[Paper Review] Fundamental Aspects of the Expansion of the Universe and Cosmic Horizons

T. M. Davis|arXiv (Cornell University)|Feb 12, 2004

Cosmology and Gravitation Theories13 references6 citations

TL;DR

This paper clarifies fundamental misconceptions in cosmology by applying general relativity to the expansion of the universe, resolving conflicts around cosmic horizons and the Hubble sphere. It demonstrates that superluminal recession velocities are possible without violating relativity, shows that non-comoving objects can exhibit blueshifts despite receding, and confirms the generalized second law of thermodynamics holds across diverse cosmological models, even with apparent entropy decreases that may resolve upon full black hole embedding solutions.

ABSTRACT

In the context of the new standard LambdaCDM cosmology we resolve conflicts in the literature regarding fundamental aspects of the expansion of the universe and cosmic horizons and we link these concepts to observational tests. We derive the dynamics of a non-comoving galaxy and use this to demonstrate the counter-intuitive result that objects at constant proper distance can have a non-zero redshift. Receding galaxies can be blueshifted and approaching galaxies can be redshifted, even in an empty universe for which one might expect special relativity to apply. We then test the generalized second law of thermodynamics (GSL) and its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the relative entropic 'worth' of black hole versus cosmological horizon area. An intriguing set of models show an apparent entropy decrease but we anticipate this apparent violation of the GSL will disappear when solutions are available for black holes embedded in arbitrary backgrounds. Recent evidence suggests a small increase in the fine structure constant (alpha =e^2/hbar c) over cosmological time scales. This raises the question of which fundamental quantities are truly constant and which might vary. We show that black hole thermodynamics may provide a means to discriminate between alternative theories invoking varying constants, because some variations in the fundamental 'constants' could lead to a violation of the generalized second law of thermodynamics.

Motivation & Objective

• To resolve widespread misconceptions about cosmic expansion, horizons, and recession velocities in standard cosmology.
• To clarify the physical meaning of superluminal recession and the Hubble sphere in Friedmann-Robertson-Walker (FRW) spacetimes.
• To investigate the behavior of non-comoving systems, particularly the tethered galaxy problem, and show that zero peculiar velocity does not imply zero redshift.
• To test the generalized second law of thermodynamics (GSL) in cosmological models with event horizons, especially regarding black hole and cosmological horizon entropy.
• To explore whether black hole thermodynamics can constrain theories of varying fundamental constants, such as the fine structure constant.

Proposed method

• Uses standard general relativity and the FRW metric to model cosmic expansion and derive dynamics for non-comoving galaxies.
• Applies the relativistic Doppler shift and cosmological redshift formalism to compare with special relativity in the empty universe limit.
• Constructs spacetime diagrams to visualize particle horizons, event horizons, and causal structure in various ΩM, ΩΛ models.
• Derives the time evolution of peculiar velocity decay and shows it is non-zero even when proper distance is constant.
• Evaluates horizon entropy using the Bekenstein-Hawking area law and tests GSL for dust, radiation, and black holes crossing cosmological event horizons.
• Performs numerical extensions to non-de Sitter FRW models and corrects naive area calculations for overlapping or superhorizon-sized black holes.

Experimental results

Research questions

• RQ1 Why can galaxies recede faster than light without violating relativity, and how does this relate to the Hubble sphere?
• RQ2 How can a galaxy at constant proper distance exhibit a non-zero redshift, and what does this imply for velocity definitions?
• RQ3 Can receding galaxies be blueshifted, and approaching galaxies redshifted, in an expanding universe?
• RQ4 Does the generalized second law of thermodynamics hold when cosmological event horizons are involved, especially with matter or black holes crossing them?
• RQ5 Can black hole thermodynamics distinguish between theories of varying fundamental constants, such as α?

Key findings

• Recession velocities exceeding c are physically allowed in general relativity due to metric expansion, not motion through space.
• Galaxies at constant proper distance still exhibit redshift due to the time evolution of the scale factor, even without peculiar velocity.
• Receding galaxies can be blueshifted and approaching galaxies redshifted in FRW spacetimes, a counterintuitive result explained by the interplay of metric expansion and light propagation.
• The generalized second law of thermodynamics is satisfied for a wide range of cosmological models, including those with event horizons, despite apparent entropy decreases in certain configurations.
• Numerical corrections to horizon area calculations are essential for accurate entropy evaluation, especially for large or overlapping black holes.
• Black hole thermodynamics may serve as a discriminant for theories of varying constants, as some variations could violate the generalized second law.