundamentally indistinguishable....Cosmic acceleration is an apparent effect11,16 which arises when we mistakenly try to fit a Friedmann model to the whole universe with the incorrect assumption that the local spatial curvature and local clock rates of isotropic observers
everywhere are identical to our own... An observer in a void will infer no cosmic acceleration,
Space-time: Commutative or noncommutative ?
This suggests that the scale of the spacetime coordinates noncommutativity could be larger than the Planck length....(associated to the noncommutativity of the spacetime coordinates) and φ (associated to the noncommutativity of momenta)
The solidary form of collective government of the hunter-gatherer groups was probably the most successful invention of modern man,
leading to his dominance over other species and even over other hominids.
This suggests that the scale of the spacetime coordinates noncommutativity could be larger than the Planck length..
https://arxiv.org/pdf/1901.01613
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