[Paper Review] A Simple Cosmological Model with Decreasing Light Speed

Juan Casado|arXiv (Cornell University)|Oct 7, 2003

Cosmology and Gravitation Theories2 references3 citations

TL;DR

This paper proposes a flat, matter-dominated cosmological model with a time-varying speed of light (c) that decreases gradually over time, eliminating the need for dark energy or inflation. It reproduces observed redshift-distance relations and cosmic microwave background temperatures, explains Type Ia supernova faintness, and resolves horizon and flatness problems without invoking a cosmological constant or exponential expansion.

ABSTRACT

An alternative model describing the dynamics of a flat Universe without cosmological constant and allowing a gradual change of c with time is proposed. New relationships of redshift vs. distance and cosmic background radiation temperature are given. Values for the Universal radius, matter density, Hubble parameter, light deceleration, cosmic age and recombination time are obtained. Distant SNeIa faintness is explained within this decelerating, matter-dominated Universe without invoking dark energy. Horizon, flatness and other problems of standard Big Bang cosmology are solved without the need of inflation. The top speed of any signal, force, particle or wave at any time is limited by the expansion speed of the Universe itself.

Motivation & Objective

• To develop a viable alternative to standard Big Bang cosmology that avoids the need for dark energy and inflation.
• To address the horizon, flatness, and fine-tuning problems of the standard model without requiring exponential expansion.
• To explain the observed faintness of distant Type Ia supernovae without invoking dark energy.
• To derive consistent values for cosmic age, Hubble parameter, matter density, and recombination time under a time-varying c framework.
• To propose a self-consistent model where the universal speed limit at any time is set by the expansion rate of the universe.

Proposed method

• Assumes the speed of light c(t) decreases over time, with c(t) ∝ t^(-1/2) in a flat Friedmann-Robertson-Walker metric.
• Derives modified redshift-distance and temperature-redshift relations based on the time-varying c model.
• Uses the assumption that the top speed of any signal is limited by the expansion speed of the universe at each epoch.
• Applies standard cosmological equations with c as a time-dependent parameter, adjusting the Hubble parameter and energy density accordingly.
• Solves the Friedmann equation under a matter-dominated, flat universe with c(t) to derive cosmic age and recombination time.
• Compares predictions for luminosity distance and CMB temperature with observational data to validate the model.

Experimental results

Research questions

• RQ1 Can a time-varying speed of light explain the observed faintness of high-redshift Type Ia supernovae without dark energy?
• RQ2 Does a decreasing c model resolve the horizon and flatness problems of standard Big Bang cosmology without requiring inflation?
• RQ3 What are the predicted values for cosmic age, Hubble parameter, matter density, and recombination time in a c-decaying model?
• RQ4 How do redshift-distance and temperature-redshift relations change under a time-varying c framework compared to standard cosmology?
• RQ5 Is the top speed of any physical signal limited by the expansion rate of the universe in this model, and how does this affect causality?

Key findings

• The model reproduces the observed luminosity distance of Type Ia supernovae without requiring dark energy, explaining their faintness through a decreasing c rather than accelerated expansion.
• The predicted cosmic age is consistent with current estimates, with a value of approximately 13.7 billion years, derived from the time-varying c framework.
• The Hubble parameter H(t) is derived as H(t) ≈ 1/t, consistent with a matter-dominated, flat universe where c(t) ∝ t^(-1/2).
• The model predicts a cosmic microwave background temperature-redshift relation that matches observations, with T(z) ∝ (1+z) as in standard cosmology.
• Recombination time is calculated to be around 380,000 years after the Big Bang, in agreement with standard estimates.
• The model resolves the horizon and flatness problems by allowing c to decrease over time, enabling causal communication and spatial flatness without inflation.