A Modified Dynamical Model of Cosmology I. Theory

TL;DR

This paper develops a modified cosmological model using Neumann boundary conditions, leading to late-time acceleration without a cosmological constant and differences from ΛCDM at high redshifts.

Contribution

It introduces a novel boundary condition-based modification to cosmological equations, resulting in a model with late acceleration and distinct observational predictions.

Findings

Late-time accelerated expansion without cosmological constant

Modified Hubble parameter due to boundary condition

Differences in luminosity distance at high redshifts

Abstract

Wheeler (1964) had formulated Mach's principle as the boundary condition for general relativistic field equations. Here, we use this idea and develop a modified dynamical model of cosmology based on imposing Neumann boundary condition on cosmological perturbation equations. Then, it is shown that a new term appears in the equation of motion, which leads to a modified Poisson equation. In addition, a modified Hubble parameter is derived due to the presence of the new term. Moreover, it is proved that, without a cosmological constant, such a model has a late time-accelerated expansion with an equation of state converging to $w < -1$. Also, the luminosity distance in the present model is shown to differ from that of the $\Lambda CDM$ model at high redshifts. Furthermore, it is found that the adiabatic sound speed squared is positive in radiation-dominated era and then converges to zero at later times. Theoretical implications of the Neumann boundary condition have been discussed, and it is shown that, by fixing the value of the conjugate momentum (under certain conditions), one could derive a similar version of modified dynamics. In a future work, we will confine the free parameters of the Neumann model based on hype Ia Supernovae, Hubble parameter data, and the age of the oldest stars.